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REFERENCE 


CONCRETE 
ENGINEERS'  HANDBOOK 


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CONCRETE 
ENGINEERS'  HANDBOOK 

DATA  FOR 

THE  DESIGN  AND  CONSTRUCTION  OF  PLAIN 
AND  REINFORCED  CONCRETE  STRUCTURES 

BY 

GEORGE  A.  HOOL,  S.  B. 

PROFESSOR  OF  STRUCTURAL  ENGINEERING,  THE  UNIVERSITY 
OP  WISCONSIN 

AND 

NATHAN  C.  JOHNSON,  M.  M.  E. 

CONSULTING  CONCRETE  ENGINEER,  NEW  YORK  CITY 

ASSISTED  BY 

S.  C.  HOLLISTER,  B.  S. 

RESEARCH  ENGINEER,  CORRUGATED  BAR  CO. 

with  chapters  by 
Harvey  Whipple,  Adelbert  K  LIjiLls,.,     -     ,       «  ^.  „ 
Walter  S.  Edge,  A.  G.  Hillberg  '  ' 

AND  Leslie  H.  ALLfi;<j  ^ i.^;  ;^       =  > 


First  Edition 
Third  Impression 


McGRAW-HILL  BOOK  COMPANY,  Inc. 
239  WEST  39TH  STREET.    NEW  YORK 


LONDON:  HILL  PUBLISHING  CO.,  Ltd. 

6  &  8  BOUVERIE  ST.,  E.  C. 
1918 


COMS 

TA 

IfiS 


Copyright,  1918,  by  the 
McGraw-Hill  Book  Company,  Inc. 


First  printing^  May,  1918 

Second  printing,  November,  1918 
Third  printing,  April,  1919 


Total  Issue,  11,000 


X  11  K  MAPIiE  PKESS  TT  O  R  K  F  A. 


PREFACE 


This  handbook  has  been  prepared  to  make  available  in  concise  form  the  best  of  present  day 
knowledge  concerning  concrete  and  reinforced  concrete  and  to  present  complete  data  and 
details,  as  well  as  numerous  tables  and  diagrams,  for  the  design  and  construction  of  the  principal 
types  of  concrete  structures.  Although  intended  as  a  working  manual  for  the  engineer,  the 
first  few  sections  of  the  book  may  be  read  with  profit  by  any  one  engaged  in  concrete  work. 
In  these  sections  an  effort  has  been  made  to  present  the  latest  authoritative  knowledge  in 
regard  to  the  making  and  placing  of  concrete  in  such  form  that  it  may  be  applied  in  the  field 
to  the  betterment  of  construction. 

In  preparing  this  book  the  authors  have  been  ably  assisted  by  Mr.  S.  C.  Hollister,  Research 
Engineer  of  the  Corrugated  Bar  Company.  Special  credit  is  due  Mr.  Hollister  for  his  applica- 
tion of  the  slope-deflection  method  to  the  development  of  formulas  for  rigid  frame  structures; 
also  for  material  relating  to  flexure  of  annular  sections  and  to  restraint  of  standpipe  sides 
by  connection  with  the  base,  this  material  being  published  here  through  the  courtesy  of 
the  Corrugated  Bar  Company. 

The  authors  also  are  greatly  indebted  to  Messrs.  Harvey  Whipple,  Adelbert  P.  Mills, 
Walter  S.  Edge,  A.  G.  Hillberg,  and  Leslie  H.  Allen  for  the  important  chapters  which  they  have 
prepared.  These  men  are  specialists;  and  their  contributions  will  prove  of  great  value  to  the 
engineering  profession. 

The  chapter  on  dams,  written  by  Mr.  A.  G.  Hillberg,  has  been  made  brief,  but  a  sufficiently 
extensive  presentation  is  given  to  enable  the  reader  to  decide  intelligently  what  type  of  dam 
to  adopt.  It  is  desired  to  call  attention  to  the  paragraphs  dealing  with  siphonic  spillways 
as  there  is  practically  no  text-book  information  on  that  subject. 

In  writing  this  book  the  authors  have  drawn  from  the  three  volumes  of  Hool's  "Reinforced 
Concrete  Construction"  only  where  the  preparation  of  new  material  would  have  been  sub- 
stantial duplication. 

The  authors  are  under  obligation  to  Messrs.  Wm.  J.  Fuller  and  Frank  C.  Thiessen  for  many 
helpful  suggestions  and  for  assistance  in  making  calculations  for  some  of  the  tables  and  diagrams. 
Acknowledgments  are  also  due  to  Mr.  C.  M.  Chapman  and  others  for  suggestions  and  criticisms 
of  manuscript;  and  to  a  large  number  of  engineers  who  have  supplied  data  and  details,  and  have 
generously  given  their  views  in  regard  to  both  theory  and  practice. 

The  authors  are  indebted  to  Mr.  Clifford  E.  Ives  for  his  excellent  work  in  preparing  all 
drawings  made  expressly  for  this  handbook. 

G.  A.  H. 

April,  1918.  N.  C.  J. 


V 


Digitized  by  the  Internet  Archive 
in  2015 


https://archive.org/details/concreteengineerOOhool 


STANDARD  NOTATION 
USED  THROUGHOUT  THIS  VOLUME 
SEE  APPENDIX  D 


TABLE  OF  CONTENTS 


Section  1.  Materials 


Cement 

Art.  Page 

1.  Classification,  composition,  and  uses 

of  the  principal  cementing 

materials   1 

a.  Gypsum  plasters   1 

h.  Common  lime   1 

c.  Hydraulic  lime   2 

d.  Puzzolan  or  slag  cement.   2 

e.  Natural  cement   3 

/.  Portland  cement   4 

2.  Portland  and  natural  cements  com- 

pared   4 

3.  Constitution  of  Portland  cement   5 

4.  Setting  and  hardening  of  Portland 

cement   5 

5.  Manufacture  of  Portland  cement ....  6 

a.  Raw  materials   6 

h.  Proportioning  the  raw  materials .  7 

c.  Grinding  and  mixing   7 

d.  Burning  the  cement  mixture   7 

e.  Treatment  of  the  clinker   7 

6.  Manufacture  of  natural  cement   8 

a.  Raw  material   8 

h.  Process  of  manufacture   8 

7.  Testing  of  cement   8 

a.  Sampling   8 

6.  Uniformity  in  cement  testing ....  8 

c.  The  personal  factor   8 

d.  Kinds  of  tests   8 

e.  Fineness   8 

/.  Normal  consistency   9 

g.  Time  of  setting   9 

h.  Tensile  strength   10 

i.  Relation    between    tensile  and 

compressive  strength   10 

j.  Compressive  strength   10 

k.  Soundness   10 

I.  Specific  gravity   11 

m.  Chemical  analysis   11 

8.  Specifications  for  cement   11 

9.  Containers  for  cement   11 

10.  Storing  of  cement   11 

11.  Seasoning  of  cement   12 


Art.  Page 

12.  Use  of  bulk  cement   12 

13.  Weight  of  cement  12 

Aggregates 

14.  Definitions   12 

15.  General  requirements   12 

16.  Classification — Coarse  and  fine   12 

17.  Qualities  of  fine  aggregates — General  13 

18.  Qualities  of  coarse  aggregates — Gen- 

eral  13 

19.  Materials  suitable  for  coarse  aggre- 

gates  13 

20.  Igneous  rocks   13 

a.  Granite   13 

h.  Trap-rock  of  diabase   14 

21.  Sedimentary  rocks   14 

a.  Sandstone   15 

h.  Limestone   15 

22.  Metamorphic  rocks   16 

23.  Gravel   16 

24.  Blast-furnace  slag   17 

25.  Cinders   17 

26.  Materials  suitable  for  fine  aggregates  17 
a.  Special  characteristics  of  sand.  .  .  18 
6.  Crushed  stone  and  screenings. ...  19 

c.  Sea  sand   19 

d.  Standard  sand   19 

27.  Requirements  of  fine  aggregate  as  to 

shape  and  size  of  particles   19 

28.  The  selection  of  sand   20 

29.  Requirernents  of  coarse  aggregate  as 

to  shape  and  size  of  particles   20 

30.  Impurities  in  aggregates   21 

31.  Size  and  gradation  of  aggregate  par- 

ticles  22 

a.  Grading  of  mixtures   22 

h.  Grading,  density,  and  strength. . .  22 

c.  Money  value  of  grading   23 

32.  Mechanical  analysis  of  aggregates ...  23 

33.  Specific  gravity  of  aggregates   25 

34.  Voids  in  aggregates   25 

a.  Percentage  of  voids   25 


CONTENTS 


Art.  Page 

h.  General  laws   25 

c.  Effect  of  moisture  on  voids  in  sand 

and  screenings   26 

d.  Percentage  of  voids  determined 

by  weight   26 

35.  Tests  of  aggregates   27 

36.  Notes  on  the  selection  and  testing  of 

aggregates   30 

37.  Specifications  for  aggregates   30 

Water 

38.  General  requirements   31 

39.  Examination  of  water   31 

40.  Functions  of  water   31 

41.  Influence  of  quantity  of  water  on 

strength  of  concrete   32 

42.  Influence  of  quantity  of  water  on  flux- 

ing of  cement   32 

43.  Influence  of  quantity  of  water  on 

lubrication  of  concrete  mixture. .  33 

44.  Influence  of  quantity  of  water  on 

space  occupied  in  resulting  con- 
crete   33 

45.  Harmful  effects  of  voids  caused  by 

excess  water   34 

46.  Excess  water  the  cause  of  ''day's 

work  planes"   34 

47.  Excess  water  the  cause  of  large  lait- 

ance  deposits   34 

48.  Excess  water  and  waterproof  concrete  35 

49.  Excess  water  causes  unsatisfactory 

concrete  floor  surfaces   35 

50.  Excess  water  prevents  bonding  new 

concrete  to  old   35 

51.  Excess  water  and  concreting  in  cold 

weather   35 

52.  Suggested     procedures     to  guard 

against  use  of  excess  water   36 

Reinforcement 

53.  Types  of  reinforcement   36 

54.  Surface  of  reinforcement   37 

55.  Quality  of  steel   37 

56.  Working  stresses   37 

57.  Coefficient  of  expansion   37 


Proportioning  Concrete 
1.  Properties    of    concrete,  dependent 
upon  properties  and  relative  pro- 
portions of  constituent  materials  63 


Art.  Page 

58.  Modulus  of  elasticity   37 

59.  Steel  specifications   37 

a.  For  bars  rolled  from  billets   37 

h.  For  rerolled  bars   40 

60.  Factors  affecting  cost  of  reinforcing 

bars   42 

61.  Deformed  bars   42 

a.  Diamond  bar   42 

h.  Corrugated  bars   43 

c.  Havermeyer  bars   43 

(i.  Rib  bar   44 

e.  Inland  bar   44 

/.  American  bars   44 

62.  Wire  fabric   45 

a.  Welded  wire  fabric   46 

h.  Triangle-mesh  wire  fabric   47 

c.  Unit  wire  fabric   48 

d.  Lock-woven  steel  fabric   49 

e.  Wisco  reinforcing  mesh   50 

63.  Expanded  metal   50 

d.  Streelcrete   51 

h.  Kahn  mesh   52 

c.  Corr-X-metal   52 

d.  Econo   53 

e.  G.  F.  expanded  metal   53 

64.  Rib  metal   55 

65.  Self-centering  fabrics   55 

a.  Hy-rib   56 

h.  Corr-mesh   56 

c.  Self-centering   56 

d.  Chanelath   56 

e.  Ribplex   57 

/.  Dovetailed  corrugated  sheets ....  57 

66.  Reinforcing  systems  for  beams,  gird- 

ers and  columns   57 

a.  Kahn  system   57 

h.  Cummings  system                     .  58 

c.  Unit  system   58 

d.  Corr  system   60 

c.  Hennebique  system   60 

/.  Pin-connected  system   60 

g.  Luten  truss   60 

h.  Xpantruss  system   60 

i.  Shop    fabricated  reinforcement 

system   60 

2.  Theory  of  proportioning   63  . 

3.  The  strength  elements  of  concrete. ...  64 

4.  Proportioning  for  high  strength  con- 

cretes   64 


Section  2.    General  Methods  of  Construction 


CONTENTS 


Art.  Page 

5.  Weakness  due  to  poor  proportioning .  64 

6.  Unit  of  proportioning   65 

7.  Arbitrary  proportions   65 

8.  Proportioning  by  void  determinations  65 

9.  Proportioning  by  mechanical  analy- 

sis   68 

10.  Proportioning  by  maximum  density 

tests   68 

1 1 .  Checking  materials  on  the  j ob   69 

12.  Proportions  and  the  measurement  of 

materials   70 

13.  Proportioning  bank-run  gravel   70 

14.  Proportioning  crusher-run  stone   71 

15.  Proportioning  blast-furnace  slag  and 

cinders   71 

16.  Proportioning  water   71 

.  17.  Success  in  proportioning   72 

Mixing,  Transporting  and  Placing  Con- 
crete 

18.  Mixing  concrete   72 

19.  Amount  of  water  to  be  used  in  mixing 

concrete   72 

20.  Transporting  concrete   72 

21.  Depositing  concrete  in  forms   73 

22.  Continuous  and  even  depositing  in 

forms   73 

23.  Continuous  depositing  to  avoid  stop- 

page planes   74 

24.  Bonding  set  and  new  concrete   75 

25.  Removal  of  entrained  air   75 

26.  Spading,  puddling  and  tamping   75 

27.  Depositing  concrete  through  water.  .  76 

28.  Remixed  and  retempered  concrete, .  .  76 

29.  Concreting  in  hot  weather  and  in 

cold  weather   76 

a.  Pre-heating  aggregates  and  water  77 

h.  Means  for  heating  aggregates. ...  77 

c.  Enclosure  and  heating  of  forms. .  77 

d.  Protection  against  frost   78 

e.  Freezing  of  concrete   78 

/.  Use  of  anti-freezing  mixtures ....  78 

g.  Protection  against  heat   78 

Field  Tests  of  Concrete 

30.  Object  of  field  tests   78 

31.  Limitations  inherent  in  field  tests.  .  .  78 

32.  Comparative  tests  on  field-molded 

and  structural  specimens   79 


xi 

Art,  Page 


33.  Value  of  tests  on  field-molded  test 

specimens   79 

34.  Transverse  tests  on  beam  specimens. .  79 

35.  Core  drill  test  specimens  from  actual 

structures   79 

36.  Suggested  methods  for  making  and 

testing  field  specimens  of  con- 
crete  79 

37.  Pre-use  tests  of  materials   82 

Waterproofing  Concrete 

38.  Meaning  of  "waterproof  "   82 

39.  Resistance  of  concretes  to  water  ac- 

tion   82 

40.  Resistance  of  concretes  to  water  pene- 

tration   83 

41.  Degree  of  impermeability  attainable.  83 

42.  Porosity  of  commercial  concretes . .  .  ,  83 

43.  Excess  water  as  a  cause  of  porosity. .  84 

44.  Shrinkage  cracks   84 

a.  Types  of  shrinkage  cracks   84 

h.  Shrinkage  cracks  and  porosity.  .  .  85 

c.  Prevention  of  shrinkage  cracks. . .  85 

45.  Pervious  concretes  and  laitance   86 

46.  Effect  of  temperature  and  atmos- 

pheric effects  on  water-tightness  86 

47.  Integral  waterproofing  compounds . .  86 

a.  Integral  waterproofing  classifica- 

tion  87 

b.  Value  of   integral  waterproofing 

compounds   87 

c.  Rendering    defective  structures 

impervious   87 

48.  Waterproofing  by  cement  grouting.  .  88 

49.  Membranous  waterproofings   88 

a.  Application      of  membranous 

waterproofing   88 

b.  Continuity  of  membrane   89 

c.  Protection  of  waterproofing   89 

50.  Rules  for  making  concrete  impervious  89 

Finishing  Concrete  Surfaces 

51.  Character  of  surface  finish  desired. .  .  90 

52.  Removing  form  marks   90 

a.  Tooling   90 

b.  Rubbing   91 

c.  Brushing   92 

d.  Sand-blasting   92 

53.  Use  of  colored  aggregates   92 


xii 


CONTENTS 


Art.  Page 

54.  Addition  of  colors  to  concrete   93 

55.  Use  of  white  cement   93 

56.  Plaster  finishes   93 

57.  Surfacing  concrete  floors   93 

58.  Specification  for  the  production  of  a 

rubbed  surface   93 

Forms 

59.  General  requirements   93 

60.  Economical  considerations   94 

61.  Lumber  for  forms   94 

62.  Removal  of  forms   95 

63.  Number  of  sets  of  forms  in  building 

work   96 

64.  Examples  of  form  design   96 

a.  Column  forms  ;  96 

h.  Beam  and  girder  forms   103 

c.  Slab  forms   104 

d.  Column  heads   108 

e.  Wall  and  pier  forms   Ill 

65.  Design  of  forms   120 

a.  Values  to  use  in  design   121 

h.  Drafting  room  methods   123 

66.  Tables  and  diagrams  for  designing 

forms   124 

a.  Notation.   124 

h.  Fiber  stresses  allowed   124 

c.  Formulas  used   125 

67.  Systematizing  form  work  for  build- 

ings  131 

a.  Saw  mill  and  yard   131 

6.  Shop  procedure   131 

c.  Cleat  spacing   134 

d.  Planning  of  field  work   134 

e.  Stripping  of  forms   134 

68.  Steel  forms   135 

69.  Construction  notes   138 

Bending  and  Placing  Reinforcement 

70.  Checking,  assorting  and  storing  steel  139 

71.  Bending  of  reinforcement   139 

o.  Types  of  bends   139 

h.  Hand  devices   139 

c.  Power-operated  benders   141 

d.  Care  to  be  exercised  in  bending. .  141 

e.  Bending  of  slab  reinforcement. . . .  142 

72.  Placing  of  reinforcement   142 

73.  Devices  for  supporting  reinforcing 

bars   143 


Manufacture  and  Use  op  Concrete 


Stone,  Block  and  Brick 
Art.  Page 

74.  Development  of  the  industry   146 

75.  Two  main  lines  of  work   147 

76.  Methods  of  manufacture   147 

a.  Dry  tamp  method   147 

h.  Pressure  method   148 

c.  Wet-cast  method   148 

77.  Consistency   148 

78.  Commercial  molds   149 

79.  Operation  of  machines   150 

a.  Tamping   150 

80.  Gang  molds  for  wet-cast  products ..  .  151 

81.  Materials   151 

a.  Cement  (storage  and  conveying)  151 

h.  Aggregates  (kind  and  quality) . .  .  152 

82.  Mixing  >.   152  . 

a.  Mixers  (general  type)   153 

h.  Mixing  dry  and  mixing  wet   153 

c.  Agitation  subsequent  to  mixing 

in  wet-cast  work   153 

d.  Mixing  facing  materials   153 

83.  Placing   154 

a.  Buckets  and  hoppers   154 

h.  Wheelbarrows   155 

c.  Pallets   155 

d.  Bankers   156 

84.  Curing   156 

a.  Natural  curing   156 

h.  Steam  curing   157 

85.  Special  molds   159 

a.  Wood  molds   159 

h.  Plaster  molds   159 

c.  Glue  molds   160 

d.  Combination  molds   161 

e.  Waste  molds   161 

86.  Sand  molds  and  casting  in  sand   161 

87.  Surfaces   162 

a.  Face  design  in  standard  units. ...  162 

h.  Facing  materials   163 

c.  Colors   164 

d.  Spraying   165 

e.  Brushing   165 

/.  Rubbing   166 

g.  Tooling   166 

h.  Mosaics   167 

i.  EflSorescence   167  ■ 

j.  Air  bubbles   167 

k.  Crazing   167 

88.  Specifications  of  the  American  Con- 

crete Institute   168 


CONTENTS 
Section  3.    Construction  Plant 


Preparation  of  Concjiete  Aggregates 
Art.  Page 

1.  Preparation  of  crushed-stone  aggre- 

gate  171 

a.  Preparation  of  site  for  quarrying.  171 
h.  Quarrying   171 

c.  Drills   171 

d.  Stone  crushers   172 

e.  Screening  and  grading  of  crushed 

stone   172 

/.  Washing  crushed  stone   172 

g.  Crushed  limestone   172 

2.  Screening  of  sand  and  gravel   172 

3.  Washing  of  sand  and  gravel   173 


Handling  and  Storage  of  Materials 


4. 

General  considerations  

173 

5. 

174 

6. 

Shoveling  materials  directly  from  cars 

174 

7. 

Storage  and  care  of  sand  

174 

8. 

174 

9. 

Unloading  economies  

175 

10. 

Proper  size  and  type  of  shovel  

175 

11. 

176 

12. 

Bucket  unloaders  and  conveyors.  .  .  . 

177 

13. 

Belt  conveyors  

177 

14. 

Storage  and  handling  of  sack  cement 

177 

15. 

Bundling    and    storage    of  empty 

cement  sacks  

178 

16. 

Storage  and  handling  of  water  

179 

17. 

A  typical  installation  

179 

Concreting  Plant 

18. 

Plant  economics  

181 

a.  First  cost  

181 

6.  Cost  of  installation  

181 

Concrete  Floors  and  Floor  Surfaces 


1. 

The  concrete  floor  problem  

205 

2. 

"Dusting"  of  concrete  floors  

206 

3. 

Making  good  concrete  floors  and  floor 

surfaces  

206 

4. 

Special  surface  finishes  

206 

a.  Surface  grinding  

206 

206 

Art.  Page 

c.  Cost  of  operation   181 

d.  Cost  of  maintenance   181 

e.  Cost  of  removal   181 

/.  Salvage   181 

19.  Balancing  the  plant   181 

20.  Typical  plants   181 

21.  Machine  vs.  hand  mixing   186 

22.  Types  of  mixers   187 

a.  Drum  mixers   187 

6.  Trough  mixers   187 

c.  Gravity  mixers   188 

d.  Pneumatic  mixers   188 

23.  Machine  mixing   189 

a.  Time  of  mixer  operations   189 

6.  Time  of  mixing   189 

c.  Drum  speeds   190 

d.  Loading  the  mixer   190 

Charging  hoppers   190 

Power  loaders   191 

Low  charging  mixers   191 

e.  Measuring  materials   192 

/.  Discharge  of  the  mixer   192 

24.  Transporting  and  placing  concrete .  .  193 

a.  Barrows   193 

6.  Concrete  carts   193 

c.  Buckets   194 

d.  Cableways  and  buckets   195 

e.  Spouts  or  chutes   195 

/.  Sections  used  in  spouting   196 

g.  Hoists   200 

25.  Spouting  plants   .  .  203 

a.  Boom  plants   203 

h.  Guy  line  plants   203 

c.  Tower  plants   203 

d.  Combinations  of  spouting  systems  203 

e.  Regulating  flow  of  concrete  in 

spouting  plants   203 

c.  Finish  produced  by  removal  of 

water  from  surface   207 

d.  Integral  hardeners  and  surface 

compounds   207 

5.  Causes  of  common  defects  in  concrete 

floors   207 

6.  Remedial  measures   209 

a.  Retopping   209 

h.  Chemical  hardeners   210 


Section  4.    Concrete  Floors  and  Floor  Surfaces,  Sidewalks,  and  Roadways 


xiv 


CONTENTS 


Abt.  Page 

c.  Use  of  oils   210 

d.  Floor  coatings  and  paints   210 

Concrete  Sidewalks 

7.  Structural  functions   210 

8.  Essential  qualities   210 

9.  The  making  of  concrete  sidewalks. .  .  211 

a.  Porous  subbase   211 

h.  Concrete  base   211 

c.  Top  of  wearing  surface   211 

d.  Surface  finishing   211 

e.  Surface  protection  and  curing.. .  .  211 
/.  Protecting  sidewalks  in  hot  weather  212 
g.  Special  surface  finishes   212 

10.  Vault  light  pavements   212 

Strength  of  Cement  Mortar  and  Plain 
Concrete 

1.  Strength  in  general   215 

2.  Laboratory  tests,  their  use  and  signifi- 

cance  215 

3.  Neat,  mortar,  and  concrete  strength 

compared   217 

4.  Aggregates  of  mortar  and  concrete.  .  .  218 

5.  Effect  of  mineral  character  of  aggre- 

gates  219 

6.  Effect  of  shapes  and  size  of  aggre- 

gates .•   221 

7.  Relation  between  density  and 

strength   222 

8.  Effect  of  mica,  clay,  and  loam  in  ag- 

gregates   224 

9.  Effect  of  consistency   225 

10.  Compressive   and  tensile  strengths 

compared   227 

1 1 .  Strength  of  plain  concrete  columns . .  229 

12.  Effect  of  method  of  mixing   230 

13.  Effect  of  method  of  placing   231 

14.  Effect  of  regaging   232 

15.  Effect  of  curing  conditions   234 

16.  Effect  of  freezing   236 

17.  Effect  of  salts   236 

18.  Effect  of  hydrated  lime  and  water- 

proofing compounds   238 

19.  Effect  of  sea  water  used. in  gaging. . .  238 

20.  Effect  of  oils  used  in  gaging   240 

21.  Effect  of  laitance   241 

22.  Rate  of  increase  in  mortar  strength, 

retrogression   241 


Abt.  Page 

11.  Concrete  curbing   212 

12.  Summary   212 

Concrete  Roadways 

13.  Structural  functions   213 

14.  Essential  qualities   213 

15.  One-course    and    two-course  pave- 

ments  213 

16.  The  making  of  concrete  roadways.  .  .  213 

a.  Porous  subbase   213 

h.  Proportioning   and   selecting  of 

materials   213 

c.  Joints   214 

(/.  Curing   214 

e.  Consistency   214 

23.  Transverse  strength   242 

24.  Shearing  strength   243 

25.  Adhesive  strength   246 

a.  Adhesion  to  concrete  previously 

placed   246 

h.  Adhesion  or  bond  to  steel  (see 

Art  2,  Sect.  6)   247 

26.  Strength  of  natural  cement  mortar 

and  concrete   247 

27.  Strength  of  cinder  concrete   248 

28.  Working  stresses  (see  Appendix  B) .  .  250 

Elastic  Properties  of  Cement  Mortar 
AND  Concrete 

29.  Stress-strain  curves  for  mortars  and 

concretes   250 

30.  Yield  point   251 

31.  Modulus  of  elasticity   251 

Contraction  and  Expansion  of  Cement 
Mortar  and  Concrete 

32.  Coefficient  of  expansion   252 

33.  Moisture  changes   253 

Durability  of  Cement  Mortar  and  Con- 
crete 

34.  Fire-resistant  properties   254 

35.  Weathering  qualities   255 

36.  Abrasive  resistance   255 

37.  Action  of  sea  water   256 

38.  Action  of  alkali   257 

39.  Action  of  acids,  oils,  and  sewage ....  257 

40.  Electrolysis  in  concrete   258 


Section  5.    Properties  of  Cement  Mortar  and  Plain  Concrete 


CONTENTS 


XV 


Art.  Page 

41.  Effect  of  manure   259 

Miscellaneous    Properties    of  Cement 
Mortar  and  Concrete 

42.  Rise  of  temperature  in  setting   259 

1.  Advantages  of  combining  concrete 

and  steel   265 

2.  Bond  between  concrete  and  steel   265 

Pull-out  tests   266 

Relation  of  bond  stress  to  slip  of 
bar  as  load  increases   266 

Bond  resistance  in  terms  of  com- 
pressive strength  of  concrete .  .  .  267 

Distribution  of  bond  stress  along 
a  bar   267 

Variation  of  bond  resistance  with 
size,  shape,  and  condition  of  sur- 
face of  bar   267 

Anchoring  of  reinforcing  bars   268 

Influence  of  method  of  curing 
concrete   268 

Rectangular  Beams  and  Slabs 

1.  Forces  to  be  resisted   273 

2.  Distribution  of  stress  in  homogeneous 

beams   273 

3.  Assumptions  in  theory  of  flexure  for 

homogeneous  beams   .  275 

4.  Plain  concrete  beams   275 

5.  Purpose  and  location  of  steel  rein- 

forcement  275 

6.  Tensile  stress  lines  in  reinforced  con- 

crete beams   275 

7.  Flexure  formulas  for  reinforced  con- 

crete beams   276 

8.  Assumptions  in  flexure  calculations  .  .  276 

9.  Flexure  formulas  for  working  loads — 

straight  line  theory   276 

10.  Flexure  formulas  for  ultimate  loads .  .  279 

11.  Flexure  formulas  for  working  loads 

and  for  ultimate  loads  compared  280 

12.  Lengths  of  simply  supported  beams. .  280 

13.  Shearing  stresses   280 

14.  Methods    of    strengthening  beams 

againstf  ailurein  diagonal  tension  281 

15.  Moment  and  diagonal-tension  tests — 

General  281 


Art.  Page 

43.  Porosity   261 

44.  Permeability  and  absorptive  proper- 

ties  262 

45.  Protection  of  embedded  steel  from 

corrosion   262 

46.  Weight  of  mortar  and  concrete   263 

Influence  of  freezing  of  concrete. . .  268 

Influence  of  age  and  mix  of  con- 
crete  268 

Effect  of  continued  and  repeated 
load   268 

Effect  of  concrete  setting  under 

pressure   269 

Beam  tests   269 

3.  Length  of  embedment  of  reinforcing 

bars  to  provide  for  bond   270 

4.  Ratio  of  the  moduli  of  elasticity   270 

5.  Behavior  of  reinforced  concrete  under 

tension   271 

6.  Shrinkage  and  temperature  stresses .  .  271 

7.  Weight  of  reinforced  concrete   272 

16.  Bond  stress   284 

17.  Web  reinforcement  in  general   285 

18.  Region  where  no  web  reinforcement 

is  required   286 

19.  Vertical  stirrups   289 

20.  Method  of  placing  stirrups  from  the 

moment  diagram   291 

21.  Bent  rods  and  vertical  stirrups  for 

web  reinforcement   296 

22.  Points  where  horizontal  reinforce- 

ment may  be  bent   297 

23.  Transverse  spacing  of  reinforcement  300 

24.  Depth  of  concrete  below  rods   300 

25.  Ratio  of  length  to  depth  of  beam  for 

equal  strength  in  moment  and 
shear   301 

26.  Economical  proportions  of  rectangu- 

lar beams   302 

27.  Rectangular  beams  with  steel  in  top 

and  bottom   302 

a.  Formulas  for  determining  per- 
centages of  steel  in  double-rein- 
forced rectangular  beams   304 

28.  Deflection  of  rectangular  beams   304 

a.  Maney's  method   305 


Section  6.    General  Properties  of  Reinforced  Concrete 


Section  7.    Beams  and  Slabs 


CONTENTS 


Art.  Page 


h.  Turneaure  and  Maurer's  method  305 

29.  Slabs   306 

a.  Moments  in  continuous  slabs   306 

h.  Provision  for  negative  moment  in 

continuous  slabs   306 

c.  Floor  slabs  supported  along  four 

sides   307 

d.  Cross  reinforcement  in  slabs   307 

T-Beams 

30.  T-beams  in  floor  construction   307 

31.  Tests  of  T-beams   307 

32.  Flange  width   308 

33.  Bonding  of  web  and  flange   308 

34.  Flexure  formulas   308 

a.  Formulas  for  determining  dimen- 
sions and  steel  ratio  for  given 
working  stresses   309 

35.  Designing  for  shear   310 

36.  General  proportions  of  T-beams   310 

37.  Economical  considerations   310 

38.  Conditions  met  with  in  design  of  T- 

beams   310 

39.  Design  of  a  continuous  T-beam  at  the 

supports   311 

40.  T-beams  with  steel  in  top  and  bottom  313 
a.  Formulas  for   determining  per- 
centages of  steel  in  double-rein- 
forced T-beams   313 

41.  Deflection  of  T-beams   313 

Special  Beams 

42.  Wedge-shaped  beams   314 

1.  Column  types   371 

2.  Plain  concrete  columns  or  piers   371 

3.  Columns  with  longitudinal  reinforce- 

ment  371 

4.  Columns  with  hooped  and  longitudi- 

nal reinforcement   372 

5.  Columns  reinforced  with  structural- 

steel  shapes   372 

1.  Theory  in  general   385 

2.  Analytical  determination  of  stresses  in 

rectangular  sections   387 

a.  Case  I. — Compression  over  the 

whole  section — steel  top  and 

bottom   387 

h.  Case  II. — Tension  over  part  of 

section — steel  top  and  bottom .  .  394 


Art.  Page 

43.  Beams  of  any  complex  or  irregular 

section   314 

a.  Analytical  method   314 

h.  Graphical  method   316 

Shear  and  Moment  in  Restrained  and 
Continuous  Beams 

44.  Span  length  for  beams  and  slabs   318 

45.  Recommendations   of   Joint  Com- 

mittee as  to  positive  and  negative 

moments   318 

46.  Theorem  of  three  moments   318 

47.  Uniform  load  over  all  spans   323 

48.  Fixed    and    moving  concentrated 

loads   324 

a.  Influence  lines   324 

49.  Moving  uniform  loads   329 

50.  Maximum  moments  from  uniform 

loads   330 

51.  Beam  concentrations   331 

52.  Negative  moment  at  the  ends  of  con- 

tinuous beams   334 

53.  Bending  up  of  bars  and  provision  for 

negative  moment   335 

54.  Continuous    beams    with  varying 

moment  of  inertia   339 

Designing    Tables    and    Diagrams  for 
Beams  and  Slabs 

55.  Illustrative  problems  (12  in  all)   341 

56.  Leffler's  comprehensive  beam  chart.  348 

57.  Beard  and  Schuler's  comprehensive 

charts   350 

6.  Working  stresses   373 

7.  Recommendations  of  the  Joint  Com- 

mittee  373 

8.  Tables  and  diagrams   374 

9.  Reduction  formula  for  long  columns. .  381 
10.  Columns  supporting  bracket  loads .. .  381 


c.  Case  III. — Tension  over  part  of 


section — steel  in  tension  face  only  403 

3.  Graphical  determination  of  stresses .  .  406 

o.  Rectangular  sections   406 

h.  Hollow-circular  sections   407 

c.  Solid  circular  and  other  sections . . .  409 


Section  8.  Columns 


Section  9.    Bending  and  Direct  Stress 


CONTENTS 


Section  10.  Moments 

Art.  Page 

1.  Importance  of  the  subject   411 

2.  Method  of  analysis   411 

3.  AppUcation  of  method  of  analysis  to 

simple  cases   414 

4.  Conception  of  rigidity  of  building 

frames   415 

5.  Moments   at   interior   columns  in 

beam-and-girder  construction.  .  416 

a.  All  terminals  hinged   416 

b.  All  terminals  fixed   417 

c.  Columns  hinged.    Outer  girders 

with  constant  moment   418 

(I  Columns  fixed.      Outer  girders 

with  constant  moment   418 

e.  Point  of  inflection  at  center  of 

columns.  Outer  girders  hinged .  418 
/.  Point  of  inflection  at  center  of 

columns.  Outer  girders  fixed. . .  418 
g.  Point  of  inflection  at  center  of 

columns.    Outer  girders  with 

constant  moment   419 


in  Rigid  Building  Frames 

Art.  Page 

h.  Point  of  inflection  at  center  of 

upper  columns.  Lower  columns 
fixed.  Outer  girders  with  con- 
stant moment   419 

i.  Point  of  inflection  at  center  of 

upper  columns.  Lower  columns 
fixed.    Outer  girders  hinged.  .  .  419 
j.  Point  of  inflection  at  center  of 
upper  columns.  Lower  columns 
fixed.    Outer  girders  fixed   420 

6.  Moments   at   exterior   columns  in 

beam-and-girder  construction. . .  420 

a.  Inner  end  of  girder  hinged   425 

b.  Inner  end  of  girder  fixed   425 

7.  Moments  in   columns  in  flat-slab 

construction   425 

8.  Criteria    for    maximum  combined 

stresses  in  columns   426 

a.  Interior  columns   426 

b.  Exterior  columns   426 

9.  Wind  stresses  in  building  frames ....  427 

10.  Roof  frames   428 

11.  L-frames   429 


Section  11.  Buildings 


Floors — General  Data 


1.  General  types  of  concrete  floors.  .  .  .  431 

2.  Floor  loads   431 

3.  Economic  considerations   432 

4.  Floor  surfaces   432 

5.  Small  floor  openings   433 

6.  Provision   for    the    attachment  of 

shaft-hangers  and  springer  pipes  434 

7.  Bedding  machinery   437 

8.  Waterproof  floors   438 

9.  Tests   438 

10.  Basement  floors   438 

Monolithic  Beam  and  Girder  Con- 
struction 

11.  Ordinary  type  of  beam  and  girder 

construction   439 

12.  Hollow  tile  construction   447 

Flat  Slab  Construction 

13.  General  description   457 

14.  Advantages  over  the  beam-and-girder 

type   457 


15.  Classes  of  buildings  to  which  adapted  458 

16.  Remarks  regarding  design   459 

17.  Systems   461 

a.  Barton  Spider  Web  system   461 

b.  Cantilever  Flat-slab  construction  463 

c.  Simplex  system   465 

d.  Mushroom  system   465 

e.  Watson  system   466 

/.  Akme  system   467 

g.  Corr-plate  floors.   470 

h.  S-M-I  system   471 

i.  Three-way  system   476 

18.  Patents   479 

19.  Loading  tests   480 

20.  Methods  of  design  and  problems   487 

a.  Computations  for  Akme  system..  488 

b.  Computations     for  Corr-plate 

floors   489 

c.  Computations   based   on  Pitts- 

burgh Ruling   492 

d.  Computations  based  on  Chicago 

Ruling   494 

e.  Computations  based  on  Ruling  of 

American  Concrete  Institute . . .  495 


xviii 


CONTENTS 


Art.  Page 

/.  Roof  design   496 

g.  Beams  in  flat-slab  floors   497 

h.  Columns   497 

i.  Brick  exterior  wall  supports   498 

21.  Tables   498 

22.  Construction  methods  and  safeguards  506 

Unit  Construction 

23.  Method  of  construction  in  general. . .  .  508 

24.  Advantages  of  the  unit  method   508 

25.  "  Unit-bilt"  system   508 

26.  Ransome  unit  system   509 

Steel  Frame   Construction   with  Con- 
crete Slabs 

27.  Types  of  construction   511 

28.  Wrapping  of  I-beams   511 

29.  Types  illustrated   511 

Roofs 

30.  Structural  design   512 

31.  Loading   512 

32.  Prevention  of  condensation  on  con- 

crete roof  slabs   513 

33.  Concrete  roof  surfaces   516 

34.  Separate  roof  coverings   517 

35.  Drainage  '.   518 

36.  Parapet  walls   521 

37.  Saw-tooth  construction   526 


Art.  Page 

38.  Trainshedof  C/m7-5z7f  construction .  . .  527 

Columns 

39.  Details  of  design   527 

40.  Loading   530 

41.  Column  brackets   530 

Walls  and  Partitions 

42.  Bearing  walls   532 

43.  Curtain  walls   533 

44.  Brick  and  other  veneer   539 

45.  Window  openings   540 

46.  Door  openings   543 

47.  Basement  walls   545 

48.  Partitions   545 

Stairs 

49.  General  design   549 

50.  Methods  of  supporting  stairs   550 

51.  Stair  details   551 

Elevator  Shafts 

52.  Elevator-shaft  pits   552 

53.  Pent  houses   553 

Provisions  for  Contraction  and  Expan- 
sion 

54.  Methods  employed   554 


Section  12.  Foundations 


1.  Bearing  capacity  of  soils   557 

2.  Pressure  on  the  soil   558 

3.  Plain  concrete  footings   558 

4.  Advantages  in  using  reinforced  con- 

crete for  foundations   558 

5.  Wall  footings   559 

6.  Types  of  column  footings   559 

7.  Single  column  footings   559 


8.  Combined  column  footings   565 

9.  Cantilever  footings   568 

10.  Raft  foundations   570 

11.  Examples  of  column  footings   571 

12.  Concrete  piles   572 

a.  Piles  molded  in  place   572 

b.  Piles  molded  before  driving   574 


Section  13.    Retaining  Walls 


1.  Earth  pressure   575 

a.  Rankine's  formula  for  resultant 

active  earth  pressure   576 

h.  Coulomb's  wedge  of  maximum 

pressure   577 

c.  Comparison  of  Coulomb  and  Ran- 

kine  results   580 


d.  Useful  interpretation  of  results  of 

earth  pressure  theories   580 

2.  Live  load  on  top  of  fill — Equivalent 

surcharge   580 

3.  Live  load  on  top  of  fill — Pressure  dis- 

tribution   58 1 

4.  Stability  of  a  retaining  wall   581 


CONTENTS 


xix 


Akt.  Page 

a.  So-called  "Factor  of  Safety"   584 

b.  Factor  of  limitation   584 

5.  Types  of  retaining  walls   584 

6.  Design  of  plain  concrete  walls   584 

a.  Formulas  and  diagrams  for  the 

two  principal  types   584 

h.  Trautwine's  table   586 

c  Selection  of  preliminary  section. . .  587 

7.  Design  of  cantilever  or  T-walls  of 

reinforced  concrete   587 

a.  To  determine  approximate  base 

width   587 

b.  Stem   589 

c.  Base  slab   590 


Art.  Page 

d.  Expansion  joints   592 

8.  Design  of  counterforted  walls   592 

a.  Thickness  and  spacing  of  counter- 

forts  592 

b.  Vertical  or  face  wall   593 

c.  Back  floor  slab   593 

d.  Cantilever  toe  slab   596 

e.  Methods  of  reinforcing  counter- 

forted wall   596 

9.  Special  types  of  reinforced-concrete 

walls..   600 

10.  Construction  of  retaining  walls   601 

a.  Back-filling  and  drainage   601 

6.  Forms   602 


Section  14.    Slab  and  Girder  Bridges 


Slab  Bridges 


1.  Slabs  under  concentrated  loading.  .  .  603 

a.  Illinois  tests   603 

b.  Ohio  tests   604 

c.  Tests  by  Goldbeck   605 

2.  Slab  bridges  of  single  span   605 

3.  Slab  bridges  of  multiple  spans   607 

a.  Concrete  pile  trestles   607 

b.  Pier  trestles   610 

c.  Trestles  with  framed  bents   610 

d.  Cantilever  flat-slab  construction..  612 

Simple  Girder  Bridges 

4.  Deck  girders   613 

5.  Through  girders   617 

Continuous  Girder  Bridges 
(Monolithic  construction) 

6.  Expansion  joints   622 

7.  Examples  of  typical  bridges  of  the 

continuous  girder  type   623 


8.  Analysis  of  stresses  in  rigid  viaduct 

structures   625 

a.  Viaduct  frames   628 

b.  Four-span   viaduct  frame  with 

rigidly  connected  column  tie ... .  629 

c.  Three-span  viaduct  frame  with 

rigidly  connected  column  tie. ...  631 

d.  Two-span   viaduct   frame  with 

rigidly  connected  column  tie .  .  .  632 

e.  One-span    viaduct    frame  with 

rigidly  connected  column  tie .  .  .  633 
/.  Four-span  viaduct  frame   633 

g.  Three-span  viaduct  frame   634 

h.  Two-span  viaduct  frame   634 

i.  One-span  frame,  unequal  columns  636 

j.  Temperature  stresses   636 

k.  Effect  of  fixed  bases   638 

I  Viaduct  bent   638 

Cantilever  Bridges 

9.  Theory  of  design   639 

10.  Examples  of  cantilever  bridges   639 


Section  15.    Concrete  Floors  and  Abutments  for  Steel  Bridges 


1.  Concrete  floors  on  steel  bridges   643 

2.  Abutments  for  steel  bridges   645 

3.  Types  of  abutments   645 

4.  Pier  abutments  of  plain  concrete. .  .  .  645 

5.  Pier  abutments  of  reinforced  concrete  646 

6.  Wing  abutments   646 


7.  Cellular  abutments   647 

8.  U-abutments   647 

9.  T-abutments   647 

10.  Buried-pier  abutments   648 

11.  Skeleton  and  arched  abutments   648 

12.  Care  in  constructing  abutments   649 


XX 


CONTENTS 


Section  16.  Arches 


General  Data 
Art.  Page 

1.  Definitions   651 

2.  Curve  of  the  in  trades   651 

a.  Three-centered  curve   652 

b.  Semi-elUpse   652 

c.  Parabola   653 

3.  Arrangement  of  spandrels   653 

4.  Piers  and  abutments   653 

5.  Depth  of  filling  at  crown   654 

6.  Loads   654 

7.  Empirical  rules  for  thickness  of  arch 

ring   656 

8.  Approximate  formula  for  best  shape 

of  arch  axis   658 

9.  Proper  thickness  of  arch  ring  in  the 

haunch  for  given  thicknesses  at 
crown  and  springing   658 

10.  Dead  loads  and  their  action  lines   658 

11.  Approximate  method  of  testing  trial 

arch   658 

12.  Use  of  temporary  hinges  in  arch 

erection   659 

13.  Use   of  reinforcement  in  concrete 

arches   660 

14.  Classification  of  arch  rings   660 

Analysis  of  the  Arch  by  the  Elastic 
Theory 

15.  Deflection  of  curved  beams   660 

16.  General  procedure  in  arch  analysis .  .  661 

17.  Notation   662 

18.  Formulas    for   thrust,    shear,  and 

moment   663 

19.  Division  of  arch  ring  for  constant  j . .  663 

20.  Loadings  to  use  in  computatioi\s   664 

21.  Use  of  influence  lines   664 

22.  Internal  temperature  investigations.  664 

23.  Shrinkage  stresses   664 

24.  Deflection  at  any  point   664 

25.  Method  of  procedure  in  arch-ring 

design   665 

26.  Uncertainty  as  to  fixedness  of  ends  of 

arch   665 

27.  Skew  arches   665 

28.  Unsymmetrical  arches   665 


Art.  Page 

a.  Origin   of   coordinates  between 

divisional  lengths   665 

b.  Origin  of  coordinates  at  crown. .  .  666 

c.  Origin    of    coordinates    at  left 

springing   667 

29.  Arch  structure  of  two  spans  with 

elastic  pier   667 

Cochrane's  Formulas  and  Diagrams  for 


Use  in  the  Design  of  Symmetrical 
Arches  in  Accordance  with 
the  Elastic  Theory 


30.  Accuracy  of  formulas  and  diagrams .  .  669 

3 1 .  Difficulties  and  uncertainties  involved 

in  applying  the  elastic  theory .  .  669 

32.  Best  shape  of  arch  axis   669 

33.  Variation  in  thickness  of  arch  ribs. .  .  .  670 

34.  Influence-line  diagrams   673 

35.  Diagrams  for  moments,  thrusts,  and 

average  stresses   681 

36.  Approximate  method  of  correcting 

maximum  moments  when  actual 
arch  axis  deviates  from  assumed 
axis   686 

Details  of  Arch  Bridges 

37.  Spandrel     details     in  earth-filled 

bridges   691 

38.  Spandrel   details   in  open-spandrel 

bridges   694 

39.  Piers  and  abutments   702 

40.  Railing  and  ornamental  details   702 

Construction  of  Arches 

41.  Arch-ring  construction   702 

42.  Centering   704 

a.  Timber  centers   704 

b.  Steel  centers   712 

Three-hinged  Arches 

43.  General  discussion   715 

44.  Methods  of  analysis   715 

45.  Common  type  of  hinges   717 

46.  Methods  of  construction   717 

47.  Details  of  design.   719 


CONTENTS 
Section  17.    Hydraulic  Structures 


Dams 

Art.  Page 

1.  Preliminary  studies   723 

a.  Locating   723 

h.  Geological  investigations   723 

c.  Selecting  a  suitable  type  of  dam.,  724 

d.  Height  of  structure   724 

e.  Hydrographic  investigations   725 

/.  Capacity  of  reservoir   726 

2.  Design  of  foundation   728 

a.  Grouting   728 

6.  Cut-off  walls  "   728 

c.  Caissons   728 

d.  Pilings   728 

6.  Sheet  piling   728 

3.  Design  of  dams  of  gravity  section .  .  .  729 

a.  Hydrostatic  pressure   729 

h.  Profiles  of  dams   729 

c.  Uplift   731 

d.  Wind  pressure   732 

e.  Ice  thrust   732 

/.  Initial  stress   732 

g.  Temperature  stresses.   732 

h.  Stresses  in  masonry  and  on  foun- 

dation  733 

i.  Shearing  stresses   734 

j.  Final  calculation   734 

4.  Design  of  arched  dams   736 

a.  Constant  radius  dams   736 

h.  Constant  angle  dams   738 

5.  Design  of  reinforced-concrete  dams. .  739 

a.  Cut-off  walls   740 

h.  Foundation  mattress   740 

c.  Buttresses   740 

d.  Bracing    741 

e.  Apron   741 

/.  Multiple-arch  dams   743 

6.  Earthern  dams  with  concrete  core 

wall   745 

7.  Passing  the  discharge   748 

a.  Form  of  spillway.   748 

h.  Discharge  capacity   749 

c.  Profiles  of  spillways   749 

d.  Overflow  dams   753 

e.  Sluices   754 

/.  Siphonic  spillways   755 

8.  Movable  dams   758 

a.  Requiring  operating  machinery.  .  759 
h.  Operating  under  hydrostatic  pres- 
sure differences   759 


Art.  Page 

c.  Automatically  operating   759 

9.  Fish  ladders   759 

Reservoirs 

10.  General  types   760 

11.  Quality  of  concrete    for  reservoir 

masonry   760 

12.  Open  basins  with  embankment  walls,.  761 

13.  Concrete  floors  for  reservoirs   761 

14.  Groined  and  flat  floors   762 

15.  Concrete  walls  for  open  reservoirs. .  .  .  763 

16.  Partition  and  outside  walls   764 

17.  Provision  for  ice   764 

18.  Covers  or  roofs  for  reservoirs  and 

basins   764 

19.  Groined  arch  construction   764 

20.  Construction  details  of  columns  and 

roof   764 

Standpipes  and  Small  Tanks 

21.  Analysis  of  stresses  in  standpipes .  .  .  .  765 

22.  Restraint  at  base   765 

23.  Shear  at  base   767 

24.  Small  tanks   768 

25.  Construction  details  of  tanks  and 

standpipes   769 

26.  Precautions  in  construction   771 

Elevated  Tanks 

27.  Analysis  of  stresses   771 

28.  Supporting  tower   774 

Culverts 

29.  General  considerations   775 

30.  Factors  in  culvert  design   776 

a.  Culvert  efficiency   776 

h.  Waterway  required   776 

c.  Length  of  culverts   776 

d.  Design  of  ends   777 

31.  Pipe  culverts   777 

a.  Pressure  in  trenches   778 

h.  Strength  of  pipe   781 

c.  Circular  culverts  cast  in  place,,.  .  782 

32.  Box  culverts   783 

a.  Forms  of  box  culverts   785 


CONTENTS 


Art.  Page 
h.  Loading   785 

c.  Design  of  cross-section   785 

Type  I.  The  closed  frame. ...  787 
Type  II.  Open  frame  with  fixed 

walls   788 

Type  III.  Open  frame  hinged 

at  the  base   789 

Diagrams   794 

d.  Construction   794 

33.  Arch  culverts   796 

a.  Design  of  cross-section   796 


Art.  Page 

h.  Forms   797 

Conduits  and  Sewers 

34.  Stresses  due  to  internal  pressure   799 

35.  External  earth  pressure  on  circular 

pipe   799 

36.  Large  conduits  and  sewers  not  circu- 

lar  799 

37.  Construction   802 

38.  Longitudinal  reinforcement   802 

39.  Examples  of  reinforced-concrete  pipe.  803 

40.  Forms  for  sewers   803 


Section  18.    Miscellaneous  Structures 


Deep  Grain  Bins  or  Silos 

L  Action  of  grain  in  deep  bins   805 

2.  Janssen's  formulas  for  pressure  in 

deep  bins   805 

3.  Conclusions  from  tests   806 

4.  Design  of  walls   808 

a.  Vertical  load  carried  by  walls. .  808 
h.  Wind  stresses  on  a  horizontal  sec- 
tion  808 

c.  Thickness  of  walls   808 

d.  Horizontal  reinforcement — circu- 

lar sections   808 

e.  Rectangular  sections   808 

/.  Hexagonal  bins   809 

5.  Construction   809 

Shallow  Bins 

6.  Sloped  sides — level  full  (Case  I)   811 

7.  Partly  vertical  sides — level  full  (Case 

II)   811 


8.  Sloped  sides — fill  heaped  to  angle  of 

repose  (Case  III)   811 

9.  Partly    vertical    sides — fill  heaped 

(Case  IV)   812 

10.  Thrust  due  to  P4   812 

11.  Data  for  bin  design   812 

12.  Submerged  storage  for  coal   813 

13.  Dock  pockets   815 

Chimneys 

14.  Dead  load  stresses   816 

15.  Stresses  on  annular  sections  in  flexure  816 

16.  Wind  stresses  in  chimneys  of  rein- 

forced concrete   818 

17.  Chimney  with  no  vertical  reinforce- 

ment  818 

18.  Longitudinal  shear  in  chimneys   819 

19.  Temperature  stresses  in  chimneys. .  .  .  819 

20.  Chimney  construction   820 

21.  Bases  for  chimneys   820 


Section  19. 


Estimating  Unit  Costs 

1.  Division  of  the  work   823 

2.  Estimating  unit  cost  of  concrete   823 

a.  Materials   823 

h.  Labor   824 

c.  Plant   825 

d.  Summary   825 

3.  Estimating  unit  cost  of  forms   826 

a.  Considerations  involved   826 

h.  Materials   827 

c.  Labor   827 


Estimating 

d.  Summary   828 

4.  Estimating  unit  cost  of  steel  rein- 

forcement  828 

5.  Estimating  unit  cost  of  surface  finish  829 

Estimating  Quantities 

6.  Systematic  procedure  advisable   830 

7.  Rules  for  measurement  of  concrete 

work   830 

8.  Estimating  amount  of  form  work..  .  .  831 

9.  Estimating  amount  of  steel   832 

10.  Estimating  amount  of  surface  finish . .  832 


CONTENTS 


XXIU 


Appendix  A 


Page 


Standard  specifications  and  tests  for  Port- 
land cement   833 

Appendix  B 

Working  stresses   845 

Appendix  C 

Rulings  Pertaining  to  Flat-Slab  Design 

Ruling  on  the  design  of  cantilever  flat- 
slab  construction  in  the  city  of 
Pittsburgh   847 

Ruling  covering  design  of  flat-slab  con- 
struction in  the  city  of  Chicago. . .  849 

Chicago  reinforced-concrete  flat-slab  rul- 
ing amended   851 


Page 

Final  report  of  special  committee  of  the 
American  Society  of  Civil  Engi- 
neers— part  pertaining  to  flat-slab 
design   854 

Standard  building  regulations  for  the  use 
of  reinforced  concrete.  American 
Concrete  Institute,  1917 — part 
pertaining  to  flat-slab  floors   858 


Appendix  D 

Standard  notation  


861 


Appendix  E 


Index 


Concrete  barges  and  ships — extract  from 
report  of  the  Joint  Committee  of 
the  American  Concrete  Institute 
and  Portland  Cement  Association  863 

  867 


CONCRETE  ENGINEERS^ 
HANDBOOK 


SECTION  1 

MATERIALS 
CEMENT 

1.  Classification,  Composition,  and  Uses  of  the  Principal  Cementing  Materials. — Cement- 
ing materials  used  in  structural  work  may  be  divided  into  two  main  classes — non-hydraulic 
and  hydraulic.  Non-hydraulic  cements,  as  the  name  implies,  will  not  set  and  harden  under 
water;  while  hydraulic  cements  will  harden  in  either  water  or  air.  Following  is  a  list  of  the 
•structural  cements  of  commercial  importance: 


Non-hydraulic 


Hydraulic 


Gypsum  plasters 
Common  lime 

Hydraulic  lime 

{Grappier  cement,  a  by-product) 
Puzzolan  cement 
Natural  cement 
Portland  cement 

(Adulterated  or  modified  Portland  cement) 


la.  Gypsum  Plasters. — Gypsum  plasters  are  made  by  partial  or  complete  de- 
hydration of  relatively  pure  or  impure  natural  gypsum.  The  setting  of  these  plasters  is  a 
recrystallization  from  a  solution  formed  by  admixture  of  the  partially  or  totally  dehydrated 
material  with  water,  reforming  the  original  substance.  [Pure  gypsum  is  a  hydrous  crystalline 
calcium  sulphate  (CaS04  +  2H2O) ;  and  in  its  raw  uncalcined  state  is  used  as  an  adulterant 
to  retard  the  setting  of  Portland  and  natural  cements.  Plaster  of  Paris  (CaS04  +  3'^H20) 
is  also  used  for  the  same  purpose  and  is  a  refined  plaster  made  from  pure  gypsum  by 
dehydration.] 

Gypsum  plasters,  of  one  variety  or  another,  are  used  principally  on  interior  walls  and  floors. 
They  are  also  used  in  the  form  of  molded  hollow  blocks  and  tiles  for  fireproof  interior  partition 
walls,  and  as  one  variety  of  "stucco"  for  the  architectural  adornment  of  buildings. 

16.  Common  Lime. — Common  lime  is  made  by  burning  limestone  (CaCOs) 
at  a  temperature  of  about  900°C.  until  its  carbon  dioxide  (CO2)  is  driven  off  as  gas.  The  residue 
is  common  lime  (CaO),  known  commercially  as  ''quicklime."  On  addition  of  water  this 
product  slakes  with  evolution  of  heat  and  much  increase  of  volume,  forming  a  paste  of  lime 
hydrate,  or  calcium  hydroxide  (Ca[0H]2)  known  as  "Hme  putty"  or,  on  dilution  with  water,  as 
"cream  of  lime." 

Even  in  the  purest  limestone  to  be  found  in  nature  some  impurities  are  present.  Generally 
a  part  of  the  lime  (CaO)  is  found  replaced  by  a  certain  percentage  of  magnesia  (MgO),  and  clay 

1 


2 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-lc 


is  also  present  to  some  extent.  [Clay  is  composed  chiefly  of  silica  (Si02)  and  alumina  (AI2O3), 
and  usually  contains  some  iron  oxide  (Fe203).]  In  the  manufacture  of  quicklime,  magnesia 
acts  in  much  the  same  manner  and  may  be  considered  the  equivalent  of  lime,  which  makes  it 
possible  to  use  limestone  which  is  high  in  magnesia.  Quicklimes  are  divided  into  four  main 
types  according  to  the  relative  content  of  calcium  oxide  (CaO)  and  magnesium  oxide  (MgO). 
These  are: 

1.  High-calcium;  quicklime  containing  90%  or  over  of  calcium  oxide. 

2.  Calcium;  quicklime  containing  not  less  than  85%  and  not  more  than  90%  of  calcium 
oxide. 

3.  Magnesian;  quicklime  containing  between  10  and  25%  of  magnesium  oxide. 

4.  Dolomitic;  quicklime  containing  over  25%  of  magnesium  oxide. 

Following  is  an  average  analysis  of  ten  high-calcium  quicklimes  and  two  dolomitic  quick- 
limes : 


Si02 

AI2O3 

FezOs 

CaO 

MgO 

% 

% 

% 

% 

% 

High-calcium . . 

0.81 

0  22 

0.23 

94.98 

1.39 

Dolomitic  

0.87 

0.32 

0.29 

60.13 

36.12 

[Analysis  also  shows  carbon  dioxide  (CO2)  and  water  (H2O)  to  be  present  in  small  amounts.] 
Practically  all  lime  used  in  construction  is  made  into  mortar  by  adding  sand  to  the  paste 
of  lime  hydrate,  as  sand  is  not  only  cheaper  than  lime  but  diminishes  the  great  shrinkage  which 
accompanies  the  setting  and  hardening  of  lime  putty.  This  hardening  is  due  mainly  to  crys- 
tallization, but  in  addition  some  of  the  water  in  the  hydroxide  is  gradually  replaced  by  carbon 
dioxide  from  the  atmosphere,  causing  a  small  part  of  the  hydroxide  to  revert  to  the  original  cal- 
cium carbonate  (CaCOs). 

Although  common  lime  is  used  chiefly  in  combination  with  sand  as  a  mortar  in  laying 
ordinary  brick  and  stone  masonry,  it  is  also  used  extensively  as  an  interior  wall  plaster  and 
for  gaging  hydraulic  cement  mortars,  either  to  make  them  easier  to  work  or  to  reduce  their 
permeability. 

Hydrated  lime  is  quicklime  slaked  at  the  place  of  manufacture.  Its  market  form  is  that  of 
a  dry  powder,  and  as  such  it  can  be  mixed  with  sand  more  easily  than  can  lime  paste  made  by 
slaking  ordinary  quicklime  on  the  work. 

Ic.  Hydraulic  Lime. — Hydraulic  lime  is  made  by  burning  argillaceous  or  silicious 
limestone  at  a  temperature  not  less  than  1000°C.  When  showered  with  water  the  product 
slakes  completely  or  partially  without  sensibly  increasing  in  volume,  and  possesses  hydraulic 
properties  due  to  the  combination  of  calcium  with  silica  contained  in  the  limestone  as  an 
impurity,  forming  calcium  silicate.  It  is  the  universal  practice  to  slake  the  lime  at  the  place 
of  manufacture  on  account  of  the  better  results  obtained. 

Grappier  cement  is  a  by-product  in  the  manufacture  of  hydraulic  lime,  produced  by  grind- 
ing the  lumps  of  underburned  and  overburned  material  which  do  not  slake.  As  might  be 
inferred,  grappier  cement  possesses  properties  similar  to  those  of  hydraulic  lime. 

Hydraulic  lime  is  not  manufactured  in  the  United  States  on  account  of  the  abundance 
of  raw  materials  suitable  for  the  manufacture  of  Portland  cement,  with  which  hydraulic  lime 
cannot  compete  as  a  structural  material.  A  number  of  hydraulic  limes  and  grappier  cements 
are  marketed  as  "non-staining  cements" — that  is,  they  do  not  stain  masonry  For  this  reason 
a  considerable  amount  of  this  cementing  material  is  annually  imported  from  Europe  for  purposes 
of  architectural  decoration. 

Id.  Puzzolan  or  Slag  Cement. — Puzzolan  cement  is  made  by  incorporating 
hydrated  lime  with  a  silicious  material,  such  as  granulated  blast-furnace  slag,  of  suitable  fine- 
ness and  chemical  composition.    In  Europe  a  natural  puzzolanic  material,  such  as  volcanic  ash. 


Sec. 


MATERIALS 


3 


is  used  at  some  plants  in  place  of  the  blast-furnace  slag.  Silica,  when  finely  enough  divided,  is 
soluble  in  water  and  chemically  active.  For  this  reason  the  materials  are  finely  pulverized  and 
intimately  mixed  by  grindmg,  but  are  not  calcined,  the  formation  of  calcium  silicate  taking 
place  slowly  and  at  ordinary  temperatures. 

Although  this  type  of  cement  possesses  hydraulic  properties,  it  should  not  be  confused  with 
slag  Portland  cement  (sometimes  called  steel  Portland  cejnent)  which  is  produced  by  calcining 
finely  divided  slag  and  lime  in  a  kiln  and  pulverizing  the  resulting  clinker.  Analysis  of  the  small 
number  of  puzzolan  or  slag  cements  manufactured  in  this  country  shows  approximately  the 
following  range  in  composition: 


Si02 
% 

AI2O3  +  FeaOa 
+  FeO 

% 

CaO 

% 

MgO 

S 

% 

CO2  +  H2O 

% 

27.2  to  31.0 

11.1  to  14.2 

50.3  to  51.8 

1,4  to  3.4 

0.15  to  1.42 

2 . 6  to  5 . 3 

They  are  normally  slower  in  setting  than  Portland  cements  and  on  this  account  are  usually 
treated  with  materials  which  will  hasten  the  set — such  as  burned  clay,  high-alumina  slags,  caus- 
tic soda,  sodium  chloride,  or  potash.  Puzzolan  cements  made  from  slag  may  be  distinguished 
by  their  light  lilac  color,  absence  of  grit,  and  low  specific  gravity  (2.60  to  2.85).  They  also  are 
high  in  sulphides,  which  render  them  liable  to  disintegration  in  air,  nor  are  they  suited  for  use  in 
sea  water,  where  there  is  always  an  excess  of  sulphates. 

Puzzolan  cement  is  not  as  strong  or  reliable  as  either  natural  or  Portland  cement  and  should 
be  used  only  in  unimportant  structures  or  in  unexposed  work,  such  as  foundations,  where  weight 
and  bulk  are  more  important  than  strength. 

le.  Natural  Cement. — Natural  cement,  as  its  name  implies,  is  made  from  rock  as 
it  occurs  in  nature.  This  rock  is  an  argillaceous  (clayey)  hmestone,  or  other  suitable  natural 
rock,  and  it  is  burned  at  a  temperature  of  from  900°  to  1300°C.,  the  clinker  being  then  finely 
pulverized.  The  product  does  not  slake,  but  possesses  strong  hydraulic  properties,  calcium 
silicate  being  formed  and  acquiring  strength  and  rigidity  through  crystallization. 

Unfortunately,  the  composition  and  characteristics  of  natural  cement  are  subject  to  consider- 
able variation.  This  is  to  be  expected,  since  the  composition  of  the  rock  from  which  it  is  made 
not  only  varies  in  different  localities  but  is  further  subject  to  variation  to  some  extent  at  least, 
even  in  the  same  deposit.  Portland  cement,  on  the  contrary,  is  an  artificial  mixture,  subject 
to  control.  This  fact,  together  with  its  slow  setting,  is  mainly  responsible  for  the  decrease  in  the 
use  of  natural  cement  and  the  adoption  of  Portland  cement  in  all  important  structures. 

In  spite  of  these  disadvantages,  however,  it  is  a  significant  fact  that  natural  cements  do  not 
show  disintegration  with  passage  of  time,  while  Portland  cements  frequently  are  most  erratic 
in  behavior.  On  comparing  analyses  of  typical  natural  and  Portland  cements,  it  is  at  once 
noticed  that  natural  cements  have  a  higher  percentage  of  silica,  about  the  same  percentage  of 
alumina  and  a  lower  percentage  of  lime  than  have  Portland  cements.  Excess  hme,  so  generally 
prevalent  in  hydrated  Portland  cements,  and  not  necessarily  resultant  on  "free  lime,"  is  fre- 
quently the  cause  of  much  trouble.  There  is  a  distinct  field  of  usefulness  for  natural  cement 
which  is  largely  overlooked  by  engineers  at  the  present  time.  In  many  cases,  perplexing  prob- 
lems could  be  effectively  solved  by  its  employment. 

The  following  summary  shows  the  range  in  composition  of  an  average  analysis  of  six  well- 
known  American  natural  cements: 


Si02 

AI2O3 

Fe203 

CaO 

IMgO 

% 

% 

% 

% 

% 

22.3  to  29.0 

5 . 2  to  8 . 8 

1 . 4  to  3 .  2 

31.0  to  57.6 

1.4  to  21.5 

4 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-1/ 


[Analysis  also  shows  varying  small  amounts  of  alkalies  (K2O  and  Na20),  anhydrous  sulphuric 
acid  or  sulphur  trioxide  (SO3),  carbon  dioxide  (CO2),  and  water  (H2O).  Magnesia  (MgO)  is 
usually  regarded  as  equivalent  to  lime  in  its  action.]  The  specific  gravity  of  natural  cements 
range  from  2.7  to  3.1,  with  an  average  of  2.85. 

Natural  cement  is  adapted  to  many  uses,  but  its  relatively  low  strength  and  slow  hardening 
limit  its  field  to  structures  where  high  stresses  will  not  be  imposed  for  several  months  after  plac- 
ing the  concrete,  as  in  large  or  massive  structures  where  weight  and  mass  are  more  essential  than 
early  strength — that  is,  in  such  structures  as  dams,  abutments,  foundations,  and  many  under- 
ground structures.  Mortar  made  with  natural  cement  (either  alone  or  mixed  with  lime  mor- 
tar) is  excellent  for  laying  ordinary  brick  and  stone  masonry. 

If,  Portland  Cement. — Portland  cement  is  made  by  finely  pulverizing  the  clinker 
produced  by  burning  a  definite  artificial  mixture  of  silicious  (containing  silica),  argillaceous 
(containing  alumina),  and  calcareous  (containing  lime)  materials  to  a  point  somewhat  beyond 
where  they  begin  to  fuse  or  melt.  The  product  is  one  that  does  not  slake  and  possesses  strong 
hydraulic  properties.  The  essential  components  of  Portland  cement — namely:  silica,  alumina, 
and  lime — are  obtained  from  many  different  sources,  but  the  proportions  used  of  the  raw  mate- 
rials are  always  such  that  the  chemical  composition  of  the  different  Portland  cements  is  constant 
within  narrow  limits.    The  percentages  of  the  principal  components  range  about  as  follows: 


Si02 

AI2O3 

Fe203 

CaO 

MgO 

% 

% 

% 

% 

% 

19  to  25 

5  to  9 

2  to  4 

60  to  64 

1 . 0  to  2 . 5 

[Small  amounts  of  alkalies  (K2O  and  Na20)  and  sulphur  trioxide  (SO  3)  are  also  present.  Mag- 
nesia (MgO)  is  considered  by  some  as  an  impurity,  while  other  investigators  claim  it  is  equiva- 
lent to  lime  (CaO)  in  its  action.  Alumina  (AI2O3)  and  iron  oxide  (Fe203)  do  not  act  entirely 
alike  but  are  usually  considered  to  have  the  same  functions.]  The  specific  gravity  of  Portland 
cements  range  from  3.1  to  3.20,  with  an  average  of  3.15. 

Portland  cement  is  by  far  the  most  important  cementing  material  used  in  modern  engineer- 
ing construction.  It  is  adapted  for  use  in  concrete  and  mortar  for  all  types  of  structures  where 
strength  is  of  special  importance,  or  in  structures  exposed  to  wear  or  to  the  elements.  It 
should  invariably  be  employed  in  reinforced-concrete  construction  because  of  its  high  early 
strength  and  generally  uniform  quality. 

A  number  of  special  cements  employing  Portland  cement  as  a  base  are  made  by  grinding  in 
adulterating  materials  after  calcination.  These  adulterants  include  clay,  slaked  lime,  sand, 
slag,  natural  cement,  limestones,  and  natural  puzzolanic  material  or  tufa.  The  action  of  these 
materials  is  essentially  to  promote  combination  between  lime  from  the  cement  and  silica  from 
the  adulterant,  with  formation  of  silicate  of  lime.  In  some  cases  these  silicious  adulterants 
improve  the  quality  of  concrete  made  from  such  cements,  but  this  result  cannot  be  expected 
from  all  forms  of  adulteration. 

Sand  and  puzzolanic  material  have  perhaps  been  used  the  most  extensively  and  successfully 
of  any  of  the  adulterants,  producing  products  known  as  sand  cement  and  tnfa  cement  respectively. 
These  cements  have  been  used  principally  on  large  work  where  freight  rates  are  high  and  long 
wagon  hauls  combine  to  make  the  cost  of  undiluted  Portland  cement  excessive.  Cement 
specifications  in  common  use  are  of  a  character  to  exclude  any  grinding  in  of  materials  after 
calcination,  presumably  on  the  ground  that  specifications  permitting  any  adulteration  would 
be  subject  to  abuse  so  that  the  results  obtained  would  be  uncertain. 

2.  Portland  and  Natural  Cements  Compared. — The  distinguishing  properties  of  natural  and 
Portland  cements  and  the  chief  differences  in  manufacture  may  be  summarized  as  follows: 


Sec.  1-3] 


MATERIALS 


5 


Natural  cement 


Portland  cement 


Calcination  temperature 
Chemical  composition.  .  . 


Raw  material .... 
Type  of  kiln  used 


Natural  rock 

Mostly  the  vertical  stationary 
type 

Low,  but  variable 

Variable,   not   under  control 


Artificial  mixture 

Slanting  cylindrical  revolving 

type 
Relatively  high 
Controllable    within  narrow 

limits 

Bluish  or  steel  gray 


Specific  gravity  

Rate  of  setting  

Strength  

Degree  of  grinding 
Soundness  


Color 


Yellow  to  brown 
2.7  to  3.1 
Relatively  rapid 
Low,  especially  at  early  age 
Usually  rather  coarse 
Will  not  usually  stand  steam 
test 


3 . 1  to  3 . 2 


Relatively  slow 
Relatively  high 
Relatively  fine 


Required  to  stand  steam  test 


In  structures  where  either  natural  or  Portland  cement  may  be  used,  and  where  economy 
is  the  governing  consideration,  the  choice  of  cement  should  be  based  on  a  comparison  of  the 
costs  per  cubic  yard  of  the  required  mortar  or  concrete  mixtures.  Decisions  usually  are 
desired  either  between  a  1:2  natural  cement  mortar  and  a  1:3  Portland  cement  mortar,  or 
between  a  1:2:4  natural  cement  concrete  and  a  1:4:8  Portland  cement  concrete. 

3.  Constitution  of  Portland  Cement.^ — The  latest  optical  and  microscopical  examinations 
of  Portland-cement  clinker,  and  of  all  the  substances  which  were  formally  considered  as  likely 
to  be  formed  in  manufacture,  show  Portland  cement  to  be  made  up  largely  of  the  three  com- 
pounds 3CaO-Si02,  2CaO-Si02,  and  3CaO-Al203.  The  tri-calcium  silicate  appears  the  best 
cementing  compound  and  it  is  probable  that  the  higher  its  percentage,  the  better  the  cement. 
The  small  amounts  present  of  Fe203,  MgO,  alkalies,  etc.  have  but  little  effect  on  the  three 
major  compounds  but  their  presence  aids  materially  in  manufacture  by  promoting  the  combina- 
tion of  CaO  with  AI2O3  and  Si02. 

A  perfectly  burned  cement  clinker  consists  of  about  36%  of  tri-calcium  silicate,  3CaO-Si02; 
33%  of  di-calcium  silicate,  2CaO-Si02;  21%  of  tri-calcium  aluminate,  3CaO-Al203;  and  10% 
of  minor  constituents.  The  principal  cementing  compound,  tri-calcium  silicate,  3CaO-Si02, 
is  the  last  constituent  to  form  completely  in  Portland-cement  manufacture;  and  this  compound 
is  formed  by  the  combination  of  CaO  with  2CaO-Si02.  When  cement  clinker  is  not  perfectly 
burned  there  is  evidently  less  3CaO-Si02. formed  and  more  2CaO-Si02.  There  is  also  a  certain 
percentage  of  free  lime  (CaO)  present,  the  amount  depending  upon  the  degree  of  burning. 

4.  Setting  and  Hardening  of  Portland  Cement. ^ — The  setting  and  hardening  of  Portland 
cement  is  caused  principally  by  hydration  in  the  order  named  of  the  three  major  constituents — 
3CaO  Al203,  3CaO  Si02,  and  2CaO  Si02.  When  water  is  added  to  Portland  cement,  these 
constituents  form  first  amorphous  and  later  both  crystalline  and  amorphous  hydrated  materials 
which  act  much  as  does  ordinary  glue,  except  that  since  they  are  of  mineral  origin  and  largely 
insoluble,  hardening  progresses  even  under  water. 

Of  these  hydration  products,  the  compound  tri-calcium  aluminate  (3CaO-Al203)  when 
mixed  with  water  sets  and  hardens  very  quickly;  tri-calcium  silicate  (3CaO-Si02)  sets  and 
hardens  somewhat  less  rapidly;  and  di-calcium  silicate  (2CaO-Si02)  reacts  slowly.  Hardening 
occurs  only  after  the  lapse  of  a  long  period  of  time.  The  initial  set  of  cement  is  due  undoubtedly 
to  the  hydration  of  3CaO-Al203;  the  early  hardness  and  cohesive  strength  is  due  to  this  hydration 

1  From  paper  before  Am.  Cone.  Inst.,  Feb.,  1916,  by  G.  A.  Rankin,  Geophysical  Laboratory,  Carnegie  Inst, 
of  Wash. 

2  See  Klein  and  Phillips:  Tech.  Paper,  43,  U.  S.  Bureau  of  Standards. 

Bates  and  Klein:  Tech.  Paper,  78,  U.  S.  Bureau  of  Standards. 


6 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-5 


and  to  that  of  the  3CaO  Si02;  while  the  gradual  increase  in  strength  is  due  to  the  further  hydra- 
tion of  these  two  compounds  together  with  the  hydration  of  the  2CaO-Si02. 

The  compound  3CaO-Si02  appears  to  be  the  best  cementing  constituent  of  this  group,  as 
it  is  the  only  one  of  the  three  which  when  mixed  with  water  will  set  and  harden  within  a  reason- 
able time  to  form  a  mass  which  is  comparable  in  hardness  and  strength  to  Portland  cement. 
Although  3CaO-Al203  sets  and  hardens  rapidly,  it  is  rather  soluble  in  water  and  is  not  particu- 
larly durable  or  strong.  The  compound  2CaO-Si02,  however,  requires  too  long  a  time  to  harden 
to  be  in  itself  a  valuable  cementing  material. 

5.  Manufacture  of  Portland  Cement. 

5a.  Raw  Materials. — Silica,  alumina,  and  lime — the  essential  components  of 
Portland  cement — occur  as  ingredients  in  a  large  number  of  natural  materials  of  widely  vary- 
ing character.  In  none  of  these,  however,  do  the  three  components  occur  in  the  exact  pro- 
portions required  in  Portland-cement  manufacture  so  that  an  artificial  mixture  of  several 
materials  has  to  be  resorted  to.  The  following  combinations  of  raw  materials  are  used  in  differ- 
ent cement  plants  in  this  country: 

1.  Cement  rock  and  limestone. 

2.  Marl  and  clay  (or  shale). 

3.  Limestone  and  clay  (or  shale). 

4.  Blast-furnace  slag  and  limestone. 

5.  Chalk  and  clay. 

Cement  rock  is  an  argillaceous  limestone  containing  about  68  or  72%  of  lime  carbonate, 
18  to  27%  of  clayey  matter,  and  not  over  5%  of  magnesium  carbonate.  It  is  a  dark  slatey 
limestone,  rather  soft  in  texture,  and  is  almost  ideal  for  cement  making  due  to  the  fact  that 
it  is  easy  to  quarry  and  grind,  and  is  usually  so  well  balanced  in  composition  that  but  a  small 
amount  of  comparatively  pure  limestone  needs  to  be  added.  This  rock  is  found  in  many  parts 
of  the  country  but  so  far  has  been  used  in  the  manufacture  of  Portland  cement  only  in  the 
Lehigh  district  of  eastern  Pennsylvania  and  western  New  'Jersey,  a  district  producing  nearly 
one-third  the  entire  output  of  the  United  States. 

Limestone  suitable  for  cement  manufacture  is  composed  principally  of  calcium  carbonate 
together  with  more  or  less  impurities.  The  following  shows  the  approximate  range  of  com- 
position of  such  limestones : 


CaCOa 

% 

Si02 

% 

AI2O3  +  Fe203 
% 

MgCOa 

% 

88.0  to  98.0 

0 . 3  to  8 . 0 

0.2  to  2.1 

0.2  to  4.2 

Sulphur  as  SO3  and  various  alkalies  may  also  be  present  in  small  percentages. 

Marl  is  almost  pure  calcium  carbonate.  It  is  a  soft,  wet  earth  found  in  the  basins  of  dried- 
up  lakes  and  in  swamp  regions,  deposited  either  by  chemical  agencies  or  through  the  phys- 
ico-chemical agencies  of  certain  forms  of  vegetable  and  animal  life. 

Clays  and  shales  are  of  the  same  general  composition,  differing  only  in  degree  of  solidifi- 
cation. Clays  result  from  the  decay  of  shales,  and  like  their  parent  rock,  are  composed  chiefly  of 
sihca  (Si02)  and  alumina  (AI2O3),  and  usually  iron  oxide  (Fe203).  The  proportion  of  silica  in 
clay  suitable  for  cement  manufacture  should  not  be  less  than  55  to  65%;  and  the  combined 
amount  of  alumina  and  iron  oxide  should  be  between  one-third  and  one-half  the  amount  of 
silica.  A  clay  with  these  proportions  of  principal  constituents  is  highly  siliceous,  producing 
a  cement  clinker  which  is  comparatively  easy  to  grind.  Clay  containing  a  greater  portion  of 
alumina  produces  a  hard  clinker  and  a  quick-setting  cement  which  is  more  severely  attacked  by 
sea  water. 

Blast-furnace  slag  is  a  compound  formed  from  impurities  in  the  iron  ore  and  the  limestone 


Sec.  1-56] 


MATERIALS 


7 


used  as  a  flux  in  the  blast  furnace.  Following  is  a  typical  analysis  of  slag  used  in  the  manu- 
facture of  cements: 


Si02 

% 

AI2O3  +  Fe203 

% 

CaO 

% 

MgO 

% 

33.10 

12.60 

49.98 

2.45 

Slag,  when  allowed  to  cool  quickly,  becomes  a  hard  glassy  mass,  very  tough  and  durable.  In 
order  to  use  slag  economically  in  cement  manufacture  the  molten  slag  is  run  into  large  cisterns, 
and  there  converted  into  a  granular  substance  by  directing  against  it  innumerable  little  streams 
of  air  and  water.  This  disintegrated  slag  has  the  appearance  of  coarse  brown  sugar;  and  in  this 
form  it  is  used  as  a  raw  material  for  Portland  cement. 

Chalk  is  a  soft  earthy  variety  of  calcium  carbonate,  formed  from  the  remains  of  minute 
organisms.  It  also  sometimes  contains  small  amounts  of  silica,  alumina,  and  magnesia. 
Its  use  as  a  material  for  cement  manufacture  is  limited. 

5b.  Proportioning  the  Raw  Materials. — Two  rules  are  in  use  for  proportioning 
the  raw  materials  used  in  the  manufacture  of  Portland  cement.    Newberry's  rule  is  as  follows: 

Max.  lime  =  2.8  (%Si02)  +  1.1  (roAlgOa) 

Eckel's  rule  (called  the  ''cementation  index"),  which  is  really  a  modification  of  the  above  rule, 
takes  the  magnesia  and  iron  oxide  into  account : 

2.8  (%Si02)  +  1-1  (%Al203)  +  0.7  (%Fe203)  ^ 
%CaO  +  1.4  (%MgO) 

A  value  of  the  cementation  index  below  1  means  an  excess  of  lime  or  magnesia  in  the  cement 
which  will  cause  expansion,  or  unsoundness.  In  practice  it  is  customary  to  reduce  by  about 
10%  the  proportion  of  lime  found  by  the  above  rule  to  avoid  any  chance  of  obtaining  an  unsound 
cement.  Although  the  above  rules  are  not  based  on  the  most  recent  investigations  of  the 
constitution  of  Portland  cement  there  is  no  immediate  prospect  of  any  change  being  made  in 
practice  in  the  methods  of  proportioning  because  the  present  rules  are  known  by  experience  to 
produce  excellent  results. 

5c.  Grinding  and  Mixing. — The  admixture  and  grinding  of  the  raw  materials 
before  calcination  is  accomplished  by  either  a  wet  or  ai  dry  process.  In  the  wet  process,  prin- 
cipally for  plants  using  marl,  the  raw  materials  are  ground  and  fed  into  rotary  kilns  in  the 
form  of  a  slurry  containing  sufficient  water  to  make  it  of  a  fluid  consistency.  In  the  dry  process 
raw  materials  are  ground  and  mixed  in  the  dry  state.  The  larger  portion  of  Portland  cement 
manufactured  in  the  United  States  at  the  present  time  is  made  by  plants  using  the  dry  process, 

5d.  Burning  the  Cement  Mixture. — Rotary  kilns  are  used  in  almost  all  American 
Portland-cement  plants.  These  kilns  are  slightly  inclined  to  the  horizontal  and  revolve  at 
about  the  rate  of  one  revolution  per  minute.  The  ground  raw  materials  are  fed  in  at  the  upper 
end  and  are  carried  forward  and  tumbled  over  and  over  by  the  slant  and  revolution  of  the  kiln. 
As  the  materials  advance  they  are  reduced  by  the  hot  gases  from  the  burning  fuel  which  is  fed 
in  at  the  lower  end.  The  clinkers  formed  vary  in  size  from  in.  up  to  about  1}4  in.  in 
diameter.  It  takes  about  an  hour  for  a  particle  of  raw  material  to  traverse  the  entire  dis- 
tance from  the  feed  to  the  outlet. 

5e.  Treatment  of  the  Clinker. — After  cement  clinker  is  cooled  it  is  crushed  and 
passed  through  preliminary  grinding  mills.  Then  gypsum  is  added  and  the  clinker  ground  to 
a  fine  powder.  If  the  clinker  was  used  without  the  addition  of  gypsum,  it  would  take  an 
almost  immediate  set.  Approximately  2  lb.  of  gypsum  (CaS04)  (or  plaster  of  Paris)  is  used  to 
every  100  lb.  of  clinker. 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-6 


6.  Manufacture  of  Natural  Cement. 

6a.  Raw  Material. — The  raw  material  used  in  the  manufacture  of  natural  cement 
is  a  natural  argillaceous  limestone  containing  from  13  to  35%  of  clayey  material.  About  15% 
of  the  clayey  material  is  silica,  the  balance  being  alumina  and  iron  oxide.  The  kind  of  limestone 
generally  used  contains  a  considerable  proportion  of  magnesium  carbonate  in  place  of  calcium 
carbonate.  When  the  rock  varies  greatly  in  composition,  materials  from  different  strata  are 
mixed  together  to  give  as  uniform  a  product  as  possible.  The  wide  range  allowed  in  the  com- 
position of  natural  cement,  however,  does  not  warrant  great  refinement  in  the  analysis  of  the  rock, 

66.  Process  of  Manufacture. — Natural  cement  is  usually  manufactured  in  ver- 
tical kilns  lined  with  firebrick.  These  kilns  are  of  the  mixed-feed  type,  the  rock  (not  crushed) 
and  fuel  being  charged  in  alternate  layers.  The  temperature  required  in  burning  is  considerably 
below  that  required  in  Portland-cement  manufacture  because  temperatures  higher  than  1300°C. 
would  fuse  the  material  to  a  slag  having  no  hydraulic  properties.  The  temperature  employed, 
however,  is  sufficient  to  cause  the  formation  of  silica  compounds  with  the  lime  and  magnesia. 
The  clinker  is  taken  out  at  the  bottom  of  the  kiln  as  it  is  burned;  and  then  it  is  crushed  and 
ground.  Grinding  of  the  clinker  is  not  usually  carried  as  far  as  that  of  Portland  although  some 
of  the  newer  mills  use  grinding  machinery  similar  to  that  in  Portland-cement  plants. 

7.  Testing  of  Cement. — For  standard  methods  of  cement  testing,  see  Appendix  A. 

7a.  Sampling. — Tests  should  be  conducted  only  on  representative  samples. 
For  method  of  sampling,  see  Appendix  A,  page  834. 

76.  Uniformity  in  Cement  Testing. — In  order  to  obtain  results  in  cement  testing 
which  will  be  of  the  greatest  value,  definite  and  uniform  methods  should  be  used.  Results 
depend  not  only  on  the  quality  of  the  cement  but  also  on  the  temperature  and  percentage  of 
water  used  in  mixing,  the  method  of  mixing  and  molding  test  specimens,  the  temperature  and 
humidity  of  the  air,  the  character  of  the  sand  used,  and  the  type  of  apparatus  employed. 

7c.  The  Personal  Factor. — The  personal  factor  has  considerable  effect  on  results 
obtained  in  cement  testing  and,  on  this  account,  only  experienced,  well-qualified  men  should  be 
employed  in  making  tests.  Results  by  untrained  or  careless  operators  are  really  worse  than 
nothing  and  may  be  positively  misleading.  The  comparative  results,  however,  by  any  one 
experienced  observer  are  generally  consistent  and  are  of  value.  It  is  usually  advisable  to  have 
the  testing  done  at  some  well-established  and  properly  equipped  cement-testing  laboratory. 

7d.  Kinds  of  Tests. — The  following  cement  tests  made  regularly  are  recom- 
mended for  construction  work  of  importance  and  also  in  all  cases  where  the  cement  to  be  used 
does  not  work  satisfactorily : 
Fineness. 
Time  of  setting. 

Tensile  strength  of  standard  mortar.    (Compressive  strength  of  standard  mortar  the 

best  criterion.) 
Soundness. 

On  unimportant  construction  it  is  generally  safe  to  use  a  well-known  brand  of  Portland  cement 
without  testing,  or  to  make  simply  the  test  for  soundness. 

7e.  Fineness. — Fine  grinding  has  a  great  influence  on  the  properties  of  cement. 
It  increases  the  ability  of  the  cement  to  react  readily  with  water  and  enables  the  cement 
particles  to  coat  the  sand  grains  more  thoroughly.  In  other  words,  the  finer  the  cement,  all 
other  conditions  being  the  same,  the  stronger  will  be  the  mortar  produced  with  a  given  sand. 

The  fineness  of  cement  is  measured  by  determining  the  percentage  by  weight  which  will 
be  retained  on  a  standard  200-mesh  sieve. Standard  specifications^  require  that  the  residue 
shall  not  exceed  22%.  Most  mills  are  now  equipped  to  grind  cement  to  such  a  fineness  that 
even  less  than  10%  is  retained. 

It  has  long  been  generally  recognized  that  the  coarser  particles  in  cement  are  practically 

1  For  description  of  standard  sieve,  see  Appendix  A,  p.  836. 

2  For  standard  specifications,  see  Appendix  A,  p.  833. 


Sec.  1-7/] 


MATERIALS 


9 


inert  and  that  at  least  the  earlier  cementing  value  is  due  chiefly  to  the  grains  that  will  pass  the 
No.  200  sieve.  Because  of  this  fact  the  present  standard  method  of  testing  for  fineness  is  unsat- 
isfactory, as  no  attempt  is  made  therein  to  determine  the  further  fineness  of  the  greater  and 
more  valuable  part  of  the  cement.  To  remedy  this  defect  an  air-analyzer^  has  recently  been 
perfected  at  the  Bureau  of  Standards  which  makes  it  possible  to  further  divide  a  cement  which 
passes  a  200-mesh  sieve  into  four  definite  sizes.  This  apparatus  had  been  standardized  and  will 
undoubtedly  come  into  extensive  use. 

Increased  fineness  has  the  effect  of  making  a  cement  quicker  in  setting  and  hardening, 
the  high-alumina  cements  being  the  most  affected.  Fine  grinding  also  affords  additional 
opportunity  for  seasoning  and  thus  indirectly  improves  the  soundness  of  cement. 

7/.  Normal  Consistency. — Tests  for  time  of  setting,  strength,  and  soundness 
are  greatly  influenced  by  the  quantity  of  water  used  in  mixing.  In  order  to  have  all  results 
comparable  with  one  another,  a  determination  is  made  in  each  case  of  the  quantity  of  water 
necessary  to  be  added  to  a  given  weight  of  cement  to  give  a  standard  or  normal  consistency. 

A  simple  method  of  finding  normal  consistency  is  to  mix  a  quantity  of  cement  paste  and 
make  up  from  the  paste  a  ball  about  2  in.  in  diameter.  The  ball  is  then  dropped  upon  the 
testing  table  from  a  height  of  2  ft.  The  paste  is  of  normal  consistency  when  the  ball  does  not 
crack  and  does  not  flatten  more  than  one-half  of  its  original  diameter.  The  finer  the  cement, 
the  more  water  is  required  for  normal  consistency.  For  this  test  the  room  and  the  mixing 
water  should  be  kept  at  standard  temperature. 

Another  method  of  finding  normal  consistency  which  is  more  commonly  used  and  gives 
more  concordant  results  is  by  the  use  of  the  Vicat  needle  apparatus  (see  Fig.  2,  Appendix  A, 
page  837).    The  manner  of  making  this  test  is  explained  in  Appendix  A,  page  838. 

Ig.  Time  of  Setting. — The  time  of  setting  of  a  cement  may  vary  within  wide 
limits  and  is  no  certain  criterion  of  quality,  but  it  is  important  in  that  it  indicates  whether  or 
not  the  cement  can  be  used  advantageously  in  ordinary  construction.  A  cement  may  set  so 
quickly  that  it  is  worthless  for  use  as  a  building  material  (since  handling  cement  after  it  com- 
mences to  set  weakens  it  and  causes  it  to  disintegrate),  or  it  may  set  so  slowly  that  it  will 
greatly  delay  the  progress  of  the  work. 

Age  of  cement  has  a  great  effect  upon  the  setting  time,  and  tests  should  preferably  be  made 
after  delivery  of  the  cement  on  the  work.  Most  cements  absorb  moisture  from  the  air  and  lose 
some  of  their  hydraulic  property  on  storage.  It  also  occasionally  happens  that  the  gypsum 
added  in  manufacture  loses  its  effectiveness  in  a  short  time,  and  in  consequence  the  cement 
becomes  quick  setting.  The  cause  of  this  loss  of  effectiveness  of  the  gypsum  is  due  usually  to 
the  composition  of  the  cement  and  may  be  remedied  by  increasing  the  lime  content. 

Aside  from  the  consideration  of  age,  the  conditions  which  accelerate  setting  are:  finely 
ground  and  lightly  burned  material;  dry  atmosphere;  small  amount  of  water  used  in  gaging; 
and  high  temperature  of  both  water  and  air.  Since  the  time  of  set  is  influenced  by  so  many 
factors,  tests  should  alwaj'-s  be  made  with  extreme  care  under  standardized  conditions. 

There  are  two  distinct  stages  in  setting:  (1)  the  initial  set;  and  (2)  the  hard  or  final  set. 
The  best  cements  should  be  slow  in  taking  the  initial  set  but  after  that  should  harden  rapidly. 
Portland  cement  should  acquire  the  initial  set  in  not  less  than  45  min.  when  the  Vicat  needle 
is  used  (see  Appendix  A,  page  837),  and  hard  set  in  not  more  than  10  hr.2  The  time  of  initial 
set  is  controlled  largely  by  the  amount  of  sulphate  (gypsum  or  plaster  of  Paris)  which  is  added 
in  making  the  cement. 

A  cement  has  taken  its  initial  set  when  it  will  not  thoroughly  reunite  along  the  nurf  aces  of 
a  break.    It  has  taken  its  final  set  when  it  begins  to  have  appreciable  strength  and  hardness. 

There  are  two  methods  in  common  use  for  finding  the  time  of  setting.  The  method  usually 
preferred  is  by  the  use  of  the  Vicat  needle  apparatus  explained  in  Appendix  A,  page  838.  The 

1  Copies  of  Tech.  Paper  48,  the  publication  upon  this  subject,  may  be  obtained,  free  of  charge,  upon  appli- 
pation  to  the  Bureau  of  Standards,  Washington,  D.  C. 
?  3ee  standard  specifications  in  Appendix  A,  p.  833, 


10 


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[Sec.  l-7h 


other  method  is  by  the  use  of  the  standardized  Gillmore  needles  described  in  Appendix  A, 
page  841. 

7h.  Tensile  Strength. — The  testing  of  cement  in  tension  is  to  obtain  some  meas- 
ure of  the  strength  of  the  material  in  actual  construction.  In  other  words,  tests  of  tensile 
strength  are  made  primarily  to  determine  whether  the  cement  will  be  likely  to  have  a  continued 
and  uniform  hardening  in  the  work,  and  whether  it  will  have  such  strength  when  placed  in 
mortar  or  concrete  that  it  can  be  depended  upon  to  withstand  the  strain  placed  upon  it. 

The  small  shapes  made  for  testing  are  called  briquettes  (see  details  of  standard  test  piece  in 
Appendix  A,  page  842)  and  have  a  minimum  cross-sectional  area  of  1  sq.  in. — that  is,  at  the 
place  where  they  will  break  when  tested.  Standard  mortar  used  in  -testing  is  composed  of  1 
part  cement  to  3  parts  of  standard  sand^  from  Ottawa,  111. 

It  is  customary  to  store  the  briquettes,  immediately  after  making,  in  a  damp  atmosphere 
for  24  hr.  They  are  then  immersed  in  water  until  they  are  tested.  This  is  done  to  secure 
uniformity  of  setting,  and  to  prevent  the  drying  out  too  quickly  of  the  cement,  thereby  prevent- 
ing shrinkage  cracks  which  greatly  reduce  the  strength. 

Specifications  for  tensile  strength  of  cement  usually  stipulate  that  the  material  must  pass  a 
minimum  strength  requirement  at  7  and  28  days.  This  is  required  in  order  to  determine  the 
gain  in  strength  between  different  dates  of  testing  so  that  some  idea  may  be  obtained  of  the 
ultimate  strength  which  the  cement  will  attain.  A  first-class  cement,  when  tested,  should 
give  the  values  for  tensile  strength  stated  in  the  standard  specifications  (see  Appendix  A, 
page  833). 

7^.  Relation  between  Tensile  and  Compressive  Strength. — Since  cements  are 
rarely  depended  upon  to  withstand  tensile  stresses,  the  test  for  tensile  strength  has  undoubtedly 
become  standard  on  account  of  the  popular  belief  that  there  exists  a  more  or  less  definite  and 
constant  relation  between  the  tensile  and  compressive  strengths.  It  can  be  shown,  however, 
that  the  ratio  of  compressive  to  tensile  strength  of  cement  mixtures  is  by  no  means  constant 
at  all  ages  and  varies  greatly  with  different  cements  and  with  different  mixtures.  Thus  the 
tensile  strength  cannot  usually  be  regarded  as  any  more  than  a  very  approximate  indication 
of  the  probable  compressive  strength  of  the  same  cement. 

7j.  Compressive  Strength. — Compressive  strength  of  cement  mortar  is  undoubt- 
edly a  better  criterion  by  which  to  judge  the  suitability  of  a  cement  for  use  in  construction. 
The  American  Society  for  Testing  Materials  has  tentative  specifications  and  methods  of  tests 
for  compressive  strength  of  Portland-cement  mortar  ^  which,  when  adopted  as  standard  by  the 
Society,  will  be  inserted  in  and  made  a  part  of  the  American  Specifications  and  Methods  of 
Tests  for  Portland  Cement.    A  foreign  standard  specification  is  as  follows: 

"Slowly  setting  Portland  cement  shall  show  a  compressive  strength  of  at  least  120  kg.  per 
sq.  cm.  (1710  lb.  per  sq.  in.)  when  tested  with  3  parts  by  weight  of  standard  sand,  after  7  days' 
hardening,  1  day  in  moist  air  and  6  days  under  water;  after  further  hardening  of  21  days  in  the 
air  at  room  temperature  (15°  to  20°C.)  the  compressive  strength  shall  be  at  least  250  kg.  per 
sq.  cm.  (3570  lb.  per  sq.  in.).    In  cases  of  controversies,  only  the  test  after  28  days  is  decisive. 

''Portland  cement  which  is  intended  for  use  under  water  shall  show  a  compressive  strength 
of  at  least  200  kg.  per  sq.  cm.  (2850  lb.  per  sq.  in.)  after  28  days'  hardening,  1  day  in  moist  air 
and  27  days  in  water." 

7k.  Soundness. — A  cement  to  be  of  value  must  be  perfectly  sound;  that  is, 
it  must  remain  constant  in  volume  and  not  swell,  disintegrate,  or  crumble.  Excess  of  either 
lime,  magnesia,  or  sulphates  may  cause  unsoundness.  The  usual  method  of  testing  is  to  form 
a  small  pat  of  neat  cement  about  3  in.  in  diameter,  }i  in.  thick  at  the  center,  and  tapering  to  a 
thin  edge.  This  pat  should  remain  24  hr.  in  moist  air  and  5  hr.  in  an  atmosphere  of  steam  at  a 
temperature  between  98  and  100°C.  upon  a  suitable  support  1  in.  above  boiling  water.  To 
pass  the  soundness  test  satisfactorily,  the  pat  should  remain  firm  and  hard,  and  show  no  signs 

1  See  Appendix  A,  p.  841. 

2  See  Proc.  of  the  Society,  vol.  xvi  (1916),  part  I  (pp.  590-593). 


Sec.  1-7/] 


MATERIALS 


11 


of  cracking,  distortion,  checking  or  disintegration.  The  steam  test  is  what  is  called  an  acceler- 
ated test  and  is  for  the  purpose  of  developing  in  a  short  time  (5  hr.)  those  qualities  which  tend  to 
destroy  the  strength  and  durability  of  a  cement.^ 

7/.  Specific  Gravity. — A  test  for  finding  the  specific  gravity  of  Portland  cement 
was  originally  considered  to  be  of  value  in  detecting  adulteration  and  underburning,  but  is  no 
longer  thought  to  be  of  much  importance  in  view  of  the  fact  that  other  tests  lead  to  niore  definite 
conclusions.  One  trouble  has  been  that  specific  gravity  is  not  alone  lowered  by  the  above 
causes.  Seasoning  of  either  cement  or  cement  clinker,  for  instance,  although  known  to  be 
desirable  and  in  some  cases  absolutely  necessary,  lowers  the  specific  gravity  materially.  On  the 
other  hand,  many  underburned  cements  show  a  specific  gravity  much  higher  than  that  set  by 
standard  specifications.  These  considerations,  together  with  the  fact  that  the  principal  adul- 
terants have  a  specific  gravity  very  near  that  of  Portland  cement,  make  it  difficult  in  the  specific 
gravity  test  to  obtain  results  from  which  accurate  conclusions  can  be  drawn.  The  test  in  any 
case  is  without  value  unless  every  precaution  is  taken  to  have  accurate  results,  as  otherwise 
only  very  large  amounts  of  adulterated  material  could  be  discovered.  When  the  specific 
gravity  of  a  cement  falls  below  3.10,  standard  specifications^  allow  a  second  test  to  be  made 
upon  an  ignited  sample — the  idea  being  that  ignition  will  lower  the  specific  gravity  of  adulter- 
ated cement.  This  second  test,  however,  is  usually  of  little  value  as  the  ignition  loss  of  most 
adulterants  is  low  and  as  the  specific  gravity  of  an  ignited  sample  of  cement  is  invariably  higher 
than  that  of  the  original  sample. 

7m.  Chemical  Analysis. ^ — If  the  tests  of  a  cement  for  time  of  setting,  strength, 
and  soundness  seem  to  indicate  adulteration,  resort  may  be  had  to  chemical  analysis.  Such 
analysis  is  not  usually  made  in  routine  commercial  testing.  Chemical  analysis  not  only  serves 
as  a  valuable  means  of  detecting  adulteration  but  shows  the  amounts  of  magnesia  (MgO)  and 
sulphuric  anhydride  (SO3)  contained  in  the  cement.  Specifications  usually  limit  the  amount  of 
MgO  to  about  5%  and  SO3  to  about  2%  because  of  fear  that  more  of  these  materials  may  make 
the  cement  unsound. 

8.  Specifications  for  Cement. — Standard  specifications  are  given  in  Appendix  A. 

9.  Containers  for  Cement. — Cement  may  be  obtained  in  cloth  or  paper  bags,  in  bulk,  and 
in  barrels. 

Cloth  bags  are  the  containers  most  generally  used  since  manufacturers  will  refund  the 
extra  charge  for  the  bags  when  returned  in  good  condition.  The  consumer,  however,  must 
prepay  the  freight  when  returning  the  empty  bags  to  the  mill.  The  cloth  bag  will  stand  trans- 
portation, and  its  size  and  shape  make  it  convenient  to  handle.  If  properly  cared  for,  it  may  be 
used  over  and  over  again.  Paper  bags  are  more  delicate  and  have  no  return  value.  Wooden 
barrels  are  advisable  when  the  work  is  in  a  damp  location,  as  in  marine  construction.  Bulk 
cement  requires  special  preparations  for  handling  and  storage. 

10.  Storing  of  Cement. — Cement  either  in  containers  or  in  bulk  should  be  stored  within 
a  tight,  weather-proof  building,  at  least  8  in.  away  from  the  ground  and  an  equal  distance  from 
any  wall,  so  that  free  circulation  of  air  may  be  obtained.  In  case  the  floor  of  a  storage  building 
is  laid  directly  above  the  ground,  it  would  be  well  to  give  the  cement  an  additional  8-in.  eleva- 
tion by  means  of  a  false  floor,  so  as  to  insure  ventilation  underneath.  The  cement  should 
further  be  stored  in  such  a  manner  as  to  permit  easy  access  for  proper  inspection  and  identifi- 
cation or  removal  of  each  shipment.  When  cement  is  not  mill-tested,  a  proper  period  before 
cement  is  needed  should  be  allowed  by  the  contractor  for  inspection  and  tests,  this  period  being 
determined  by  the  provisions  of  the  specifications  governing  his  contract. 

Where  cement  in  bags  is  stored  in  high  piles  for  long  periods,  there  is  often  a  shght  tendency 
in  the  lower  layers  to  harden,  caused  by  the  pressure  above;  this  is  known  as  warehouse  set. 

1  The  Lackawanna  Railroad  Co.  requires  that  Portland  cement  used  in  its  structures  shall  remain  sound  after 
being  subjected  to  boiling  under  a  20-atmosphere  pressure.    This  is  called  the  Autoclave  Test. 

2  See  Appendix  A,  p.  833. 

3  For  method  to  be  followed  in  making  a  chemical  analysis,  see  Appendix  A,  p.  834. 


12 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-11 


Cement  in  this  condition  is  in  every  way  fit  for  service  and  can  be  reconditioned  by  letting 
each  sack  drop  on  a  sohd  surface  before  using  the  cement  contained. 

11.  Seasoning  of  Cement. — A  moderate  amount  of  seasoning  in  weather-tight  sheds  often 
improves  the  quahty  of  the  cement.  Fresh  cement  contains  small  amounts  of  free  or  loosely 
combined  lime  which  does  not  slake  freely  and  causes  expansion  after  the  mass  has  set,  endan- 
gering the  structure  in  which  it  is  used.  During  the  time  of  seasoning  such  free  lime  is  changed 
first  to  hydrate  and  then  to  carbonate  of  lime  which  does  not  swell  on  wetting.  Usually  cement 
is  seasoned  at  the  mills  before  shipping,  but,  with  the  best  mills,  the  stock  house  may  run  so 
low  in  periods  of  rush  that  a  chance  will  be  taken  on  fresh  material.  Well-seasoned  cement, 
therefore,  may  be  lumpy,  but  the  lumps  are  easily  broken  up.  If,  however,  the  cement  has 
been  subjected  to  excessive  dampness,  or  has  been  wet,  lumps  will  be  formed  which  are  hard 
and  difficult  to  crush.  A  distinction  should  be  made,  so  that  the  latter  will  not  be  used  with- 
out sifting  and  rejection  of  hardened  portions. 

12.  Use  of  Bulk  Cement. — Within  the  past  few  years  considerable  cement  has  been  shipped 
in  bulk  to  cement-product  factories  and  to  construction  jobs  adjacent  to  railroad  tracks.  Econ- 
omy has,  in  these  instances,  resulted  from  the  saving  in  labor,  and  from  the  elimination  of  pack- 
age losses  and  expense.   There  seems  to  be  no  difficulty  in  shipping  bulk  cement  in  tight  box  cars. 

13.  Weight  of  Cement. — A  barrel  of  Portland  cement  weighs  376  lb.,  not  including  the 
barrel,  and  a  bag  of  Portland  cement  weighs  94  lb.;  in  other  words  there  are  4  bags  to  a  barrel. 

A  barrel  of  natural  cement  varies  in  weight  according  to  the  locality  in  which  it  is  manu- 
factured. A  barrel  of  Western  cement  usually  weighs  265  lb.  and  a  barrel  of  Eastern  cement 
300  lb.    A  bag  of  natural  cement  is  usually  one-third  of  a  barrel. 

A  barrel  of  puzzolan  cement  is  usually  assumed  to  contain  330  lb.  net,  and  there  are  4 
bags  to  the  barrel. 

A  cement  barrel  weighs  about  20  lb.  on  an  average. 

AGGREGATES 

14.  Definitions. — "Aggregates"  is  a  general  classifying  term  applied  to  those  inert  {i.e., 
chemicall}''  inactive)  materials,  both  fine  and  coarse,  which,  when  bound  together  by  cement, 
form  the  substance  known  as  concrete.  Fine  aggregates  are  materials  such  as  natural  sand  or 
rock  screenings.  Coarse,  or  large  aggregates,  or  ballast  are  materials  such  as  natural  gravel, 
crushed  rock,  or  by-product  materials  such  as  cinders  or  crushed  blast-furnace  slag. 

15.  General  Requirements. — Aggregates,  fine  and  coarse,  compose  approximately  90% 
or  more  of  the  substance  of  concrete.  From  this  it  follows  that  the  properties  of  aggregates 
must  correspond  and  be  at  least  equal  to  the  properties  desired  in  the  concrete. 

The  usual  service  requirements  are  that  aggregate  shall  be  dense,  hard,  durable,  structur- 
ally strong  and,  for  aggregates  in  concretes  exposed  to  water  action,  insoluble.  Further,  since 
concrete  is  formed  by  bonding  of  aggregates  with  cement,  they  must  permit  by  their  physical 
characteristics  (such  as  roughness)  the  adhesion  of  cement;  and  always  all  particles  must  be 
clean,  so  that  a  surface  coat  of  one  kind  or  another  may  not  prevent  physical  contact  with  ce- 
ment, or  destroy  its  properties  through  chemical  action. 

16.  Classification  of  Aggregates. — The  usual  classification  of  aggregates  is  into  two  divi- 
sions, based  upon  size. 

Coarse  aggregates  are  all  particles  of  gravel,  crushed  stone,  or  other  materials 
above  3^:4  in.  diameter. 

Fine  aggregates  are  all  particles  below  ^  in.  in  size.  Particles  of  such  size  are 
further  divided  by  defining  "sand"  as  all  mineral  particles  from  2  mm.  to  0.5  mm.  in 
diameter;  "silt,"  all  particles  from  0.5  mm.  to  0.005  mm.  in  diameter;  "clay,"  all  particles 
having  a  diameter  less  than  0.005  mm.;  and  "loam"  as  a  mixture  of  any  of  the  above  finer 
varieties  with  organic  matter — i.e.,  of  vegetable  or  animal  origin.  It  is  particularly  such  organic 
matter  rather  than  size  of  particle  which  renders  loam  unfit  for  concrete  work,  as  through  some 


Sec.  1-17] 


MATERIALS 


13 


chemical  action  not  yet  fully  understood,  possibly  through  formation  of  an  organic  acid,  it  injuros 
or  inhibits  the  proper  action  of  cement. 

17.  Qualities  of  Fine  Aggregates. — General. — When  it  is  remembered  that  the  finer  natural 
materials  are  derived  from  rocks  by  disintegration  and  by  "weathering,"  or  breaking  down 
through  frost  action,  water  and  wind  erosion,  or  kindred  agencies,  the  differences  in  quality 
so  often  found  in  sand  deposits,  with  possibly  the  presence  of  foreign  materials,  are  not  surprising. 
Further,  sands  necessarily  partake  of  the  qualities  of  the  rock  from  which  they  are  derived. 
Silicious  quartz  sands  are  best  for  concrete  work,  but  crushed  sands  from  any  durable  rock  will 
answer,  if  natural  sand  of  proper  quality  cannot  be  obtained. 

18.  Qualities  of  Coarse  Aggregates. — General. — For  coarse  aggregates,  any  crushed  rock  of 
durable  character,  or  any  clean,  hard,  natural  gravel  not  subject  to  ready  disintegration  may 
properly  be  used.  In  general,  the  better  the  stone  or  gravel,  the  better  the  resulting  concrete. 
For  this  reason,  granite,  trap,  or  hard  limestone  are  preferred  for  large  aggregates,  but  any  rock 
will  serve  which  is  sound,  which  has  adequate  strength  and  does  not  contain  objectionable 
mineral  inclusions  liable  to  decompose,  such  as 

iron  pyrites,  FeS2,  which  may  form  sulphuric 
acid  by  oxidation  (see  Fig.  1). 

Since  the  properties  of  any  concrete  are  so 
closely  related  to  the  properties  of  its  compo- 
nents, it  is  essential  to  an  understanding  of  the 
value  of  any  stone  as  an  aggregate  that  something 
be  known  of  the  origin,  nature,  and  properties 
of  the  varieties  in  common  use. 

19.  Materials  Suitable  for  Coarse  Aggre- 
gates.— Roughly,  rocks  suitable  for  use  as  aggre- 
gate fall  into  three  groups.  These  are:  (1)  Gran- 
ite and  other  igneous  rocks;  (2)  sandstones  and 
other  sedimentary  rocks;  (3)  limestones  and  re- 
lated rocks.  A  fourth  division  comprises  slates 
and  shales,  but  as  these  weather  rapidly  with  for- 
mation of  clay,  they  are  unsuited  for  use  in  con- 
crete. 

The  physical  character  of  a  rock  depends 
upon  two  things — its  mineral  constituents  and 
its  structure.  If  the  mineral  constituents  are  themselves  durable,  but  massed  together  in  a 
manner  structurally  weak,  rapid  weathering,  with  formation  of  sand  through  liberation  of 
mineral  grains,  is  to  be  expected.  Such  a  rock  would  make  a  poor  concrete.  On  the  other 
hand,  a  dense  structure  with  like  mineral  constituents  would  make  an  excellent  aggregate. 
A  dense  structure  and  weak  mineral  constituents  are  sometimes  associated,  but  Nature  has 
generally  cared  for  such  rocks  by  bringing  about  their  decomposition,  so  that  they  exist  only  as 
sand. 

20.  Igneous  Rocks. — Igneous  rock  is  a  general  term  descriptive  of  all  rocks  formed  from 
molten  matter  which  has  consolidated  either  into  mineral,  or  glass,  or  both.  Among  such 
rocks  are  granite  and  trap  rock.  Many  classifications  of  a  more-or-less  satisfactory  nature 
have  been  devised;  but  all  sorts  of  gradations  exist  between  the  various  types,  rendering  their 
descriptive  identification  difficult. 

20a.  Granite. — Granite  is  well-known  by  its  characteristic  appearance  (sec 
Fig.  2).  In  structure,  it  is  a  blend  of  quartz  (crystallized  silica  dioxide),  orthoclase,  and  mica, 
though  this  latter  may  be  replaced  by  hornblende.  It  is  exceedingly  dense,  hard,  and  durable, 
consisting  entirely  of  minerals  with  no  glass  or  uncrystallized  material  between  its  constituent 
grains. 

Granites  possess  the  strength  and  durability  desirable  in  an  aggregate,  but  they  are  of  low 


Fig.  1. — Iron  pyrites  (FeSj)  in  concrete  aggregate 
oxidizing  and  destroying  adjacent  matrix.  (Magni- 
fied 40  diams.) 


14 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-206 


toughness.  In  addition,  if  used  in  concretes  exposed  to  more  than  ordinary  heat,  as  in  chimneys, 
there  is  a  decided  tendency  to  disintegrate,  due  to  unequal  mineral  grain  expansions.  Granites 
are  not  often  used  as  aggregate,  their  ornamental  value  precluding  less  profitable  use. 

206.  Trap  Rock  or  Diabase. — Trap  rock  (Fig.  3)  and  fine-grained  basic  and  vol- 
canic rocks  are  generally  hard,  of  high  abrasive  value  adhering  well  to  cement.    These  rocks 


Surface  appearance.  Internal  structure. 

(Natural  size.)  (Magnified  60  diams.) 

Fig.  2. — Granite. 


have  a  closely  interlaced  mineral  structure  and  generally  good  resistance  to  stress.  Care  should 
be  taken  not  to  choose  a  trap  rock  having  a  considerable  percentage  of  iron  present  in  low  oxide 
form,  as  this  may  absorb  oxygen,  forming  a  higher  oxide,  with  expansion  and  probably  rupture. 

In  general,  trap  rock  (and  rock  of  similar  character,  in  which  class  are  included  many  of  the 
''green-stones")  makes  a  very  excellent  aggregate  although  in  some  respects  its  excellence 


Surface  appearance.  Internal  structure. 

(Natural  size.)  (Magnified  60  diams.) 

Fig.  3.— Trap  rock.  ^ 


has  been  exaggerated.  It  has,  however,  a  very  high  compressive  strength  and,  as  this  quality 
is  very  desirable  in  concretes,  its  use  has  become  widespread.  It  is  not  always  procurable 
without  excessive  cost  but,  where  price  is  not  prohibitive,  its  use  is  advantageous. 

21.  Sedimentary  Rocks. — To  the  sedimentary  series  of  rocks  belong  all  those  solidified 
deposits  which  have  accumulated  at  the  bottom  of  bodies  of  water.  Originally,  these  materials 
were  derived  from  the  land  surface  and  transported  to  the  sea  or  lakes,  either  by  mechanical 
carriage,  or  by  solution  in  water.    Many  of  the  minerals  contained  in  sedimentary  rocks  were 


Sec.  l-21a] 


MATERIALS 


15 


derived  directly  from  the  decay  of  igneous  or  volcanic  rocks,  although  additional  chemical 
changes  supplementing  this  more-or-less  complete  decomposition  of  the  original  minerals  may 
have  resulted  in  the  formation  of  new  minerals  found  in  the  sedimentary  series.  With  passage 
of  time  and  the  action  of  various  chemical  and  mechanical  agencies,  these  sedimentary  deposits 
solidified  into  the  stratified  rocks  of  one  kind  or  another  found  throughout  the  entire  surface 
of  the  earth. 

21a.  Sandstone. — One  of  the  most  important  of  the  sedimentary  rocks  is  sand- 
stone (Fig.  4).  In  structure,  it  is  natural  concrete,  composed  of  finely  divided  mineral  parti- 
cles, cemented  together  in  more-or-less  close  relation  by  iron  or  alumina  or  by  calcium  com- 
pounds. The  character  of  any  sandstone  depends,  therefore,  on  the  mineral  character  of  its 
component  grains;  on  the  size  and  shape  of  these  grains;  on  their  arrangement  within  the  rock; 
and  on  the  nature  of  the  material  cementing  them  together. 

Quartz  particles  form  by  far  the  greatest  percentage  and  the  most  desirable  constituent  of 
sandstone.  Feldspar  is  also  frequently  present,  and  occasionally,  hornblende,  chlorite,  garnet, 
magnetite,  and  calcite.    In  the  best  sandstones,  the  grains  are  arranged  uniformly  through  the 


SurfiK  c  appearance.  Internal  structure. 

(Natural  size.)  (Magnified  60  diams.) 

Fig.  4.— Sandstone. 


mass,  although  frequently  coarser  and  finer  particles  are  arranged  in  layers,  giving  a  stratified 
appearance  to  the  stone. 

So  far  as  its  use  in  concrete  is  concerned,  the  most  important  feature  of  a  sandstone  is  the 
nature  of  the  cementing  material  combining  its  constituent  grains.  Argillaceous  sandstones 
in  which  the  cementing  material  is  lime  (usually  lime  carbonate)  may  be  crushed  with  compara- 
tive ease,  but  they  disintegrate  rapidly  on  exposure  to  weathering  agents,  such  as  water  or  air. 
Such  stone  may  be  readily  identified  by  its  effervescence  when  treated  with  a  drop  of  hydro- 
chloric acid.  Sandstones  cemented  by  oxide  of  iron  are  generally  red  in  color,  the  shade  being  a 
rough  indication  of  the  amount  of  iron  present.  Many  of  these  sandstones  disintegrate  very 
rapidly  on  exposure  to  the  weather,  forming  the  so-called  ''rotten  stones"  so  often  found  in 
gravel. 

Sandstones  cemented  solely  by  clay  should  never  be  used  in  concrete,  as  the  simple  pene- 
tration of  moisture  is  sufficient  to  disintegrate  them,  rendering  them  practically  valueless  as 
aggregate.  A  good  accelerated  test  is  to  boil  }i-m.  fragments  of  the  stone  in  water.  Rapid 
disintegration  indicates  a  weak  stone,  with  a  tendency  to  weather  rapidly,  and  unsuited  for  use 
as  aggregate. 

216.  Limestone. — ^Limestone  is  carbonate  of  Ume  deposited  on  the  floors  of 
bodies  of  water  and  subsequently  hardened  into  rock.  This  precipitation  of  lime  may  have 
been  effected  from  the  water,  or  through  the  agency  of  animal  or  vegetable  life.    That  is  to  say, 


16  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  1-22 

some  limestones  are  chemical  precipitates,  while  others  are  formed  from  the  shells  and  other 
hard  parts  of  animals,  as  well  as  from  hardened  tissues  of  certain  plants.  Such  plant  and  animal 
forms  fossilized  are  often  seen  in  limestone  fragments  (see  Fig.  10,  page  19). 

Compact  limestone  (Fig.  5)  varies  in  texture  from  coarse  to  exceedingly  fine.  (It  is  prac- 
tically impossible  to  obtain  a  good  photograph  of  the  surface  of  limestone  on  account  of  its 
dark  color  and  uniform  texture.)  It  is  only  occasionally  pure  carbonate  of  lime,  usually  contain- 
ing greater  or  less  percentages  of  magnesia.  Either  magnesian  limestone,  or  pure  calcic  lime- 
stone is  very  well  suited  for  use  as  a  concrete  aggregate.  Any  considerable  percentage  of  clay 
in  limestone,  however,  is  very  undesirable,  as  it  softens  the  rock  and  renders  it  very  liable  to 
disintegration.  Limestone  is  found  in  many  colors.  White,  gray,  yellow,  blue,  and  green  are 
those  of  most  frequent  occurrence. 

In  general,  limestone  makes  a  very  good  coarse  aggregate  for  concrete.  When  crushed  to 
the  finer  sizes,  it  has  a  flaky  fracture  which  renders  it  somewhat  unsuitable  for  use  as  sand  unless 
it  is  rerolled.    Natural  limestone  sands  are  of  infrequent  occurrence,  as  limestone  is  soluble 

to  as  high  a  percentage  as  90%,  so  that  the  usual 
weathering  processes  result  in  solution,  rather  than 
fragmentary  disintegration. 

22.  Metamorphic  Rocks. — Rocks  of  either  igneous 
or  sedimentary  origin  have  often  been  subjected  to 
such  severe  treatment  in  the  long  course  of  geologic 
history,  that  their  ordinary  character  is  much  altered. 
Crushing  of  the  earth's  crust,  the  weight  of  overlying 
material,  and  contact  with  hot  molten  rock  from  the 
interior  are  among  the  causes  contributing  to  the 
change.    Such  rocks  are  classed  as  ''metamorphic." 

There  are  many  metamorphic  rocks,  the  whole 
group  constituting  a  very  high  percentage  of  the  sur- 
face of  the  earth's  crust.  Some  of  them  are  of  value 
as  aggregates  in  concrete;  while  others,  notably  the 
slates  and  shales,  have  a  weak  stratified  structure 
and  weather  so  rapidly  that  their  value  in  concrete  is 
almost  nothing. 

The  above  classification  gives  a  general  indica- 
FiG.  5.—  Internal  structure  of  limestone.       ^ion  of  those  rocks  which  when  crushed  are  of  value 
(Magnified  20  diams.)  as  Concrete  aggregates.    The  first  caution  to  be  ob- 

served in  selecting  them  is  to  be  sure  that  they  do  not 
contain  objectionable  impurities  in  their  substance;  and  the  second  important  caution  is  to  be 
sure  they  are  clean. 

23.  Gravel. — Gravel  of  good  quality  (Fig.  6)  makes  excellent  concrete  (see  Tech.  Paper  58, 
Bureau  of  Standards,  Washington,  D.  C).  Gravel  is  nothing  more  nor  less  than  natural  rock, 
broken  away  from  parent  ledges  and  worn  round  by  the  rolling  of  streams.  Its  natural  proper- 
ties, therefore,  are  identical  with  the  rock  of  which  it  once  formed  a  part.  Provided  it  has  not 
decayed  through  being  in  relatively  small  masses,  the  properties  natural  to  this  parent  rock 
are  to  be  expected  of  a  gravel.  The  surface  of  gravel  is  usually  very  rough;  and  from  consider- 
ations of  character  of  surface  presented  for  adhesion  of  cement,  it  should  produce  as  good  as,  and 
even  better,  concrete  than  crushed  stone.  Certainly,  there  is  no  reason  against  its  use,  provided 
it  is  clean  and  of  good  mineral  quality. 

It  is  desired  to  emphasize  in  this  connection  that  not  the  least  important  of  all  the  qualities 
of  stone  or  gravel  is  its  cleanness.  The  percentage  of  concretes  in  which  cement  and  aggregates 
have  little  or  no  adhesion  due  to  a  coating  of  dirt  (a  coating  of  "matter  out-of-place")  is  sur- 
prisingly large;  and  the  careless  acquiescence  of  engineers  in  the  use  of  such  materials  is  result- 
ing in  a  general  inferiority  of  concrete  structures.    ''Dirt"  in  such  cases  may  be  visible  (as 


Sec.  1-24] 


MATERIALS 


17 


Fig.  6. — Enlarged  surface  of  piece  of 
gravel,  showing  roughness.  (Magnified 
5  diams.) 


when  the  coating  is  clay,  or  of  tenacious  dust  due  to  crushing)  or  it  may  be  quite  invisible  (such 
as  a  coating  of  colloidal,  transparent,  organic  matter)  requiring  chemical  procedure  for  its 
detection.  A  coating  of  any  character  is  not  to  be  disregarded,  when  first-quality  concretes 
are  desired.  At  best  it  is  a  detriment  and  oftentimes  proves  a  serious  defect,  greatly  weakening 
the  concrete. 

24.  Blast-furnace  Slag. — Slag  from  blast  furnaces,  crushed  to  proper  size,  has  much  to 
recommend  it  for  mass  construction.  Slag  is  a  hard  though  very  porous  material,  of  high 
compressive  strength;  and  in  certain  localities  is  relatively 

cheap  as  compared  to  stone  of  good  qualities.  Offering 
a  rough,  pitted  surface  for  the  adhesion  of  cement,  it 
produces  a  very  strong  concrete,  but  care  should  be  taken 
that  its  sulphur  content  is  low,  else  passage  of  time  may 
bring  about  disintegration  of  the  concrete.  Some  steel 
companies  exercise  great  care  in  the  preparation  of  slag 
for  aggregate,  weathering  it  in  thin  layers  for  2  or  3  ^''ears 
before  marketing,  but  the  advisability  of  its  use  in  con- 
cretes exposed  to  dampness  and  especially  in  thin  sec- 
tions is  yet  in  controversy  (see  Proc.  Am.  Soc.  Test 
Mat.,  1913). 

25.  Cinders. — Furnace  cinders  as  an  aggregate  are 
used  only  in  inferior  grades  of  mass  concrete,  or  for 
fireproofing.  Cinders  have  low  structural  strength,  high 
porosity,  and  oftentimes  as  an  added  objection,  high  sul- 
phur content.  In  more  than  one  instance,  sulphuric  acid 
resulting  from  sulphur  decomposition  in  cinder  concrete 

floors  has  eaten  away  conduits  and  piping,  and  has  even  attacked  reinforcing  and  structural 
steel.  Cinder  concrete  is  of  value  chiefly  because  of  its  cheapness  and  low^  specific  gravity, 
but  discrimination  is  required  in  its  use. 

26.  Materials  Suitable  for  Fine  Aggregates. — All  fine  aggregates  are  essentially  rock 
fragments,  crushed  to  varying  degrees  of  fineness,  either  by  the  natural  processes  of  weathering, 
disintegration,  or  glacial  action,  or  by  man  with  his  machines.    Sand  deposits  are  masses  of 

weathered  rock  minerals,  transported,  collected,  and 
sorted  by  the  age-long  action  of  streams  (see  Fig.  7) . 

From  the  earliest  ages  the  formation  of  sand, 
silt,  and  clay  has  been  going  on  through  the  break- 
ing down  of  rocks.  The  changes  involved  in  these 
processes  are  part  physical  and  part  chemical.  All 
changes  produced  at  or  near  the  surface  by  atmos- 
pheric agents,  which  result  in  more  or  less  complete 
disintegration  and  decomposition,  are  classed  under 
the  general  term  of  ''weathering."  The  action  of 
physical  agents  alone,  which  results  in  the  rock  break- 
ing down  into  smaller  particles  without  destroying 
its  identity,  is  termed  "disintegration"  (see  Fig.  8). 
On  the  other  hand,  the  action  of  chemical  agents  de- 
stroys the  identity  of  many  of  the  minerals  by  the 
formation  of  new  compounds,  and  this  latter  process  is  known  as  "decomposition."  Silt 
and  clay  generally  result  from  decomposition;  and,  as  such  chemical  change  has  altered  the 
character  of  the  material  (usually  to  its  detriment  so  far  as  concrete  purposes  are  concerned), 
that  is  one  reason,  but  not  the  only  reason,  against  permitting  their  presence  in  concrete  sand. 

Since  coarse  sands  are  of  a  size  to  retain  and  partake  of  the  nature  and  properties  of  the 
parent  rock,  the  structure  of  at  least  larger  particles  should  be  identical  with  the  structures  of 
1  From  "Engineering  Geology,"  by  Ries  and  Watson. 
2 


Fig.  7. — Concretionary   sandstone  weathering 
to  form  sand.i 


18 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  l-26a 


Fig.  8. — Shale  deposit  lying  be- 
tween hard  sandstone  ledges,  disin- 
tegrating with  formation  of  clay. 


such  rocks;  and  their  strength  and  fitness  for  use  in  concrete  may  be  judged  with  more  or  less 
accuracy  from  a  consideration  of  the  structure  and  strength  of  those  rocks  known  to  be  suitable 
for  concrete  work.  There  are  few  rocks  which  do  not  contain  silica  in  greater  or  lesser 
quantities. 

Because  of  its  hardness  and  resistance  to  chemical  agents,  quartz  or  silica  is,  therefore,  the 
commonest  mineral  in  sand.    Qther  minerals  such  as  feldspar,  mica,  etc.,  though  originally 
present,  because  of  their  lesser  resistance,  have  been  more  readily  decomposed  by  the  action 
of  the  elements;  and  by  reason  of  their  complete  disintegration  with  resultant  fine  state  of  sub- 
division, have  been  removed  by  wind  and  water.    Quartz  crys- 
tals, therefore,  remain  as  the  most  evident  survivors  of  the 
parent  rock  and  their  survival  is  evidence  of  their  desirable 
qualities  for  concrete. 

26a.  Special  Characteristics  of  Sand. — A  simple 
and  illustrative  example  of  a  rock  from  which  quartz  sand  may 
be  derived  is  sandstone.  This  stone  is  built  up  almost  wholly 
of  quartz  grains,  cemented  together  by  iron  oxide,  calcium  car- 
bonate, or  clay,  and  on  the  nature  of  the  cementing  material 
depends  the  strength  and  hardness  of  the  stone.  The  struc- 
ture of  a  hard  sandstone  is  shown  in  Fig.  9.  In  this  stone  the 
cementing  material  is  iron  oxide. 
Under  certain  conditions  of  use  a  fragment  of  sandstone,  such  as  would  be  represented  by  a 
large  sand  grain,  might  be  unfit  as  a  material  for  concrete.  Such  a  condition  would  be  repre- 
sented by  subjecting  concrete  containing  such  sand  to  extreme  of  heat,  as  in  a  fire.  Under 
like  conditions  it  would  be  expected  that  a  large  fragment  of  the  same  stone  would  break  up,  or 
spall,"  and  it  is  actually  found  that  some  sand  grains  repeat  in  miniature  the  behavior  of  the 
larger  pieces  of  stone.  Such  a  condition  of  heat  is,  of  course,  unusual  and  extreme,  and  would 
not  prejudice  the  use  of  such  sand  for  most  purposes. 

If  the  cementing  material  of  a  sandstone  sand  grain  be  calcium  carbonate,  it  may  be  dis- 
solved by  natural  water,  since  such  waters  contain  an  ap- 
preciable percentage  of  carbon  dioxide,  or  carbonic-acid  gas. 
Such  a  sand,  therefore,  would  be  unsuited  for  use  in  a  water- 
storage  reservoir,  or  in  drainage  tile,  or  in  aqueducts  of  any 
kind,  or  in  other  constructions  which  are  designed  to  be  im- 
ipermeable  to  water.  Fortunately,  this  calcium-carbonate 
cement  in  sand  is  easy  of  detection  by  adding  a  drop  of 
muriatic  acid  and  noting  effervescence,  or  the  lack  of  it. 

Clay  cement  in  a  sandstone  is  quite  undesirable.  It 
is  frequently  the  case  that  a  sand  thought  to  be  quite  per- 
fect for  use  in  concrete,  by  reason  of  its  whiteness  and  good 
grading  in  size,  is  in  reality  quite  dangerous.  Clay  is  not  a 
strong  cement,  and  a  sand  of  which  the  particles  are  built 
up  with  this  cementing  material  is  readily  crushed.  This 
is  especially  true  in  concrete,  for  the  clay  readily  absorbs 
water  and  becomes  a  soft  paste,  leaving  the  component 

sand  grains  loose  and  without  contact  with  the  Portland  cement  save  at  the  outer  surface  of  the 
outside  particles.  This,  of  course,  weakens  the  concrete  seriously  if  all  the  sand  is  of  this  same 
general  character. 

Not  all  sands,  however,  are  composed  of  mineral  grains,  as  are  those  previously  mentioned. 
It  is  not  infrequently  the  case  that  the  rock  from  which  they  came  has  been  formed  by  the 
fossilizing,  or  partial  fossilizing,  of  minute  prehistoric  shells.  A  section  of  limestone,  built  up 
in  this  way,  is  shown  in  Fig.  10.  Other  rocks  contain  like  fossil  materials  in  combination  with 
quartz  grains  and  cementing  material,  as  in  fossiliferous  sandstone.    In  many  sands  derived 


Fig.  9. — Hard  sandstone.  Quartz 
grains  cemented  by  iron  oxide.  (Nat- 
ural size.) 


Sec.  1-266] 


MATERIALS 


19 


from  such  rocks  the  structure  of  the  shell  is  so  perfectly  preserved  that  the  fossils  retain 
their  hollow  struf ture  and,  further,  are  easily  decomposed  by  agents  which  either  reach  them 
before  their  incorporation  in  the  concrete,  or  afterward,  by  dissolving  out  the  softer  portions. 
The  use  of  such  a  sand,  therefore,  is  not  advisable  in  concrete  which  is  intended  to  be  impervious 
to  water,  or  to  possess  a  high  strength. 

26b.  Crushed  Stone  and  Screenings. — Crushed  stone  screenings,  when  free 
from  clay,  usually  make  excellent  sand.  These  screenings  ordinarily  give  a  stronger  mortar 
than  natural  sand  but  are  likely  to  contain  an  undue  amount  of  dust,  especially  when  obtained 
from  soft  stone,  and  should  be  screened  and  washed  to  get  rid  of  the  finest  particles  before  being 
used  in  mortar  or  concrete. 

Crushed  limestone  makes  a  concrete  of  excellent  early  strength,  provided  the  crushings  are 
rerolled,  as  limestone  breaks  with  a  flat,  scaly  fracture,  giving  particles  that  are  structurally 
weak  and  that  are  very  hard  to  compact  in  the  manner  necessary  to 
give  an  impervious  concrete.  For  work  exposed  to  water  this 
point  is  of  great  importance.  Furthermore,  if  there  is  porosity  in 
such  concretes,  the  high  solubility  of  the  limestone  fragments  in 
water  is  a  further  disadvantage.  In  such  cases,  percolation  pro- 
ceeds at  an  increasing  rate  with  passage  of  time,  due  to  bodily 
removal  of  the  fine  aggregate  by  solution,  leaving  a  honeycomb 
structure  behind. 

26c.  Sea  Sand. — Sea  sand  is  usually  well  suited 
for  use  as  fine  aggregate  for  concrete,  so  far  as  structure,  mineral 
composition,  and  cleanness  are  concerned.  It  is,  however,  usually 
of  such  fineness  that  its  use  is  inadvisable  if  undiluted  by  coarser 

J.' Hi,   X' UBOii-uceinufi,  lime- 

particles.  Saline  deposits  on  the  grains,  when  derived  from  pure  stone.  (Magnified  20  diams.) 
sea  water,  should  not  be  of  a  nature  detrimental  to  concrete.  It 

is  unwise  to  take  such  sands  close  to  tide  limits,  as  the  newer  sands  close  to  water,  teem 
with  minute  organic  life. 

2Qd.  Standard  Sand. — The  standard  sand  used  in  tests  of  mortars  is  a  natural 
sand  obtained  at  Ottawa,  111.,  passing  a  screen  having  20  meshes  and  retained  on  a  screen  having 
30  meshes  per  lin.  in.,  prepared  and  furnished  by  the  Ottawa  Silica  Co.  at  a  cost  of  2  cts.  per 
lb.,  f.o.b.  cars,  Ottawa,  111.  The  grains  of  this  sand  are  rounded  and  readily  compacted,  the 
percentage  of  voids  being  about  37%. 

It  is  to  be  noted  that  standard  sand  gives  about  the  lowest  value  attainable  with  sand  in 
combination  with  cement,  because  of  its  uniform  size  of  grain.  Yet  the  present  acceptance 
tests  for  a  commercial  sand  provide  only  that  it  shall  in  like  combination  with  a  like  cement, 
attain  not  less  than  75%  of  the  strength  of  the  lowest  value  obtainable.  This  standard  is 
decidedly  low  and  permits  the  use  of  almost  any  sand,  even  one  of  poor  quality. 

27.  Requirements  of  Fine  Aggregate  as  to  Shape  and  Size  of  Particles. — It  is  exceedingly 
difficult  in  choosing  a  fine  aggregate  for  concrete  work  to  balance  all  considerations.  Time  is  a 
factor  of  utmost  importance  in  all  construction  operations.  Therefore,  where  delays  would 
be  entailed  by  the  selection  of  one  sand,  the  qualities  of  which  are  superior  to  those  of  another 
sand  that  is  more  readily  obtained,  it  is  more  than  probable  that  considerations  of  superior 
quahty  will  have  little  weight.  It  is  unfortunately  true  that  regardless  of  all  that  has  become 
known  in  regard  to  the  importance  of  sands,  their  quality  will  be  generally  disregarded  in  favor 
of  cheapness  or  convenience  until  engineers  and  owners  demand  and  insist  upon  concretes  of 
proper  quality  and  refuse  payment  for  those  not  coming  up  to  standard.  When  inferior  materials 
at  a  less  price  are  as  readily  marketable  when  incorporated  in  concrete  as  first-grade  materials, 
the  contractor,  as  vendor,  is  not  to  be  censured  if  he  realizes  every  opportunity  afforded  him 
to  reahze  the  largest  possible  profit.    The  buyer  and  his  agents  receive  only  what  they  demand. 

Usual  specifications  for  concrete  sands  permit  of  little  discrimination  on  the  part  of  the 
supervising  engineer,  however  conscientious  he  may  be.    Provision  that  the  sand  shall  be  "clean^ 


20 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-28 


sharp  and  coarse"  means  nothing,  as  no  standards  are  defined  as  comparisons  and  the  deter- 
mination is  left  solely  to  the  judgment  of  individuals  oftentimes  quite  incompetent  and  unskilled. 

Sharpness  as  a  quality  requirement  for  sand  is  archaic.  It  has  little  or  no  definite  meaning; 
and  rarely  are  two  individuals  agreed  as  to  how  sharpness  should  be  determined.  To  some  it 
defines  the  sound  given  off  when  sand  is  rubbed  in  the  hand.  To  others,  it  is  measured  by  abra- 
sive quality,  determined  in  the  same  way.  To  others,  it  indicates  a  certain  angularity  judged 
solely  by  the  eye.  If  it  were  but  remembered  that  all  natural  sands  are  water-borne  and  water- 
worn,  with  inevitable  rounding  of  grains,  the  fallacy  of  "sharpness,"  whatever  its  interpretation, 
as  a  standard  of  quality  in  natural  sands,  would  be  evident. 

Cleanness  in  sands  is  most  important,  for  reasons  before  given.  Not  all  dirt  coatings  on  sand 
are  detectable,  short  of  laboratory  procedures;  and  unfortunately,  much  sand  is  judged  as  to 
cleanliness  by  rubbing  in  a  hand  that  itself  is  usually  none  too  clean,  the  fitness  of  the  sand  being 
judged  by  the  deposit  it  leaves  behind.  Judging  a  sand  in  this  way  without  supplemental 
tests  betokens  ignorance,  or  carelessness,  or  both.  Cleanness  is  an  imperative  necessity,  but 
it  should  be  judged  by  adequate  tests,  not  by  such  haphazard  methods  as  the  foregoing. 

Coarseness  in  sands,  as  opposed  to  excessive  fineness,  is  a  desirable  quality,  but  coarseness 
alone,  without  finer  materials  and  especially  when  judged  without  standards,  is  no  criterion 
of  fitness  for  use  in  concrete.  As  before  pointed  out,  coarse  sands  have  less  surface  area  than 
have  fine  sands,  requiring  less  cement  and  being  more  readily  coated.  Such  a,  requirement, 
if  properly  judged,  is  therefore  advantageous.  As  an  insurance  against  excessive  clay  or  loam, 
the  requirement  of  coarseness  may  also  be  of  benefit. 

What  really  is  needed  is:  (1)  a  general  and  thorough  understanding  by  engineers  and 
contractors  alike  as  to  the  fundamental  relations  existing  between  the  various  materials  forming 
concrete  (see  chapter  on  ''Proportioning"  in  Sect.  2);  (2)  an  appreciation  of  the  importance 
of  sands  in  the  production  of  good  concrete;  (3)  their  selection  on  a  basis  of  quality;  and  (4)  to 
make  the  foregoing  of  value,  a  rigid  insistence  upon  conformity  to  standard  by  tests  of  each 
shipment  made  to  the  job  with  ruthless  rejections  of  inferior  materials.  A  single  test  on  a 
sample  which  may  or  may  not  be  representative  of  the  bulk  of  material  is  of  no  value  whatever, 
unless  it  is  supplemented  by  comparative  tests  on  the  materials  actually  delivered. 

28.  The  Selection  of  Sand. — The  only  logical  procedure  in  the  selection  of  a  sand  for  con- 
crete is: 

1.  Determine  its  granulometric  analysis  by  screening. 

2.  Determine  its  cleanness  by  washing,  or  by  chemical  tests. 

3.  Determine  its  actual  strength  value  in  concrete  by  test. 

4.  Check  all  shipments  for  cleanness  and  uniformity  of  grading. 

29.  Requirements  of  Coarse  Aggregate  as  to  Shape  and  Size  of  Particles. — Since  stone  is 
one  of  the  strongest,  if  not  the  strongest  constituent  of  concrete,  the  greater  the  percentage  of 
stone  {i.e.,  the  nearer  concrete  actually  approaches  natural  stone  in  strength  and  density)  the 
stronger  is  the  concrete.  It  follows,  then,  other  things  being  equal,  that  the  larger  the  stone, 
the  stronger  will  be  the  concrete,  since  each  piece  of  stone  has  greater  mass  density  than  would 
its  components  unless  compacted  and  united  by  Nature's  unapproachable  processes. 

There  are,  however,  certain  limitations  as  to  size  of  stone  imposed  by  certain  classes  of  work. 
In  reinforced  work,  the  plastic  concrete  must  fit  itself  closely  around  the  reinforcing  metal,  so 
that  1  to  in.  is  the  greatest  diameter  of  particle  that  experience  demonstrates  is  advisable 
to  use. 

Concrete  of  this  character  obviously  requires  more  cement  than  would  concrete  using 
larger  stone,  since  the  stone  surface  to  be  coated  is  greater.  In  mass  work,  on  the  other  hand, 
crushed  stone  of  23-^  to  3  in.  diameter  may  be  advantageously  employed,  with  less  cement. 
For  these  reasons,  if  for  no  others,  richer  mixtures  are  specified  in  reinforced  work  and  leaner 
mixtures  in  mass  work.  It  should  be  borne  in  mind,  however,  that  size  of  stone  is  not  alone  the 
determining  factor  in  this  regard,  but  that  grading  of  stone  and  size  and  grading  of  sand  is  of 


Sec.  1-30] 


MATERIALS 


21 


even  more  importance  as  influencing  the  quantity  of  cement  required,  with  a  corresponding 
effect  on  the  quaUty  of  concrete. 

Plums  are  large  stone,  5  in.  or  more  in  least  diameter,  thrown  into  plastic  mass  concrete, 
largely  with  the  object  of  using  them  as  cheap  space-fillers.  Their  use  is  also  to  be  commended 
for  the  reasons  before  given,  provided  that  the  plums  themselves  are  of  the  proper  quality  of 
stone  and  that  they  are  not  of  such  size  as  to  cut  through  the  concrete  section.  A  safe  rule  to 
follow  in  the  use  of  plums  is  that  they  shall  be  of  a  maximum  size  such  that  not  less  than  6 
in.  of  concrete  shall  intervene  between  them  and  the  forms  at  any  point.  In  using  very  large 
plums,  this  thickness  of  intervening  concrete  should  be  materially  increased. 

The  shape  of  particle  of  large  aggregates  is  of  relatively  little  importance.  Cleanliness, 
grading,  and  character  of  rock  have  far  greater  influence  on  the  concrete  than  has  angularity  or 
roundness  of  particle. 

30.  Impurities  in  Aggregates. — In  order  that  cement  may  adhere  to  sand  grains  and  to 
particles  of  coarse  aggregate,  each  grain  or  particle  must  bear  no  coating  such  as  would  prevent 
either  proper  chemical  action  between  cement  and  water,  or  a  proper  bond  between  cement 
and  aggregates. 

This  requirement  applies  to  both  fine  and  coarse  aggregates,  but  is  of  relatively  more  impor- 
tance with  respect  to  the  former,  as  sand  in  its  natural  state  and  as  used  in  ordinary  concrete 
construction  is  more  likely  to  contain  dirt  in  sufficient  amount  and  of  such  kind  to  cause  appreci- 
able injury  than  is  coarse  aggregate. 

Clay  and  silt  are  impurities  of  most  frequent  occurrence  in  sand  and  gravel.  These  mate- 
rials are  the  result  of  decomposition  of  natural  rock  of  various  kinds  and  it  is  almost  inevitable 
that  they  should  be  associated  with  sand. 

Each  of  these  impurities  causes  injury  to  mortar  or  concrete  not  only  when  it  exists  as  a 
coating  on  the  sand  or  gravel  particles,  but  is  equally  undesirable  when  it  occurs  in  such 
amounts,  or  so  unequally  distributed,  that  its  extremely  fine  grains  ''ball  up"  and  stick  together 
when  wetted,  so  as  to  remain  in  lumps  in  the  finished  mortar  or  concrete.  If,  however,  the  par- 
ticles of  these  impurities  are  distributed  so  that  they  do  not  bind  together  on  the  addition  of 
water;  and  if  they  are  not  contaminated  by  organic  matter,  experiments  have  shown  that  with 
sand  that  is  not  too  fine,  no  serious  harm  results  in  lean  mortars  and  concretes  from  their  pres- 
ence to  the  extent  of  from  10  to  15%.  In  fact,  either  clay  or  silt  are  often  found  beneficial  as 
they  increase  the  density  by  filling  some  of  the  voids,  thus  increasing  the  strength  and  water- 
tightness  besides  making  the  mortar  or  concrete  work  smoothly.  In  rich  mortars  and  con- 
cretes the  density  and  consequently  the  strength  is  lowered  by  even  slight  additions  of  clay  or 
silt  as  the  cement  furnishes  all  the  fine  material  that  is  required. 

A  coating  of  organic  matter  on  sand  grains,  such  as  loam,  appears  not  only  to  prevent  the 
cement  from  adhering  but  also  to  affect  it  chemically.  In  some  cases  a  quantity  of  organic 
matter  so  small  that  it  cannot  be  detected  by  the  eye  and  is  only  sHghtly  disclosed  by  chemical 
tests  has  prevented  the  mortar  or  concrete  from  reaching  any  appreciable  strength.'-  Tannic 
acid,  colloidal  sewage,  manure,  sugar,  tobacco  juice  are  instances  of  organic  contamination 
destructive  to  concrete. 

Mica  in  sand  or  stone  is  objectionable  because  of  its  low  mechanical  strength  and  its  lami- 
nated scaly  structure.  Even  a  small  amount  of  this  impurity  in  sand  may  seriously  reduce  the 
strength  of  a  mortar  or  concrete.  Mica  is  especially  injurious  in  sands  for  concrete  surface 
work  as  the  scaly  flakes  cause  the  surface  to  dust  and  peel. 

Furthermore,  it  is  to  be  noted  that  water  does  not  wet  the  surface  of  mica.  Necessarily, 
this  precludes  attachment  of  cement,  so  that  not  only  is  the  material  weak  of  itself,  but  it  lies 
in  the  mass  without  attachment,  inviting  disintegration. 

Mica  schist  is  totally  unfit  for  use  as  large  aggregate,  both  because  of  the  foregoing  reasons 
and  also  because  of  its  rapid  decomposition  on  exposure  to  air. 

1  A  new  process  for  the  detection  of  such  coatings  is  being  developed  under  the  auspices  of  Committee  C-9 
of  the  A.S.T.M.,  at  Lewis  Institute,  Chicago,  111.  by  Prof.  Abrams  and  Dr.  Harder.    See  footnote  on  p.  29, 


22 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-31 


Mica  above  1  %  in  concrete  sands  is  very  objectionable. 

Iron  'pyrites  or  fooVs  gold — a  bright,  yellow  substance  with  metallic  luster — is  chemically 
iron  sulphide  (Fe2S).  This  is  a  very  common  impurity  in  stone;  and  its  undesirability  lies  in  its 
ready  oxidation  in  the  presence  of  water  with  formation  of  sulphuric  acid  (H2SO4),  which  latter 
readily  attacks  the  cement  of  concrete  with  disastrous  consequences  (see  Fig.  1,  page  13). 

In  large  fragments  of  stone,  as  in  coarse  aggregate,  the  presence  of  a  small  amount  of  this 
substance  is  not  objectionable,  but  when  fine  aggregates  are  made  from  this  same  rock,  the  py- 
rites previously  isolated  are  exposed,  with  resultant  increase  in  quantity  and  rate  of  oxidation 
and  with  corresponding  formation  of  acid. 

Some  sand  deposits  also  contain  unoxidized  iron  sulphide,  though  such  deposits  are  an 
exception. 

Finely  powdered  dust  present  in  crushed  stone  screenings  causes  approximately  the  same 
effect  upon  the  strength  of  mortar  or  concrete  as  does  the  presence  of  silt  or  clay  in  like  quanti- 
ties. It  is  essential  for  the  best  work  that  this  dust  be  removed  by  screening  and  washing, 
in  the  same  manner  that  silt  is  removed  from  sand  and  gravel,  though  it  may  later  be  used 
advantageously  in  known  quantities  by  recombination. 

31.  Size  and  Gradation  of  Aggregate  Particles. — The  weakest  and  most  changeable  element 
in  any  cement  (plus  water)-sand-stone  combination  is  the  cement  matrix  in  which  the  aggre- 
gates are  embedded.  The  strongest  and  least  changeable  elements  are  the  sand  and  stone. 
It  follows,  therefore,  that  strong,  enduring  concrete  should  contain  as  large  a  percentage  as 
possible  of  aggregates  consistent  with  proper  embedment  and  cohesion,  together  with  requisite 
plasticity  to  permit  ready  placing  in  forms.  This  conclusion  also  is  true  from  an  economic 
point  of  view,  since  sand  and  stone  are  much  cheaper,  bulk  for  bulk,  than  cement. 

Further,  tests  of  concrete  show  that,  with  the  same  percentage  of  cement  to  a  unit  volume 
of  concrete,  that  mixture  which  gives  the  smallest  volume  and  has,  therefore,  the  greatest  den- 
sity,^ usually  produces  the  strongest  and  most  impermeable  concrete.  This  rule,  it  should  be 
said,  does  not  strictly  apply  to  water-tightness,  as  permeability  is  influenced  by  size  of  voids 
as  well  as  density. 

31a.  Grading  of  Mixtures. — Other  things  being  equal,  the  best  aggregates,  fine 
and  coarse,  for  use  in  concrete  are  those  which  are  so  graded  in  sizes  of  particles  that  the  per- 
centage of  voids,  or  hollow  spaces,  in  the  resulting  concrete  is  reduced  to  a  minimum.  The  same 
law  applies  also  to  mortar  mixtures,  so  that  if  concrete  is  considered  as  a  quantity  of  relatively 
large  stone  set  in  a  pudding,  or  bedding  of  mortar,  the  best  sand  as  to  size  is  one  which,  if  mixed 
with  the  given  cement  in  the  required  proportions  to  standard  consistency,  yviU  produce  the 
smallest  volume  of  mortar;  and  the  best  concrete  will  be  one  in  which  the  particles  of  stone  are 
so  graded  as  to  permit  in  a  given  volume  a  maximum  quantity  of  stone  being  bedded  in  such 
a  mortar.  2 

316.  Grading,  Density,  and  Strength. — It  has  been  found  that  the  densest  mix- 
ture occurs  with  particles  of  graded  sizes;  and  also  that  the  least  density  occurs  when  the  grains 
are  all  of  the  same  size.  Coarse  sands,  or  fine  sands  alone  are  thus  inferior  to  graded  sands  for 
concrete,  but  of  the  two  extremes  the  coarse  sand  is  preferable  because  its  particles  are  more 
readily  coated  with  cement  particles.  Further,  a  coarse  sand  has  a  less  total  grain  surface  in 
a  unit  volume  than  a  fine  sand,  even  when  the  sands  considered  contain  the  same  proportion 
of  solid  matter  and  voids.  Less  total  grain  surface  means  less  cement  and  less  water  required 
to  coat  the  grains.  Furthermore,  these  interactions  are  cumulative,  for  the  additional  amount 
of  cement  and  water  required  in  the  case  of  fine  sand  reduces  the  density  of  the  resulting  mortar 
and  likewise  its  strength  as  well  as  increasing  its  cost. 

31c.  Money  Value  of  Grading. — One  reason  is  here  evident,  both  from  an 
engineering  as  well  as  from  a  purely  doUars-and-cents  standpoint,  that  care  and  attention  be 

1  The  density  of  a  mortar  or  concrete  as  here  referred  to  is  the  ratio  of  the  volume  of  the  solid  particles  to 
the  total  volume. 

2  For  the  use  of  6  to  8-in.  aggregate,  see  Eng.  Rec,  May  1,  1915. 


Sec.  1-32] 


MATERIALS 


23 


given  to  the  grading  of  sands  for  concrete.  If  it  were  possible  to  compute  the  total  saving  in 
the  annual  concrete  production  of  the  United  States,  both  direct  (by  lessened  quantity  of  cement 
required)  or  indirect  (by  increased  durability  and  usefulness  and  prevention  of  disintegration) 
that  would  result  from  the  use  of  proper  sands,  the  amount  would  be  almost  beyond  imagina- 
tion. It  is  probable  that  from  this  neglect  alone  not  less  than  20%  of  the  total  annual  expendi- 
ture for  concrete  is  unnecessary  waste.  It  has  been  proven  in  England  that  on  a  strict  1:2:4 
basis,  using  different  aggregates,  the  cement  required  for  a  quantity  of  concrete  varied  from 
100  to  130  bags — a  difference  of  30  %  in  direct  cement  cost,  without  counting  the  variation  in 
quality  of  the  several  concretes,  with  like  variation  in  their  durability  and  value.  At  the  pres- 
ent time,  a  comfortable  ignorance  is  general  among  engineers  and  contractors  alike  on  these 
important  matters,  but  in  the  not  distant  future,  an  awakened  intelligence  on  the  part  of  all 
will  demand  reform. 

32.  Mechanical  Analysis  of  Aggregates.— The  value  of  an  aggregate,  sand  or  stone,  with 
reference  to  its  size  may  be  determined  by  means  of  a  sieve  analysis.  This  analysis  consists  of 
sifting  the  material  as  supplied  through  several  different  sieves,  and  then  plotting  upon  a  dia- 
gram the  percentage  by  weight  which  is  passed  (or  retained)  by  each  sieve — abscissae  (hori- 
zontal) representing  size  of  grain  and  ordinates  (vertical)  representing  percentage  of  any  size 
passing  each  sieve. ^  Such  a  sieve  analysis  may  appear  of  little  use  as  regards  the  making  and 
placing  of  100,000  yd.  of  concrete,  but  experiment  has  developed  definite  laws  establishing  the 
relation  of  percentages  and  sizes  of  particles  to  maximum  density  and  strength  of  concrete  so 
that  such  a  sieve  analysis  may  be  directly  translated  into  terms  of  commercial  and  engineering 
economy. 

A  typical  analysis  of  three  natural  sands — a  fine,  a  medium,  and  a  coarse  sand  is  given 
in  Fig.  11.2  Uniform  grading  is  indicated  by  an  approach  to  a  straight  line  and  the  variation 
from  the  grading  found  to  give  best  results  in  practice  is  observed  without  difficulty. 

A  mechanical  or  sieve  analysis  is  also  useful  in  studying  the  size  of  the  particles  of  the  coarse 
aggregate. 3  Fig.  12  illustrates  the  analysis  of  a  bank  gravel  and  a  crushed  stone  as  it  came  from 
the  crusher,  without  screening. 

The  following  mechanical  test  for  sand  has  been  used  in  the  laboratory  of  the  Board  of 
Water  Supply  of  the  City  of  New  York: 


Samples  of  the  material  proposed  for  use  in  mortar  or  concrete  shall  be  prepared  for  testing  by  passing  them 
through  a  No.  4  sieve.  Of  the  material  passing  this  sieve  not  more  than  9.5  %  shall  pass  a  No.  8  sieve,  not  more  than 
40  %  a  No.  50  sieve,  and  not  more  than  15  %  a  No.  100  sieve. 


1  It  is  greatly  to  be  regretted  that  there  is  no  standard  in  the  United  States  in  matters  of  this  kind.  Such  va- 
riations make  for  confusion  and  waste.  A  proposed  standard,  which  has  much  to  recommend  it,  varies  successive 
screen  openings  by  a  constant  ratio  of  \/2.  The  following  sizes  of  sieves  are  desirable  for  analyzing  sand,  although 
a  very  useful  analysis  may  be  made  with  fewer  sizes: 


Commercial  No. 

5 

8 

10 

16 

20 

30 

40 

60 

100 

200 

Approximate    size   of  hole 
in  inches. 

0.165 

0.096 

0.073 

0.042 

0.034 

0.020 

0.015 

0.009 

0.0055 

0.0026 

Sieves  are  given  commercial  numbers,  which  agree  approximately  with  the  number  of  meshes  to  the  linear 
inch.  The  actual  size  of  hole,  however,  varies  with  the  gage  of  wire  used  by  different  manufacturers  and  every 
Bet  of  sieves  should  be  separately  calibrated.  The  screen  with  H-in.  openings  is  generally  used  for  separating  out 
large  material  from  sand.    The  No.  4  sieve  with  four  meshes  per  linear  inch  is  practically  its  equivalent. 

2  A  new  portable  instrument  for  making  mechanical  analysis  of  sands  quickly  in  the  field  is  now  manufactured 
by  Kolesch  &  Co.,  of  New  York  (see  Eng.  Rec,  June  26,  1915:  also  Fig.  2,  Sect.  2,  p.  69). 

3  For  coarse  aggregate  analysis,  the  following  sizes  of  sheet  brass  sieves  with  round  holes  are  desirable;  3  in., 
2H  in.,  2  in.,  IM  in.,  IM  in.,  1  in.,  H  in.,  H  in.  and  M  in.  As  is  also  the  case  with  a  like  analysis  of  sand,  a 
straight  line  on  a  mechanical-analysis  diagram  indicates  a  uniform  grading. 


24 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-32 


Material  in  which  the  percentage  passing  any  one  sieve  or  two  sieves  exceeds  the  specified  percentage  may  be 
used,  provided  there  is  a  different  percentage  passing  the  other  sieves  or  sieve  under  the  limiting  percentage  equal 
to  at  least  twice  the  excess. 

The  sieves  for  testing  shall  be  defined  as  follows: 

No.  8  mesh  holes,  0.0955  in.  wide.  No.  23  wire. 
No.  50  mesh  holes,  0.0110  in.  wide.  No.  35  wire. 
No.  100  mesh  holes,  0.0055  in.  wide,  No.  40  wire. 

In  the  standard  specifications  for  concrete  pavement  adopted  by  the  American  Concrete 
Institute,  the  fine  aggregate  is  required  to  pass,  when  dry,  a  screen  having  3^^-in.  openings. 
Not  more  than  20%  is  allowed  to  pass  a  sieve  having  50  meshes  per  linear  inch,  and  not  more 


0    ^       0.025        O.O50         0.075        0.100         0.IE5         0.150         0.175         0  EOO        Q2E5  0.250 

Diameter  of  Particle  in  (nches 
Fig.  11. — Typical  mechanical  analyses  of  fine,  medium,  and  coarse  sands. 


than  5%  is  allowed  to  pass  a  sieve  having  100  meshes  per  linear  inch.  The  coarse  aggregate 
is  specified  as  such  as  will  pass  a  iK-in.  round  opening  and  will  be  retained  on  a  screen  having 
3^-in.  openings.  It  is  also  required  that  natural  mixed  aggregate  shall  not  be  used  as  it  comes 
from  deposits,  but  shall  be  screened  and  used  as  specified. 

The  Joint  Committee  recommends  that  not 
more  than  30%  of  sand  by  weight  should  pass  a 
sieve  having  50  meshes  per  linear  inch. 

According  to  heretofore  accepted  theory,  sand 
for  mortar  or  concrete  should  have  its  grains 
uniformly  graded.  Recent  tests, ^  however,  by 
Prof.  McNeilly  at  Vanderbilt  University  seem  to 
indicate  that  there  should  be  a  jump  in  the  grading 
from  the  sieve  No.  40  size  particles  to  the  sieve 
No.  10  size  particles.  The  following  conclusions 
were  derived  from  these  tests: 

The  best  sizing  of  grains  in  a  commercially-sieved  aggre- 
gate is  about  as  follows:  53  %  to  be  caught  between  the  No.  4 
and  No.  10  sieves;  47  %  fines  to  be  passed  by  the  No.  40  sieve 
(this  includes  the  cement). 

There  is  reason  to  believe  that  the  coarse  aggregate  in  concrete  could  be  beneficially  sized  on  a  basis  similar 
to  the  above;  that  is  to  say,  there  should  be  a  jump  in  size  from  coarse  to  quite  fine  instead  of  the  usually  accepted 
graded  material. 

For  the  method  of  proportioning  by  mechanical  analysis,  as  developed  by  Wm.  B,  Fuller 
and  by  the  U.  S.  Bureau  of  Standards,  see  page  68. 

1  See  Eng.  Rec,  Ncv,  27,  1915.  (Conclusions  derived  from  these  tests  have  not  as  yet  received  general 
acceptance.) 


Fig. 


Q25         050  075  igo         1.25  150 

Diameter  of  par+icle 'in  .inches 

12. — ^Typical  mechanical  analyses  of  bank 
gravel  and  crushed  stone. 


Sec.  1-33] 


MATERIALS 


25 


33.  Tests  for  Specific  Gravity  of  Aggregates. — Ihe  specific  gravity  of  a  substance  is  the 
ratio  of  the  weight  of  an  absolutely  solid  unit  volume  of  the  substance  to  the  weight  of  a  unit 
volume  of  water.    This  ratio  for  aggregates  may  be  determined  as  follows: 

1.  By  pouring  a  given  weight  of  sand  into  a  given  volume  of  water  and  finding  the  increase 
in  volume  of  the  liquid.    (Enough  material  should  be  used  to  give  sufficient  accuracy.) 

2.  By  suspending  pieces  of  coarse  aggregate  by  a  thread  from  chemical  scales  and  noting 
weight  in  air  and  weight  when  hanging  in  water.  (The  difference  in  weight  is  the  weight  of 
the  water  which  the  aggregate  displaces.) 

Finding  specific  gravity  of  particles  of  sand  and  stone  is  preliminary  to  one  method  of 
determining  the  percentage  of  voids.  The  specific  gravity  of  sand  is  practically  a  constant, 
with  a  value  of  2.65.  The  specific  gravity  of  gravel  is  also  quite  uniform,  the  average  being 
2.66.  Average  values  for  stone  varies  with  the  kind  and  the  locality,  ranging  from  2.4  (sand- 
stone) to  2.9  (trap).    Cinders  have  an  average  specific  gravity  of  1.5. 

Before  determining  specific  gravity,  sand  or  fine  stone  should  be  dried  in  an  oven  at  a 
temperature  as  high  as  212°F.  until  there  is  no  further  loss  of  weight.  If  the  stone  is  of  a 
porous  nature,  it  should  be  moistened  sufficiently  to  fill  its  pores,  and  then  the  moisture  on  the 
surface  should  be  removed  by  means  of  blotting  paper.  Such  a  procedure,  of  course,  does  not 
determine  absolute  specific  gravity  but  gives  a  result  that  should  be  used  in  determining  the 
percentage  of  voids  for  proportioning  concrete  mixtures. 

34.  Voids  in  Aggregates. 

34a.  Percentage  of  Voids. — The  percentage  of  voids  in  dry  sand  ranges  from 
28%  for  a  coarse,  well-graded  natural  sand  to  40  to  45%  for  a  very  uniform  natural  or  screened 
sand.    The  range  for  coarse  aggregates  is  from  25  to  55%. 

The  percentage  of  voids  in  aggregates  may  be  determined  by  two  methods : 

1.  By  determining  the  specific  gravity  of  the  solid  particles  and  then  weighing  a  given 
volume  of  the  aggregate  and  computing  therefrom  the  percentage  of  voids.  (Pores  in  porous 
stone  should  be  filled  with  water.    See  Art.  33.) 

Let  S  =  specific  gravity,  W  =  weight  per  cubic  foot  of  the  dry  aggregate,  and  P  =  per- 
centage of  voids.    Then,  since  water  weighs  62.5  lb.  per  cu.  ft., 

P  =      (i  "  WEs) 

2.  By  finding  the  amount  of  water  required  to  fill  the  voids  in  a  given  volume  of  aggregate. 
Let  V  =  volume  of  water  required  to  fill  the  voids  and  T  =  total  volume,  or  given  volume 

of  the  aggregate.  Then 


With  sand  or  fine  broken  stone  the  percentage  of  voids  by  this  method  should  be  obtained 
by  dropping  the  aggregate  into  a  vessel  containing  water.  U  K  =  volume  displaced  by  the 
aggregate  and  T  =  given  volume  of  the  aggregate,  then 


Pouring  water  into  fine  aggregate  does  not  give  reliable  results  because  it  is  physically  impossible 
to  drive  out  all  the  air. 

The  percentage  of  voids  is  considerably  affected  by  the  degree  of  compactness  of  the 
aggregate.  Moderate  shaking  of  coarse  aggregate,  for  example,  will  reduce  the  volume  of 
voids  by  as  much  as  10%.  Loose  measurement  is  usually  considered  preferable  for  the  coarse 
aggregate  since  sand  and  cement  separate  the  stones  to  a  considerable  extent  in  the  concrete 
as  placed.    Voids  in  sand  are  usually  determined  with  reference  to  the  dry  material  well  shaken. 

346.  General  Laws.— 1.  A  mass  of  spheres  of  any  uniform  size  if  carefully 
piled  in  the  most  compact  manner  would  have  26%  voids.    If  the  same  mass  of  spheres  were 


26 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  l-34c 


poured  into  a  receptacle  and  the  spheres  allowed  to  arrange  themselves,  it  has  been  found  by 
experiment  that  44%  would  be  the  smallest  percentage  of  voids  which  could  be  obtained  under 
the  best  conditions. 

2.  A  material  having  particles  all  of  a  uniform  size  and  shape  contains  practically  the  same 
percentage  of  voids  as  a  material  having  particles  of  a  corresponding  similar  shape  but  of  a 
different  uniform  size. 

3.  In  any  material  the  largest  percentage  of  voids  occurs  with  particles  all  of  the  same  size 
and  the  smallest  percentage  occurs  with  particles  of  such  different  sizes  that  the  voids  of  each 
size  are  filled  with  the  largest  particles  which  will  enter  them.  Thus,  an  aggregate  consisting 
of  a  mixture  of  stones  and  sand  has  a  less  percentage  of  voids  than  sand  alone. 

4.  Materials  with  round  particles  contain  less  voids  than  materials  with  angular  particles 
screened  to  the  same  size 

34c.  Effect  of  Moisture  on  Voids  in  Sand  and  Screenings. — The  percentage 
of  voids  in  sand  is  greatly  affected  by  moisture.  The  reason  for  this  lies  in  the  fact  that  when 
water  surrounds  a  particle  of  sand  it  occupies  space  and  separates  this  particle  from  grains 
adjacent  to  it.  Since  fine  sand  has  a  larger  number  of  grains  per  unit  volume,  it  is  more 
affected  than  is  coarse  sand.  If  either  loose  or  tamped  sand  is  mixed  with  a  small  percentage 
of  water  and  kept  either  loose  or  thoroughly  tamped,  it  will  be  found  to  increase  considerably 
in  volume  and  weigh  less  per  cubic  foot.  A  maximum  volume  will  be  obtained  with  the  addition 
of  from  5  to  8%  of  water  by  weight.  Greater  percentages  will  give  a  less  increase  of  volume 
until  finally  when  the  sand  is  thoroughly  saturated  it  will  have  a  volume  slightly  less  than  the 
original.  A  sand  that  has,  say,  35%  voids,  may  contain  from  27  to  44%  of  voids  depending 
upon  the  degree  of  compactness  and  the  percentage  of  water.  Natural  sand  as  it  ordinarily 
comes  from  the  bank  contains  from  2  to  4%  of  moisture  by  weight. 

34cZ.  Percentage  of  Voids  Determined  by  Weight. — The  specific  gravity  of 
gravel  particles  and  of  sand  grains  is  usually  nearly  constant,  varying  between  2.6  and  2.7. 


Percentages  of  Voids  in  Sand  and  Gravel  Corresponding  to  Different  Weights 

PER  Cubic  Foot 

(Based  on  an  Average  Specific  Gravity  of  2.65) 


Percentages  of 
moisture  by  weight 

Weight  per  cubic  foot  of  sand  or  gravel 

75 

80 

85 

90 

95 

100 

105 

110 

115 

120 

125 

0 

54.7 

51 

7 

48.7 

45.7 

42.7 

39.6 

36.6 

33.6 

30.6 

27.5 

24.5 

1 

55.2 

52 

2 

49.2 

46.2 

43.2 

40.2 

37.3 

34.2 

31.2 

28.2 

25.3 

2 

55.6 

52 

7 

49.8 

46.7 

43.8 

40.8 

37.9 

34.8 

31.9 

28.9 

26.0 

3 

56.1 

53 

1 

50.3 

47.3 

44.4 

41.4 

38.5 

35.5 

32.6 

29.7 

26.7 

4 

56.5 

53 

6 

50.8 

47.8 

45.0 

42.0 

38.1 

36.2 

33.3 

30.4 

27.5 

5 

57.0 

54 

1 

51.3 

48.4 

45.5 

42.6 

39.8 

36.9 

34.0 

31.2 

28.3 

6 

57.5 

54 

6 

51.8 

48.9 

46.0 

43.2 

40.4 

37.5 

34.7 

31.7 

29.0 

7^ 

57.9 

55 

1 

52.3 

49.5 

46.6 

43.8 

41.0 

38.2 

35.4 

32.6 

29.8 

8 

58.3 

55 

5 

52.8 

50.0 

47.2 

44.5 

41.6 

38.9 

36.1 

33.3 

30.6 

9 

58.8 

56 

0 

53.3 

50.6 

47.8 

45.0 

42.3 

39.5 

36.8 

34.0 

31.3 

10 

59.2 

56 

5 

53.9 

51.1 

48.4 

45.6 

42.9 

40.2 

37.5 

34.7 

32.1 

Sec.  1-35] 


MATERIALS 


27 


On  account  of  this  fact  the  percentage  of  voids  in  sand  and  gravel  may  be  considered  to  vary 
inversely  as  the  weight  per  cubic  foot  of  dry  material.  Knowing  the  weight  per  cubic  foot  and 
assuming  a  specific  gravity  of  2.65,  the  percentage  of  voids  in  dry  sand  and  gravel  may  be 
readily  found  as  explained  under  Method  (1)  in  Art.  34a.  The  percentage  of  voids  in  moist 
sand  or  gravel  may  be  determined  in  the  same  manner  as  for  the  dry  aggregate  except  that  the 
weight  per  cubic  foot  of  the  moist  material  should  be  considered  as  decreased  by  the  weight  of 
moisture  which  the  sand  or  gravel  contains.  The  foregoing  table  gives  percentages  of 
voids  for  sands  and  gravels  of  different  weights  per  cubic  foot  and  with  different  percentages 
of  moisture  by  weight.  The  table  may  be  used  for  any  aggregate  with  a  specific  gravity  of 
approximately  2.65. 

35.  Tests  of  Aggregates. ^ — Tests  of  an  aggregate  for  use  in  mortar  or  concrete  may  be 
divided  into  two  general  classes: 

1.  Tests  to  determine  the  general  suitability  of  the  aggregate. 

2.  Tests  to  determine  those  characteristics  of  the  aggregate  which  have  an  influence  on 
its  general  suitability. 

Tests  of  the  first  class  comprise  those  for  determining  the  quality  of  the  mortar  or  concrete 
that  can  be  made  from  the  given  aggregate.  These  tests  may  be  called  Tests  for  Acceptance. 
Tests  of  the  second  class  include  those  which  may  be  made  to  determine  the  cause  of  any 
failure  of  an  aggregate  to  pass  the  tests  of  the  first  class.  These  tests  of  the  second  class,  which 
may  be  called  Tests  for  Quality,  are  useful  not  only  to  discover  the  cause  of  failure  of  an  aggregate 
to  pass  the  tests  for  acceptance,  but  may  be  employed  to  determine  the  methods  of  improving 
a  given  aggregate  and  of  comparing  different  aggregates  as  to  special  characteristics. 

No  standards  for  acceptance  tests  of  concrete  aggregates  have  been  established  by  the 
American  Society  for  Testing  Materials,  although  the  need  of  such  standards  is  now  fully 
realized  and  will  soon  be  satisfied.  The  most  advanced  practice  in  this  direction  is  probably 
that  represented  by  the  procedure  of  the  Materials  Testing  Division  of  the  New  York  Public 
Service  Commission  whose  methods  have  been  given  wide  publicity.  The  standards  quoted 
in  abridged  form  below  are  derived  from  this  source  (Eng.  Rec,  Jan.  8,  1916  and  Eng.  News, 
Feb.  4,  1915). 

Fine  Aggregates. — Complete  tests  of  a  fine  aggregate  comprise: 

1.  Determination  of  %  retained  on  No.  4  square-hole  sieve. 

2.  Mechanical  analysis  of  portion  passing  No.  4  square-hole  sieve. 

3.  Determination  of  silt  by  washing  on  No.  100  sieve. 

4.  Determination  of  silt  by  decantation. 

5.  Compressive  tests  of  2-in.  cubes. 

6.  Microscopical  examination. 

7.  Weight  per  cubic  foot. 

8.  Voids. 

9.  Specific  gravity. 

10.  Reaction  to  litmus. 

11.  Quantitative  test  for  organic  matter  as  indicated  by  loss  on  ignition. ^ 

12.  -  Density  in  mortar. 

13.  Determination  of  insoluble  silica. 

It  is  seldom  necessary  to  make  more  than  the  first  six  of  the  above  tests  and  frequently  only  one  or  two  of  them 
are  necessary. 

1.  The  entire  sample  is  screened  on  a  No.  4  square-hole  sieve  and  the  %  retained  is  computed  upon  the  basis  of 
the  original  weight  of  the  sample.    No  correction  is  made  for  moisture  contained. 

(A  No.  4  sieve  has  clear  openings  of  0.20  in.,  while  the  H-in.  sieve  recommended  by  the  Joint  Committee  of 
the  National  Engineering  Societies  has  0.25-in.  clear  openings  made  by  drilling  round  holes  in  a  plate.  The  differ- 
ence in  results  obtained  with  the  two  sieves  is  negligible  and  either  is  satisfactory.) 

^  See  also  the  following  articles  on  sand  testing: 

Cloyd  M.  Chapman  and  Nathan  C.  Johnson:  "The  Economic  Side  of  Sand  Testing,"  Eng.  Rec,  June  12,  19 
and  26,  1915. 

Cloyd  M.  Chapman:  "The  Testing  of  Sand  for  Use  in  Concrete,"  Eng.  News,  Feb.  5,  1914,  and  Mar.  12,  1914. 
Ralph  E.  Goodwin:  "Standard  Practice  Instructions  for  Concrete  Testing,"  Eng.  News,  Feb.  4  and  11,  1915. 
2  A  new  colorimetric  test  is  being  developed.    See  footnote  on  p.  29. 


28 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-36 


2.  The  mechanical  analysis  of  the  portion  of  the  sample  which  has  passed  the  No.  4  sieve  is  made  by  use  of 
sieves  Nos.  8,  16,  30,  50,  and  100.  About  150  grams  of  this  material  is  separated  by  the  method  of  quartering,  and 
110  grams  of  this  is  weighed  and  dried  beneath  a  gas  burner.  One  hundred  grams  of  the  dry  material  is  placed  on 
the  No.  8  sieve,  the  other-sieves  being  nested  below  the  No.  8  in  the  order  of  increasing  fineness,  and  the  entire  nest  of 
sieves  is  mechanically  agitated.  With  the  agitator  used,  the  amount  of  sieving  is  standardized  by  always  turning 
the  hand  crank  200  revolutions.  At  the  end  of  the  operation  the  material  retained  on  each  sieve,  and  that  which 
has  passed  the  No.  100  sieve,  is  weighed.  The  %  of  the  whole  sample  which  passes  each  sieve  is  now  computed, 
and  the  mechanical  analysis  curve  is  plotted  (see  Art.  32) . 

3.  Silt  by  washing  on  the  No.  100  sieve  is  determined  for  a  sample  obtained  by  quartering  which  weighs  about 
220  grams  in  its  natural  moist  condition.  The  sample  is  dried  slowly  at  temperatures  not  greatly  above  ordinary 
room  temperature  to  avoid  baking  any  clay  or  similar  matter.  Two  hundred  grams  of  the  dry  sample  is  now  weighed 
on  the  No.  100  sieve,  soaked  in  water  for  a  few  moments  to  soften  any  lumps,  washed  under  a  gentle  stream  of  water, 
dried  under  a  gas  burner,  and  reweighed.    The  %  of  silt  is  the  loss  in  weight  multiplied  by  100  and  divided  by  200. 

(The  washing  test  obtains  the  true  silt  value  because  it  removes  clay  which  adheres  to  the  grains  as  a  coating 
which  is  not  separated  by  sieving  in  a  dry  state.) 

4.  Determination  of  silt  by  decantation  is  a  test  for  field  use  only.  About  20  c.c.  quartered  from  a  carefully 
selected  sample  is  placed  in  a  100-c.c.  graduated  glass  cylinder  with  about  30  c.c.  of  lukewarm  water.  The  mixture 
is  stirred  with  a  wire  for  30  sec,  allowed  to  settle  for  30  sec,  and  the  water  decanted  into  a  second  100-c.c.  cylinder. 
The  sand  left  in  the  first  cylinder  is  stirred  up  with  a  fresh  portion  of  water  and  the  process  repeated.  This  is  done 
4  times.  After  1  hr.  the  volume  of  silt  in  cylinder  No.  2  and  the  volume  of  clean  sand  in  cylinder  No.  1  is  noted 
and  recorded.  The  %  of  silt  is  100  multipHed  by  the  number  of  cubic  centimeters  of  silt  in  cylinder  No.  2  and 
divided  by  the  sum  of  the  volumes  of  silt  in  cylinder  No.  2  and  clean  sand  in  cylinder  No.  1. 

(The  method  of  decantation  is  better  than  the  method  of  allowing  the  silt  to  settle  on  top  of  the  sand  in  one 
cylinder  but  is  not  as  satisfactory  as  the  method  of  washing.) 

5.  Compressive  tests  of  2-in.  cubes  are  made  by  the  methods  recommended  by  the  Committee  on  Uniform 
Tests  of  Cement,  of  the  American  Society  of  Civil  Engineers  {Trans.  Am.  Soc.  C.  E.,  vol.  75,  p.  665).  Fine  aggre- 
gate must  not  be  dried,  but  the  natural  moisture  is  determined  on  a  separate  sample,  and  is  counted  as  a  part  of  the 
water  used  for  mixing,  not  as  a  part  of  the  weight  of  sand.  Proportions  are  1  :  3  by  weight.  The  consistency  em- 
ployed is  60%  more  water  than  that  required  to  make  standard  Ottawa  sand  mortar  of  "normal  consistency." 
Ottawa  sand  specimens  of  the  same  consistencj'  are  made  with  each  set  of  specimens  from  commercial  sand.  Tests 
are  made  at  ages  of  3,  7,  and  28  days.  Specimens  whose  weights  vary  more  than  3  %  from  the  average  are  rejected. 
Cubes  are  stored  in  water  up  to  time  of  crushing,  A  spherical  bearing  block  and  two  thicknesses  of  blotting  paper 
above  and  below  are  used  in  testing.  Since  the  wet  consistency  used  lowers  the  strength  at  early  periods,  the  results 
are  permitted  to  fall  below  those  for  Ottawa  sand  specimens  of  standard  consistency  by  the  following  amounts  or 
less:  at  3  days — 10%;  at  7  days — 5%;  at  28  days — 1%. 

(The  wet  consistency  is  used  because  it  more  nearly  represents  working  conditions  and  because  some  sands  fail 
in  wet  consistencies  although  satisfactory  in  "normal  consistency."  No  tensile  tests  are  required  because  "it  is 
thought  that  compressive  tests  more  nearly  represent  the  conditions  of  the  work  and  that  modern  practice  is  tending 
toward  compressive  tests.") 

6.  Microscopical  examination  is  made  for  the  purpose  of  detecting  the  presence  of  a  crust  or  film  of  organic 
matter  on  the  grains  which  cannot  be  detected  by  other  means. 

7.  Weight  per  cubic  foot  is  determined  by  using  an  8  by  16-in.  cylindrical  concrete  mold  and  a  second  cylinder 
of  smaller  diameter  but  high  enough  to  have  a  cubic  capacity  slightly  greater  than  that  of  the  8  by  16-in.  cylinder. 
The  smaller  cylinder  is  placed  within  the  larger  one  and  filled  with  fine  aggregate.  It  is  now  drawn  out  allowing 
the  aggregate  to  flow  out  at  the  bottom  into  the  larger  cylinder.  The  material  is  now  struck  off  level  with  the  top  of 
the  measure  and  weighed.  After  weighing,  the  material  is  dried  and  again  placed  in  the  larger  cylinder  by  use  of 
the  smaller  cylinder  as  before.  The  weight  of  the  material  dry  is  then  determined,  the  volume  being  found  by 
measuring  down  from  the  top  of  the  cylinder. 

8.  Voids  are  determined  by  using  the  sample  whose  apparent  volume  and  dry  weight  have  been  determined  in 
test  No.  6.  It  only  remains  to  determine  the  absolute  volume  of  solid  matter.  This  can  be  computed  from  the 
weight,  assuming  the  specific  gravity  2.65,  or  it  can  be  found  by  placing  the  entire  sample  in  a  receptacle  containing 
water  and  weighing  the  whole,  emptying  out  the  aggregate,  and  reweighing  the  receptacle  filled  with  water  to  the 
previous  level.  The  difference  in  weighings  minus  the  weight  of  dry  aggregate  is  the  weight  of  a  volume  of  water 
equal  to  the  absolute  volume  of  the  aggregate.  This  divided  by  the  weight  of  water  is  the  absolute  volume  of 
aggregate.  A  hook  gage  clamped  to  the  water  receptacle  is  used  to  determine  water  levels  accurately.  Finally, 
the  %  of  voids  in  aggregate 

100  (Apparent  volume  —  Absolute  volume) 
Apparent  volume 

9.  Specific  gravity  is  determined  by  slowly  and  carefully  introducing  the  aggregate  into  a  specific  gravity 
flask  or  a  graduated  glass  cylinder  containing  water  and  noting  the  volume  of  water  displaced  by  a  known  weight 
of  material.    The  specific  gravity  of  the  aggregate 


Weight  of  aggregate  in  grams 


Displaced  volume  in  cubic  centimeters 


Sec.  1-35] 


MATERIALS 


29 


10.  The  reaction  to  litmus  demonstrates  the  presence  of  injurious  alkalies. 

11.  Organic  matter  as  indicated  by  the  ignition  loss  is  determined  as  follows:' 

Two  25-gram  samples  are  weighed  from  a  7o-gram  sample  containing  natural  moisture  which  has  been  pre- 
viously selected  by  the  method  of  quartering.  These  are  placed  in  beakers  "A"  and  "  B"  and  each  is  covered  with 
60  c.c.  of  water  at  100°F.  The  sand  and  water  in  beaker  "A"  is  stirred  briskly  with  a  glass  rod,  allowed  30  sec. 
to  settle,  and  a  part  of  the  water  decanted  onto  a  previously  dried  and  weighed  filter  paper.  The  remaining  portion 
is  again  stirred,  allowed  to  settle  and  a  further  quantity  of  water  decanted.  The  proceps  is  repeated  until  all  the 
water  has  been  filtered.  An  additional  30  c.c.  of  water  at  100°F.  is  added  to  the  sand  in  the  beaker  and  the  process 
is  repeated  again.  The  filtrate  is  allowed  to  drain,  and  the  washed  sand  is  dried  under  a  gas  burner.  The  same 
procedure  is  followed  with  beaker  "  B,"  using  a  second  filter  paper.  The  filter  papers  with  filtrate  on  them  are  now 
dried  in  an  oven  at  100°C.  to  constant  weight  (a  temperature  of  lOO^C.  must  not  be  exceeded)  and  weighed.  The 
excess  in  weight  over  the  dry  weight  of  the  filter  papers  is  the  weight  of  silt.  The  filter  papers  are  now  folded  care- 
fully and  ignited  thoroughly  in  a  platinum  crucible.  The  residue  is  weighed,  and  the  dry  washed  sand  is  also 
weighed.    Finally,  %  loss  on  ignition 

100  (Weight  of  silt  —  Weight  of  crucible  ash) 
Weight  of  silt  +  Weight  of  dry  washed  sand 

(This  test  is  seldom  necessary  because  more  direct  results  are  obtained  by  tests  of  2-in.  cubes.) 

12.  Density  is  determined  by  weighing  the  relative  amounts  of  cement,  sand,  and  water,  according  to  the 
proportions  used,  mixing,  placing  mix  in  a  graduated  cylinder  and  noting  the  final  volume  of  the  set  mortar.  The 
net  weight  of  this  mortar  is  also  determined  and  compared  with  the  sum  of  the  individual  weights  of  cement,  sand, 
and  water  in  the  mix.  The  weight  of  material  left  adhering  to  mixing  slab  and  tools  is  thus  ascertained.  This 
loss  is  apportioned  between  the  cement,  sand,  and  water  according  to  the  relative  weights  of  each  as  originally 
combined,  and  the  corrected  amount  by  weight  of  each  constituent  in  the  set  mortar  is  thus  computed.  The 
corrected  weights  of  cement  and  aggregate  in  the  set  mortar  are  now  divided  by  their  respective  specific  gravi- 
ties to  obtain  absolute  volumes  and  the  sum  of  these  absolute  volumes  divided  by  the  total  volume  of  set  mortar 
is  the  density,  or  solidity  ratio. 

13.  The  determination  of  insoluble  silica  is  seldom  called  for  but  when  required  calls  for  the  services  of  an 
experienced  analytical  chemist. 

Coarse  Aggregates. — Complete  tests  of  a  coarse  aggregate  comprise: 

1.  Mechanical  analysis.  4.  Voids. 

2.  Cleanliness.  5.  Specific  gravity. 

3.  Weight  per  cubic  foot.  6.  Crushing  strength  of  stone. 
It  is  usually  necessary  to  make  only  the  first  two  of  the  above  tests. 

1.  Mechanical  analysis  of  coarse  aggregate  is  made  by  mechanically  agitating  a  nest  of  six  sieves,  the  clear 
openings  in  the  wire  meshes  of  which  are  2  in.,  1>^  in.,  1  in.,  ?4  in.,  H  in.,  and  H  in.  respectively.  A  25-lb.  sample 
obtained  by  quartering  a  larger  sample  is  used.  The  material  retained  on  each  sieve  after  100  bumps  of  the 
rocker  apparatus  is  weighed,  and  the  percentage  passing  each  sieve  is  computed. 

2.  Cleanliness  is  judged  by  inspection  only. 

3.  Weight  per  cubic  foot  is  determined  by  pouring  the  material  slowly  into  an  8  by  16-in.  cylinder  mold  from 
a  height  of  2  ft.  above  the  bottom,  striking  off  the  top  and  weighing.  If  the  material  is  very  wet  it  is  previously 
dried  sufficiently  to  remove  surplus  water,  but  not  enough  to  dry  out  the  pores. 

4.  Voids  are  determined  by  the  method  used  for  fine  aggregate. 

5.  Specific  gravity  is  determined  by  weighing  a  number  of  representative  particles  of  the  stone  after  thorough 
drying  to  remove  all  moisture  in  the  pores,  allowing  the  material  to  cool,  filling  the  pores  by  boiling  in  water  and 

1  A  colorimetric  test  for  organic  impurities  in  sands  is  being  developed  under  the  auspices  of  committee  C-9 
of  the  A.S.T.M.  Sodium  hydroxide  (NaOH)  is  added  to  a  sample  of  sand  at  ordinary  temperature  and  the  depth 
of  color  resulting  has  been  found  to  furnish  a  measure  of  the  effect  of  the  impurities  on  the  strength  of  mortars 
made  from  such  sands.    See  Circular  No.  1  of  Structural  Materials  Research  Laboratory,  Lewis  Institute,  Chicago. 

The  method  for  field  tests  is  described  in  the  circular  as  follows: 

"Fill  a  12-oz.  graduated  prescription  bottle  to  the  4M-oz.  mark  with  the  sand  to  be  tested.  Add  a  3%  solu- 
tion of  sodium  hydroxide  until  the  volume  of  the  sand  and  solution,  after  shaking,  amounts  to  7  oz.  Shake  thor- 
oughly and  let  stand  over  night.    Obsers^e  the  color  of  the  clear  supernatant  Uquid. 

"In  approximate  field  tests  it  is  not  necessary  to  make  comparison  with  color  standards.  If  the  clear  super- 
natant liquid  is  colorless,  or  has  a  light  yellow  color,  the  sand  may  be  considered  satisfactory  in  so  far  as  organic 
impurities  are  concerned.  On  the  other  hand,  if  a  dark-colored  solution,  ranging  from  dark  reds  to  black  is  obtained 
the  sand  should  be  rejected  or  used  only  after  it  has  been  subjected  to  the  usual  mortar  strength  tests. 

"  Field  tests  made  in  this  way  are  not  expected  to  give  quantitative  results,  but  will  be  found  useful  in: 

1.  Prospecting  for  sand  supplies. 

2.  Checking  the  quality  of  sand  received  on  the  job. 

3.  Preliminary  examination  of  sands  in  the  laboratory. 

"An  approximate  volumetric  determination  of  the  silt  in  sand  can  be  made  by  measuring  or  estimating  the 
thickness  of  the  layer  of  fine  material  which  settles  on  top  of  the  sand.  The  %  of  silt  by  volume  has  been  found  to 
vary  from  1  to  2  times  the  %  by  weight." 


30 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-36 


allowing  the  material  to  stand  in  the  water  until  cool,  removing  the  surface  water  with  a  towel,  weighing,  placing 
particles  in  a  300-c.c.  graduate,  pouring  in  a  sufficient  measured  volume  of  water  to  cover  the  stone,  noting  the  com- 
bined volume  of  water  and  stone,  computing  the  volume  of  stone  alone,  and  computing  the  specific  gravity  by  divid- 
ing the  original  dry  weight  of  the  stone  in  grams  by  the  displaced  volume  in  cubic  centimeters.  Data  are  also 
afforded  by  this  test  for  determining  the  %  of  absorption  of  the  stone  based  on  dry  weight. 

6.  Crushing  strength  of  the  stone  has  never  been  used  as  an  acceptance  test  of  aggregate. 

36.  Notes  on  the  Selection  and  Testing  of  Aggregates. — Sand  and  stone  for  important  or  special 
work  should  be  tested  in  some  well-equipped  laboratory  and,  of  course,  the  tests  should  be  made 
before  the  aggregates  are  purchased  or  the  concrete  mixed.  The  tests  should  be  upon  representative 
samples,  and  materials  should  be  checked  for  uniformity  as  delivered.  In  sampling  natural  sands 
and  gravels  the  greatest  care  must  be  used. 

Sand  should  also  be  regularly  tested  as  construction  work  progresses.  Often  a  sand  that  is 
found  entirely  suitable  at  the  start  will  be  found  entirely  different  in  later  deliveries.  Proportions 
of  materials  should  change  whenever  the  mechanical  analysis  shows  a  decided  change  in  the  grada- 
tion of  the  sand  grains. 

Mechanical  analyses  of  sands,  or  volumetric  tests  of  mortars  or  concretes  made  from  the  given 
sands,  sometimes  show  that  a  stronger  mortar  or  concrete  may  be  obtained  by  mixing  two  sizes  of 
sands  from  different  portions  of  the  same  bank,  making  the  single  requirement  that  a  definite  pei- 
centage  is  to  be  retained  on  a  certain  sieve.  Mechanical  analyses  and  volumetric  tests  are  also 
useful  in  studying  two  or  more  sands  to  determine  the  one  most  suited  for  the  given  work.  Fre- 
quently a  properly  proportioned  mixture  of  sand  and  crushed  stone  screenings  will  produce  a  better 
sand  for  mortor  or  concrete  than  either  one  used  separately. 

For  the  best  results,  sand  for  mortar  requires  more  fine  material  than  sand  for  concrete. 

For  maximum  water-tightness  a  mortar  or  concrete  may  require  a  slightly  larger  proportion  of 
fine  grains  in  the  sand  than  for  maximum  density  or  strength.  Gradel  tends  to  produce  a  more  water- 
tight concrete  than  broken  stone. 

A  high  unit  weight  of  material  and  a  correspondingly  low  percentage  of  voids  are  indications  of 
coarseness  and  good  grading  of  particles.  However,  the  impossibility  of  establishing  uniformity 
of  weight  and  measurement  due  to  different  percentages  of  moisture  and  different  methods  of 
handling  make  these  results  merely  general  guides  that  seldom  can  be  taken  as  positive  indications 
of  true  relative  values.  This  is  especially  true  of  the  fine  aggregates  in  which  percentages  of  voids 
increase  and  weights  decrease  with  the  addition  of  moisture  up  to  5  to  S%. 

Aggregates  that  contain  harmful  impurities  may  sometimes  be  made  satisfactory  for  concrete 
work  by  washing. 

Some  sands  which  contain  impurities  have  been  found  to  prevent  hardening  with  one  brand  of 
cement  and  to  give  satisfactory  results  with  another  brand. 

A  chemical  analysis  of  aggregates  is  desirable  in  many  cases,  and  a  microscopical  examination 
will  often  prove  of  value. 

Cement  adheres  more  readily  to  sand  grains  with  rough,  unpolished  surfaces. 

Usually  an  artificial  sand  or  crushed  stone  will  safely  contain  a  greater  percentage  of  fine 
material  than  natural  sand. 

37.  Specifications  for  Aggregates. — The  specifications  adopted  by  the  Pubhc  Service 
Commission  for  quality  of  concrete  aggregates  used  in  New  York  City  subway  construction 
are  noted  below  (Eng.  News,  Feb.  11,  1916;  Eng.  Rec,  Jan.  8,  1916). 

Fine  aggregates  shall  conform  to  the  following  requirements: 


Mechanical  Grading. — 


Size  of  opening  square 
holes  (inches) 

Commercial  number 
of  sieve 

Limit  of  fineness  (% 
passing).    Not  more 
may  pass 

Limit  of  coarseness  (% 
passing).    Not  less 
must  pass 

0.200 

4 

100 

95 

0.100 

8 

95 

85 

0.042 

16 

75 

40 

0.021 

30 

50 

20 

0.011 

50 

30 

2 

0.006 

100 

6 

Sec.  1-38] 


MATERIALS 


31 


Silt. — Not  over  6  %  by  dry  weight  shall  pass  a  No.  100  sieve  when  screened  dry.  Not  over  10  % ,  dry  weight, 
shall  pass  a  No.  100  sieve  when  washed  on  the  sieve  with  a  stream  of  water. 

Both  of  the  above  tests  shall  be  made,  and  neither  limit  shall  be  exceeded. 
The  following  test  is  for  field  use  only: 

Not  over  10%  by  volume  shall  be  silt  when  the  test  is  made  by  decanting  from  test  tubes  (method  described 
in  Art.  35). 

Strength  in  Mortar. — Fine  aggregate  shall  be  of  such  quality  that  mortar  composed  of  1  part  Portland  cement 
and  3  parts  fine  aggregate  by  weight  will  show  a  tensile  and  compressive  strength  at  least  equal  to  the  strength  of 
1  :  3  mortar  of  the  same  consistency  made  with  the  same  cement  and  standard  Ottawa  sand.  Fine  aggregate  shall 
not  be  dried  before  being  made  into  mortar,  but  shall  contain  natural  moisture. 

Organic  Matter.^ — Loss  on  ignition  shall  not  exceed  0.1  %  of  the  total  dry  sand  by  weight,  nor  10  %  of  the  silt 
obtained  by  decantation. 

Coarse  aggregate  for  concrete  shall  conform  to  the  following  requirements: 

Mechanical  Grading — 


Size  of  opening 
square  holes 
(inches) 

Limit  of  fineness  (  % 
passing).    Not  more 
may  pass 

T,imit  of  coarseness 
(  %  passing).  Not 
less  must  pass 

2 

100 

IH 

100 

95 

1 

80 

40 

H 

60 

25 

H 

40 

10 

H 

5 

Cleanliness. — All  broken  stone  aggregate  must  be  so  free  from  dust  that  samples  caught  as  the  material  falls 
from  the  conveyor  belt  at  the  plant  will  be  within  the  limit  of  fineness.  All  gravel  must  be  thoroughly  washed  at  the 
plant. 

WATER 

38.  General  Requirements. — The  water  used  in  mixing  mortar  or  concrete  should  be  free 
from  oil,  acids,  alkalies,  or  vegetable  matter,  and  should  be  of  a  quality  fit  for  drinking  purposes. 
The  presence  of  oils  is  easily  detected  by  the  well-known  iridescent  surface  film.  Vegetable 
matter  can  sometimes  be  detected  by  observing  floating  particles,  or  by  turbidity.  Chemical 
determinations  are  better  and  more  certain. 

39.  Examination  of  Water. — Tests  of  water  for  acidity  or  alkalinity  may  be  made  by  means 
of  litmus  paper,  procured  at  any  chemist's.  "  If  blue  litmus  remains  blue  on  immersing  in  the 
water,  then  the  property  is  either  neutral  or  alkaline;  if  the  color  changes  to  red,  then  the  prop- 
erty is  acidic.  If  there  is  a  dangerous  amount  of  acid  present,  the  change  in  color  will  be  very 
rapid.  Likewise,  if  red  litmus  changes  very  quickly  to  blue,  the  water  will  be  found  to  contain 
a  dangerous  amount  of  strong  alkali.  If  the  change  of  color  is  slow  and  faint  in  either  test, 
the  indication  may  be  disregarded.  A  solution  of  phenol-phthalein  is  a  delicate  test  for 
alkalinity. 

Whenever  a  water  does  not  appear  satisfactory,  its  effect  upon  the  strength  and  setting 
quahties  of  a  cement  should  be  determined  by  direct  test  on  mixtures. 

40.  Functions  of  Water. — The  functions  of  water  in  concrete  are: 

1.  Water  reacts  with  cement  to  form  a  binding  material  which  unites  otherwise  non- 
cohering  sand  and  stone. 

2.  Water  operates  to  flux  both  dissolved  and  undissolved  cementing  substances  over  the 
surfaces  of  sand  grains  and  stone  particles  (or  pieces  of  gravel),  rendering  possible  extensive 
and  close  adhesion  by  carrying  these  substances  into  the  minute  and  multitudinous  surface 
irregularities  of  the  particles,  where  they  are  absorbed  as  water  is  later  absorbed  or  evaporated. 

3.  Water  acts  as  a  lubricant  between  sand  particles  and  stone  particles  so  that  placement 
of  harsh  and  irregular  materials  in  molds  and  forms  is  rendered  easy. 

1  For  colorimetric  test  see  footnote  on  p.  29. 


32 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-41 


4.  Water  itself  occupies  space  in  the  mass. 

41.  Influence  of  Quantity  of  Water  on  Strength  of  Concrete. — The  first  function  of  water 
cited  in  the  preceding  article  is  basic  and  essential  to  the  manufacture  of  concrete.  If  there 
is  insufficient  water,  obviously  its  reaction  with  cement  will  prematurely  cease;  and  if  there  is 
too  much  water,  it  is  equally  obvious  that  the  cementing  products  may  be  too  dilute  to  develop 
proper  strength  since  cement  depends  for  its  early  strength  and  for  a  considerable  part  of  its 
later  strength  upon  the  hardening  of  amorphous  or  glue-like  substances.  Undue  dilution  of 
these  substances  is  readily  possible,  but  it  is  accompanied  by  impairment  of  strength,  just  as 
glue  may  be  a  valuable  adhesive  when  of  proper  consistency,  while  the  same  glue,  if  too  dilute, 
may     useless  for  like  purposes  although  later  evaporation  may  gradually  restore  its  cementitious 


3250 


value.  Cement  depends  further  for  its  strength  upon  interlacing  crystals;  and  crystallization 
takes  place  only  from  saturated  or  supersaturated  solutions.  If,  therefore,  excess  water  is 
added,  such  strength  as  these  crystals  may  confer  is  further  impaired.  The  influence  of  water 
in  greater  or  less  quantities  on  the  strength  of  concrete  is  shown  in  Fig.  13.  ^ 

42.  Influence  of  Quantity  of  Water  on  Fluxing  of  Cement. — The  second  function  of  water 
cited  above — its  action  as  a  carrier  (or  flux)  of  cementing  substances — is  obvious.  In  bringing 
sand,  stone  and  cementing  substances  into  intimate  contact  (Fig.  14),  it  acts  physically  in  a 
manner  analogous  to  its  earlier  chemieal  role. 

Inevitably,  however,  this  desirable  function  of  water  is  closely  dependent  upon  its  fourth 

^  See  L.  N.  Edwards:  Proc.  Am.  Soc.  Test.  Mat.,  1917. 

D.  A.  Abrams:  Concrete  (C.  M.  Edition),  July,  1917. 


Sec.  1-43] 


MATERIALS 


33 


function — ^viz.,  its  occupancy  of  space.  It  is  readily  seen  that  if  the  minute  irregularities  in 
the  surface  of  stone  are  first  filled  with  water,  and,  because  of  initial  excess  of  water,  the  cement- 
ing solution  is  then  too  weak,  a  strong,  intimate  attachment  of  cement  will  be  inhibited,  both 
because  the  irregularities  are  already  filled  and  also  because  of  excessive  dilution. 

Furthermore,  water,  particularly  when  charged  with  gelatinous  aluminates  from  cement, 
has  ability  to  occlude  a  very  high  percentage  of  air.  This  air,  as  minute  bubbles,  firmly  attaches 
itself  to  the  sand  and  stone. ^  It  also  remains  between  parti- 
cles to  such  an  extent  as  oftentimes  to  completely  isolate  a  large 
percentage  of  the  materials.  Given  excess  water ,  therefore, 
and  a  proportionate  amount  of  occluded  air,  detriment  to  con- 
crete is  sure  to  arise  from  the  primary  fault  in  an  increasing 
ratio  (see  Fig.  15).  This  explains  to  a  large  degree  the  lower 
strengths  with  prolonged  mixing  in  present-type  machines 
found  by  some  investigators. 

43.  Influence  of  Quantity  of  Water  on  Lubrication  of 
Concrete  Mixture. — The  function  of  water  as  a  lubricant  of 
concrete  is  very  important,  but  its  importance  can  be  over- 
estimated, particularly  when  balanced  against  the  detrimental 
effects  which  may  and  often  do  result.  It  is  not  necessary  fig.  14— Cement  particles 
to  add  great  quantities  of  water  to  concrete  to  make  it  easy-    ^^i'^^  9yer  surfaces  of  sand  grains. 

°  ^  (.Magnined  20  cliams.) 

flowing  if  the  concrete  is  sufficiently  mixed.  The  more  con- 
crete is  mixed,  the  smoother  working  it  becomes  and  the  less  water  is  superficially  evident. 
Cement  is  continually  hydrating  in  the  mixing  action;  and  in  process  of  hydration,  large 
quantities  of  hydrated  lime  are  formed.  This  has  a  very  pronounced  effect  in  lubricating 
the  mass,  and  furthermore  keeps  it  coherent.  Excess  water,  on  the  other  hand,  promotes 
separation  of  the  constituent  materials,  offsetting  the  good  effects  of  hydration  and  render- 
ing the  concrete  extremely  harsh  in  working  and 
difficult  to  handle.  More  mixing,  therefore,  or 
more  efficient  mixing  through  improved  mixing 
devices,  should  -be  relied  upon  for  easy  placing, 
rather  than  excess  water, 

44.  Influence  of  Quantity  of  Water  on 
Space  Occupied  in  Resulting  Concrete. — The 
fourth  function  of  water  in  concrete — that  of 
occupying  space  in  the  mass — is  so  important 
and  so  varied  in  its  manifestations  that  a  large 
treatise  would  be  too  small  for  adequate  pre- 
sentation. A  few  leading  considerations  may, 
however,  serve  to  stimulate  individual  thought 
in  this  regard. 

There  are  few  substances  so  incompressible 
as  water.  Beyond  question,  although  water  is 
mobile,  a  given  quantity  occupies  definite  space. 
Concrete  in  forms  is  essentially  in  a  confined  space. 
In  this  form  space  are  cement,  sand,  stone,  and 
water,  each  occupying  its  proportionate  share  of 
the  total  volume  of  concrete.  So  long  as  the  form  remains  tight,  these  substances  must  all 
remain  substantially  in  place.  If  the  form  leaks,  which  is  contrary  to  practice,  more  or  less 
water,  with  a  greater  or  less  quantity  of  cement  in  solution,  may  escape.  This  escape  may  be 
before,  or  after  the  mass  has  taken  either  initial  or  final  set.    In  this  latter  case,  a  hollow  space, 

1  See  Ost,wald:  "Colloidal  Chemistry,"  p.  70-118. 
3 


Fig.  15. — Water  and  air  voids  in  concrete. 
(Natural  size.) 


34 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-45 


Fig.  16. — Water  voids  in  concrete. 
(Magnified  18  diams.) 


or  void  of  greater  or  less  volume  remains  in  the  concrete  where  once  was  water  in  greater  or  less 
(luantity  or  a  solution  too  dilute  to  solidify  (see  Fig.  16).  But  leakage  need  not  necessarily 
occur  in  this  way.  After  forms  are  removed,  any  uncombined  water  or  dilute  solution  will  be 
free  to  escape,  either  by  gravity,  or  by  capillary  suction  aided  by  evaporation,  leaving  behind  as 

a  void  the  space  it  required  in  the  mass.  Such 
action  is  evidenced  in  hundreds  of  concretes 
examined. 

45.  Harmful  Effects  of  Voids  Caused  by 
Excess  Water. — From  the  above  it  is  evident 
that  the  more  uncombined  water,  the  more  voids 
in  the  set  concrete.  Conversely,  the  more  voids, 
the  less  the  closeness  of  compacting  of  sand  and 
stone;  and  the  less  this  compacting,  the  less  the 
density,  strength,  durability  and  value  of  the 
hardened  mass.  Furthermore,  the  proportions 
of  the  concrete  are  seriously  unbalanced  (see  Arts. 
2  and  16,  Sect.  2). 

The  space  loss  referred  to  is  only  a  small 
part  of  the  ultimate  damage.  Physical  stress 
due  to  loading  may  be  the  least  intense  of  the 
stresses  to  which  concrete  is  subjected.  Physical, 
or  chemical  and  physico-chemical  stresses  set 
up  *  in  the  mass  after  hardening,  through  dis- 
ruptive freezing,  or  through  percolating  water 
alone  or  carrying  chemically  active  agents,  are  of  far  greater  intensity.  Each  pore,  or  void, 
is  a  potential  aid  to  such  destructive  agents;  and  enlarged  by  initial  attack,  soon  become 
an  active  aid  and  abettor.  First  loss,  therefore,  may  be  of  minor  importance.  Induced 
weaknesses,  augmenting  primary  deficiencies,  must  be  reckoned  with  to  an  increasing  degree. 

46.  Excess  Water  the  Cause  of  Day's  Work  Planes. — Perhaps  the  commonest  evidence, 
to  be  found  on  every  hand,  as  to  the  effects  of  excess  water  in  concrete  are  "day's  work  planes." 
In  the  early  life  of  a  structure  such  as  a  buttress  wall,  these  planes  are  hidden  either  by  a  smooth 
mortar  surface  at  contact  with  forms,  or  by  a  later-applied  wash  or  coat  of  cement  plaster. 
But  as  months  pass  and  the  structure  is  subjected  to  water  action  in  greater  or  less  degree, 
from  one  source  or  another,  these  planes  are  made  more  and  more  evident  by  seepage  along  them. 
When  such  seepage  is  in  quantity,  it  may  be  detected  as  a  film  of  water,  or,  with  rapid  evapora- 
tion, by  crystalline  deposits.  When  seepage  is  less,  it  may  be  evidenced  by  a  patch  of  efflores- 
cence, but  in  each  case  the  underlying  cause  of  water  passage  is  "laitance, "  which  is  largely 
caused  by  the  use  of  excess  water. 

47.  Excess  Water  the  Cause  of  Large  Laitance  Deposits. — "Laitance,"  or  "day's  work 
planes,"  may  be  of  small  bulk,  relative  to  the  total  mass  of  concrete,  yet  in  some  instances, 
laitance  is  found  to  an  exaggerated  and  oftentimes  to  a  dangerous  extent.  Whenever  forms 
are  filled  by  dumping  concretes  continuously  in  one  spot,  with  dependence  upon  hoeing-down, 
or  natural  flow  for  distribution  of  heavier  materials  into  lower  parts  of  forms,  it  is  inevitable 
that  water  and  the  finer  materials  suspensible  in  water,  including  much  of  the  cement,  should 
separate  from  the  heavier  materials;  and  that  they  should  form,  when  solidified  above  the  con- 
crete a  deposit  or  stratum  of  greater  or  less  thickness  and  extent,  which  will  be  entirely  composed 
of  muck  or  "laitance."  This  material  is  chalky  and  of  low  strength.  It  is  very  absorbent; 
and  when  saturated  is  of  little  better  value  than  so  much  wet,  sandy  clay. 

Instances  of  the  formation  of  "laitance  "  in  quantities  and  in  situations  where  it  is  dangerous 
are  foinid  in  columns  poured  in  two  or  more  sections.  Although  not  approved  by  building  codes, 
contractors,  for  their  own  convenience  or  to  save  on  forms,  will  sometimes  pour  half  a  column, 
allowing  it  to  set  before  continuing  to  the  top.    Inevitably,  lighter  materials  rise  in  the  form. 


Sec.  1-48] 


MATERIALS 


35 


Necessarily  the  joint  thus  formed  in  the  middle  of  the  column  is  of  inferior  material;  and  of 
a  material  which  cannot  bond  with  material  subsequently  poured.  If  this  procedure  is  again 
followed,  the  lighter  part  of  this  latter  also  rises  so  that  a  stratified  column,  with  another 
''laitance"  section  at  the  column  head  will  result.  If  after  removal  of  forms  this  material 
should  become  wet  from  any  cause,  crushing  and  sHding  is  to  be  expected  with  possibly  collapse 
of  the  column  and  its  supported  load.  Columns  should  not  only  be  poured  in  one  section,  but 
they  furthermore  should  be  poured  of  concrete  of  such  consistency  that  "laitance"  will  not 
accumulate;  and  it  would  also  be  a  desirable  precaution  to  overflow  the  form  to  remove  such 
accumulations  as  may  rise.  It  is  better  to  waste  a  portion  of  material  at  the  top,  in  order  to 
be  sure  that  there  may  be  no  ''laitance"  at  the  column  head,  rather  than  to  have  any  question 
as  to  strength  or  security.  ^ 

48.  Excess  Water  and  Waterproof  Concrete. — It  is  difficult  to  find  a  truly  waterproof 
field  concrete,  largely  because  excess  water  is  so  generally  used  in  mixing.  The  majority  of 
structures  are  of  such  size  that  they  cannot  be  poured  continuously.  This  necessarily  means 
stoppage  of  work  for  greater  or  less  intervals.  Stoppage  of  work  with  wet  concretes  always 
means  a  layer  of  ''laitance;"  and  this  inevitably  prevents  succeeding  layers  from  bonding, 
entailing  a  chain  of  consequences.  A  radical  change  in  such  field  procedures  is  demanded,  if 
these  difficulties  are  to  be  overcome. 

49.  Excess  Water  Causes  Unsatisfactory  Concrete  Floor  Surfaces.  ^ — It  is  difficult  to 
insure  that  concrete  floors  shall  be  dustless.  The  functions  of  a  concrete  floor  are  to  bear  loads 
as  well  as  to  withstand  abrasion  and  impact,  these  latter  being  the  severest  service  to  which 
it  is  subjected.  It  is  unfortunate  that  the  top  of  a  concrete  floor  is  the  surface  on  which  depend- 
ence is  placed,  as  in  possibly  nine  cases  out  of  ten,  this  surface  coat,  both  by  virtue  of  its  initial 
consistency  and  also  because  of  water  later  brought  to  the  surface  through  troweling,  is  partly 
or  wholly  composed  of  ''laitance." 

To  remedy  these  defects,  floor  hardeners  of  one  kind  or  another,  are  added  to  the  concrete 
in  mixing.  Few  of  these  substances  should  have  any  real  place  in  the  concrete-floor  industry. 
Most  are  inferior  to  quartz  sand  in  hardness  and  strength,  but  because  of  the  prevalence  of 
unsatisfactory  concrete  floors  and  because  of  the  human  tendency  to  escape  consequences  by 
purchasing  immunities,  such  alleged  remedies  find  ready  sale.  If,  instead  of  buying  integral 
floor  hardeners,  less  water  were  put  into  concrete  floors  and  a  good  quality  of  graded  sand  with 
Portland  cement  used  in  well-mixed  and  properly  placed  concrete,  there  would  be  less  need  of 
tonics. 

60.  Excess  Water  Prevents  Bonding  New  Concrete  to  Old. — One  result  that  can  be  gua- 
ranteed is  the  failure  of  effective  bonding  between  new  concrete  and  old.  Various  expedients 
from  time  to  time  have  been  claimed  to  bring  about  effective  results  in  this  regard,  but  little 
has  as  yet  been  unquestionably  accomplished.  Washing  the  surface  of  old  concrete  with  hydro- 
chloric acid  is  ineffective  and  wrong  except  so  far  as  it  may  clean  off  surface  dirt  and  carbonated 
deposits.  Picking  the  surface  rarely  goes  deep  enough  or  covers  enough  surface.  The  inher- 
ent difficulty  underlying  all  attempts  at  bonding,  is  the  identical  trouble  that  causes  day's 
work  planes,  or  that  makes  the  wearing  surface  of  concrete  floors  unsatisfactory,  i.e.,  the  exist- 
ence of  a  light,  chalky,  insecure  material,  substituted  at  the  critical  plane  for  a  substance  which 
should  be  durable  and  secure. 

51.  Excess  Water  and  Concreting  in  Cold  Weather. — Concreting  in  cold  weather  is  always 
attended  by  some  risk,  even  when  forms  remain  in  place  until  milder  weather.  Heating  of 
aggregates  is  seldom  adequate,  and  the  heat  transmitted  through  wooden  forms  after  pouring 
is  small  in  quantity.  It  should  be  remembered  that  at  40°F.  the  reaction  between  water  and 
cement  and  the  production  of  cementing  strength  is  only  one-fourth  as  rapid  as  at  50°F.  and 
less  than  one-ninth  as  rapid  as  at  70°F.  Dilution  by  excess  water  of  such  feeble  solutions 
increases  the  danger,  as  is  evidenced  by  frequent  winter  failures.    Furthermore,  at  39°F. 

^See  Gillmore:  "On  Limes,  Hydraulic  Cements  and  Mortars,"  1872;  p.  242. 
2  See  Sect.  4,  "Concrete  Floors  and  Floor  Surfaces,  Sidewalks,  and  Roadways." 


36 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-52 


some  subtle  change  occurs  in  water  which  decreases  its  chemical  ability  even  before  actual 
freezing ;i  and  at  this  latter  point  occurs  expansion  of  8%  by  volume,  with  exertion  of  some  300 
tons  disruptive  pressure  per  square  inch  of  surface. 

The  greater  the  quantity  of  water  in  a  cold-weather  concrete,  therefore,  the  greater  the 
liability  to  dilution,  little  strength,  frost  disruptions,  and  failures.  The  potency  of  excess 
water  in  these  respects  is  just  beginning  to  receive  due  recognition. 

52.  Suggested  Procedures  to  Guard  Against  Use  of  Excess  Water. — Excess  water  in  con- 
crete should  be  rigidly  guarded  against.  To  insure  the  use  of  less  water,  specifications  must 
embody  provisions  giving  the  engineer  authority  for  its  regulation.  To  this  end,  the  following 
partial  specification  is  suggested: 

1.  Concrete  shall  be  an  intimate  mixture  of  sand,  stone  (or  gravel),  cement  and  water 
of  the  several  kinds  and  qualities  herein  specified  and  in  proportions  as  specified,  subject  to 
modification  by  the  Engineer. 

2.  The  proportions  and  quantities  of  all  materials,  including  water,  shall  be  as  directed  by 
the  engineer  and  shall  be  subject  at  all  times  to  such  change  as  his  tests  or  judgment  may 
dictate  as  advisable. 

3.  All  materials  shall  be  accurately  measured  in  measures  of  approved  type  and  known 
capacity. 

Cement  shall  be  measured  by  the  standard  sack  or,  if  in  bulk,  by  weight,  94  lb.  being 
taken  as  an  equivalent  of  one  sack.    Loose  measurement  of  cement  is  prohibited. 

Sand  and  stone  shall  be  measured  in  struck  measures  of  a  capacity  and  type  approved  by 
the  engineer.  Measurement  in  wheelbarrows  of  a  type  which  do  not  admit  of  a  struck  measure- 
ment will  not  be  permitted. 

Water  shall  be  measured  at  each  mixer  in  containers  adapted  to  ready  adjustment  and  to 
accurate  delivery  of  variable  quantities.  Supplementing  the  delivery  of  such  measuring  con- 
tainers by  additions  of  water,  because  of  slowness  of  discharge  or  for  any  other  reason,  will  not 
be  permitted. 

4.  Concrete  of  a  plastic  consistency  shall  be  required  in  all  parts  of  the  work,  unless  per- 
mission be  given  by  the  engineer  for  the  use  of  drier  and  stiffer  mixtures.  Sloppy  and  overwet 
concretes  are  strictly  prohibited.  The  quantity  of  water,  therefore,  will  be  subject  to  regulation 
at  all  times  by  the  engineer  according  to  the  requirements  of  the  aggregates  in  use  at  that  time.  The 
rejection  and  removal  of  overwet  concretes  either  before  or  after  placing  in  forms  may,  at 
the  engineer's  discretion,  be  required  of  the  contractor  without  compensation. 

REINFORCEMENT 

53.  Types  of  Reinforcement. — The  reinforcing  steel  in  reinforced-concrete  construction 
is  mostly  in  the  form  of  rods,  or  bars,  of  round  or  square  cross-section.  These  vary  in  size  from 
K  to  %  in.  for  light  floor  slabs,  up  to  iVi  to  1}4  in.  as  a  maximum  size  for  heavy  beams  and 
columns.  Both  plain  and  deformed  bars  are  used.  With  plain  bars  the  adhesion  between  steel 
and  concrete  is  depended  upon  to  furnish  the  necessary  bond  strength.  With  deformed  bars 
the  usual  adhesion  is  supplemented  by  a  mechanical  bond,  the  amount  of  this  bond  in  any 
given  case  depending  upon  the  shape  of  the  bar.  The  adhesion  of  concrete  to  flat  bars  is  less 
than  for  round  or  square  bars,  but  the  flat  deformed  bar  possesses  advantages  over  other  forms 
when  used  as  hooping  for  tanks,  pipes,  and  sewers  where  the  reduc  ed  thickness  of  the  bar  allows 
the  concrete  section  to  have  a  greater  effective  depth  for  the  same  total  thickness  of  concrete. 

Wire  fabric  and  expanded  metal  in  various  forms  are  used  to  a  considerable  extent  in 
slabs,  pipes,  and  conduits.  These  types  of  reinforcement  are  easy  to  place  and  are  especially 
well  adapted  to  resist  temperature  cracks  and  to  prevent  cracking  of  the  concrete  from  impact 
or  shock. 

1  See  O.  D.  Van  Engelen:  Century  Magazine,  April,  1917. 


Sec.  1-54] 


MATERIALS 


37 


A  number  of  combinations  of  forms  are  employed  to  a  greater  or  less  extent.  These 
combinations  are  known  as  systems. 

54.  Surface  of  Reinforcement. — A  rough  surface  on  steel  has  a  higher  bond  value  for  use 
in  concrete  than  a  smooth  surface,  consequently  a  thin  film  of  rust  on  reinforcement  should  not 
cause  its  rejection.  In  fact  in  the  case  of  cold-drawn  wire  which  presents  a  very  smooth  surface, 
a  slight  coating  of  rust  is  a  decided  advantage.  Loose  or  scaly  rust,  however,  should  never  be 
allowed.  Reinforcement  in  this  state  of  corrosion  may  be  used  if  first  cleansed  with  a  stiff 
wire  brush  or  given  a  bath  of  hydrochloric  acid  solution  (consisting  of  3  parts  acid  to  1  part 
water)  and  then  washed  in  clean  running  water.  Oiling  and  painting  of  reinforcing  steel 
should  not  be  permitted  as  its  bonding  value  is  greatly  reduced  thereby. 

55.  Quality  of  Steel. — Authorities  differ  as  to  the  quality  of  steel  to  be  used  for  reinforce- 
ment. Mild  steel  is  the  ordinary  structural  steel  occurring  in  all  structural  shapes.  High  steel 
or  steel  of  hard  grade  has  a  greater  percentage  of  carbon  than  mild  steel  and  is  also  known  as 
high-carbon  or  high  elastic-limit  steel. 

Brittleness  is  to  be  feared  in  high  steel,  although  this  quality  is  not  so  dangerous  when  the 
metal  is  used  in  heavy  reinforced-concrete  members — for  example,  in  heavy  beams  or  slabs — ■ 
as  the  concrete  to  a  large  extent  absorbs  the  shocks  and  pro- 
tects the  steel.    All  high  steel  should  be  carefully  inspected 
and  tested  in  order  to  prevent  any  brittle  or  cracked  material 
from  getting  into  the  finished  work.    Steel  of  high  elastic      Fig.  17.— Cold-twisted  square  bar. 
limit  is  seldom  employed  where  plain  bars  are  used. 

Cold  twisting  increases  the  elastic  limit  and  ultimate  strength  of  mild-steel  bars.  The 
increase,  however,  is  not  definite,  varying  greatly  with  slight  variations  in  the  grade  of  the 
rolled  steel.    A  square  twisted  bar  is  shown  in  Fig.  17. 

56.  Working  Stresses. — The  generally  accepted  working  stress  for  mild  steel  is  16,000 
lb.  per  sq.  in.  and  18,000  to  20,000  lb.  per  sq.  in.  for  high  steel  and  cold-twisted  steel.  A  stress 
not  greater  than  16,000  lb.  per  sq.  in.  is  recommended  by  the  Joint  Committee  for  all  grades  of 
steel. 

57.  Coefficient  of  Expansion. — The  coefficient  of  expansion  of  steel  is  approximately 
0.0000065  degree  Fahreinheit. 

58.  Modulus  of  Elasticity. — The  modulus  of  elasticity  of  all  grades  and  kinds  of  steel  is 
about  the  same  and  is  usually  taken  as  30,000,000  lb.  per  sq.  in.  in  both  tension  and  compression. 

59.  Steel  Specifications. — The  following  specifications  are  those  of  the  Association  of 
American  Steel  Manufacturers  for  concrete  reinforcement  bars  rolled  from  billets,  adopted 
March  22,  1910  (revised  1912  and  1914) : 

Manufacturers'  Standard  Specifications  for  Concrete  Reinforcement  Bars 

Rolled  from  Billets 

1.  Manufacture. — Steel  may  be  made  by  either  the  open-hearth  or  Bessemer  process.  Bars  shall  be  rolled 
from  standard  new  billets. 

2.  Chemical  and  Physical  Properties. — The  chemical  and  physical  properties  shall  conform  to  the  limits  as 
shown  in  the  table  on  the  following  page. 

3.  Chemical  Determinations. — In  order  to  determine  if  the  material  conforms  to  the  chemical  limitations 
prescribed  in  paragraph  2  herein,  analysis  shall  be  made  by  the  manufacturer  from  a  test  ingot  taken  at  the  time 
of  the  pouring  of  each  melt  or  blow  of  steel,  and  a  correct  copy  of  such  analysis  shall  be  furnished  to  the  engineer 
or  his  inspector. 

4.  Yield  Point. — For  the  purposes  of  these  specifications,  the  yield  point  shall  be  determined  by  careful  ob- 
servation of  the  drop  of  the  beam  of  the  testing  machine,  or  by  other  equally  accurate  method. 

5.  Form  of  Specimens. — (a)  Tensile  and  bending  test  specimens  may  be  cut  from  the  bars  as  rolled,  but 
tensile  and  bending  test  specimens  of  deformed  bars  may  be  planed  or  turned  for  a  length  of  at  least  9  in.  if  deemed 
necessary  by  the  manufacturer  in  order  to  obtain  uniform  cross-section. 

(b)  Tensile  and  bending  test  specimens  of  cold-twisted  bars  shall  be  cut  from  the  bars  after  twisting,  and  shall 
be  tested  in  full  size  without  further  treatment,  unless  otherwise  specified  as  in  (c),  in  which  case  the  conditions 
thereon  stipulated  shall  govern. 

(c)  If  it  is  desired  that  the  testing  and  acceptance  for  cold-twisted  bars  be  made  upon  the  hot-rolled  bars 
before  being  twisted,  the  hot-rolled  bars  shall  meet  the  requirements  of  the  structural-steel  grade  for  plain  bars 
shown  in  this  specification. 


38 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-59 


Structural-steel 

Intermediate 

Hard  errade 

grade 

grade 

Cold- 

Properties  considered 

Plain 
bars 

ue- 
formed 
bars 

Plain 
bars 

Via 

formed 
bars 

Plain 
bars 

De- 
formed 
bars 

twisted 

Phosphorus  maximum:  Bessemer.  .  .. 

0.10 



0.10 

0.10 

0.10 

0.10 

0.10 

0.10 

0.06 

0.06 

0.06 

0.06 

0.06 

0.06 

0  06 

Ultimat/6  tensile  strength^  lb.  per  sq. 

Tn/s"!  nnn 

80,000 

80,000 

in. 

min. 

min. 

only 

Yield  point,  minimum  lb.  per  sq.  in. . 

33,000 

33.000 

40,000 

40,000 

50,000 

50,000 

•^^  nnn 

Elongation,  %  in  8-in.  minimum.  .  .  . 

1,400,000 

1,250,000 

l,oOO,OUO 

1,125,000 

1,200,000 

1,000,000 

5% 

Tens.  str. 

Tens.  str. 

Tens.  str. 

Tens.  str. 

Tens.  str. 

Tens.  str. 

Cold   bend   without   fracture:  Bars 

180  deg. 

180  deg. 

180  deg. 

180  deg. 

180  deg. 

180  deg. 

180  deg. 

under  ?4-in.  diameter  or  thickness. 

d  =  It 

d  =  2t 

d  =  2t 

d  =  3t 

d  =  St 

d  =  4< 

d  =  2t 

Bars  ?4-in.  diameter  or  thickness  and 

180  deg. 

180  deg. 

90  deg. 

90  deg. 

90  deg. 

90  deg. 

180  deg. 

over. 

d  It 

d  =  2t 

d  =  2t 

d  =  3t 

d  =  3t 

d  =  4t 

d  =  3t 

The  intermediate  and  hard  gra 

des  will  be 

used  only 

when  spe 

cified. 

6.  Number  of  Tests. — (a)  At  least  one  tensile  and  one  bending  test  shall  be  made  from  each  melt  of  open- 
hearth  steel  rolled,  and  from  each  blow  or  lot  of  10  tons  of  Bessemer  steel  rolled.  In  case  bars  differing  H  in.  and 
more  in  diameter  or  thickness  are  rolled  from  one  melt  or  blow,  a  test  shall  be  made  from  the  thickest  and  thinnest 
material  rolled.  Should  either  of  these  test  specimens  develop  flaws,  or  should  the  tensile  test  specimen  break 
outside  of  the  middle  third  of  its  gaged  strength,  it  may  be  discarded  and  another  test  specimen  substituted  there- 
for.   In  case  a  tensile  test  specimen  does  not  meet  the  specifications,  an  additional  test  may  be  made. 

(6)  The  bending  test  may  be  made  by  pressure  or  by  light  blows. 

7.  Modifications  in  Elongation  for  Thin  and  Thick  Material. — For  bars  less  than  Yie  in.  and  more  than  % 
in.  nominal  diameter  or  thickness,  the  following  modifications  shall  be  made  in  the  requirements  for  elongation: 

(o)  For  each  increase  of  }^  in.  in  diameter  or  thickness  above  %  in.  a  deduction  of  1  shall  be  made  from  the 
specified  percentage  of  elongation. 

{b)  For  each  decrease  of  Me  in.  in  diameter  or  thickness  below  Yie  in.  a  deduction  of  1  shall  be  made  from  the 
specified  percentage  of  elongation. 

(,c)  The  above  modifications  in  elongation  shall  not  apply  to  cold-twisted  bars. 

8.  Number  of  Twists. — Cold-twisted  bars  shall  be  twisted  cold  with  one  complete  twist  in  a  length  equal  to 
not  more  than  12  times  the  thickness  of  the  bar. 

9.  Finish. — Material  must  be  free  from  injurious  seams,  flaws  or  cracks,  and  have  a  workmanlike  finish. 

10.  Variation  in  Weight. — Bars  for  reinforcement  are  subject  to  rejection  if  the  actual  weight  of  any  lot  varies 
more  than  5  %  over  or  under  the  theoretical  weight  of  that  lot. 

The  following  specifications  are  those  of  the  American  Society  for  Testing  Materials  for 
concrete  reinforcement  bars  rolled  from  billets: 

Standard  Specifications  for  Billet-steel  Concrete  Reinforcement  Bars 

(American  Society  for  Testing  Materials) 

1.  (o)  These  specifications  cover  three  classes  of  billet-steel  concrete  reinforcement  bars,  namely:  plain, 
deformed  and  cold-twisted. 

(6)  Plain  and  deformed  bars  are  of  three  grades,  namely:  structural-steel,  intermediate  and  hard. 

2.  (a)  The  structural-steel  grade  shall  be  used  unless  otherwise  specified. 

(fe)  If  desired,  cold-twisted  bars  may  be  purchased  on  the  basis  of  tests  of  the  hot-rolled  bars  before  twist- 
ing, in  which  case  such  tests  shall  govern  and  shall  conform  to  the  requirements  specified  for  plain  bars  of  structural- 
steel  grade. 

Manufacture. — 3.  (a)  The  steel  may  be  made  by  the  Bessemer  or  open-hearth  process. 
(6)  The  bars  shall  be  rolled  from  new  billets.    No  reroUed  material  will  be  accepted. 

4.  Cold  twisted  bars  shall  be  twisted  cold  with  one  complete  twist  in  a  length  not  over  12  times  the  thickness 
of  the  bar. 

Chemical  Properties  and  Tests. — 5.  The  steel  shall  conform  to  the  following  requirements  as  to  chemical 
composition: 


Sec.  1-591 


MATERIALS 


39 


Phosphorus,  Bessemer  not  over  0.10% 

Open-hearth  not  over  0 . 05  % 

6.  An  analysis  of  each  melt  of  steel  shall  be  made  by  the  manufacturer  to  determine  the  percentages  of  car- 
bon, manganese,  phosphorus  and  sulphur.  This  analysis  shall  be  made  from  a  test  ingot  taken  during  the  pouring 
of  the  melt.  The  chemical  composition  thus  determined  shall  be  reported  to  the  purchaser  or  his  representative, 
and  shall  conform  to  the  requirements  specified  in  Sect.  5. 

7.  Analyses  may  be  made  by  the  purchaser  from  finished  bars  representing  each  melt  of  open-hearth  steel, 
and  each  melt,  or  lot  of  10  tons,  of  Bessemer  steel.  The  phosphorus  content  thus  determined  shall  not  exceed  that 
specified  in  Sect.  5  by  more  than  25%. 

Physical  Properties  and  Tests. — 8.  (a)  The  bars  shall  conform  to  the  following  requirements  as  to  tensile 
properties: 


Plain  bars 

Df;formed  bars 

Cold- 
twisted 
bars 

Properties  considered 

Structural- 
steel 
grade 

Inter- 
mediate 
grade 

Hard 
grade 

Structural- 
steel 
grade 

Inter- 
mediate 
grade 

Hard 
grade 

Tensile  strength,  lb.  per  sq. 

55,000 

70,000 

80,000 

55,000 

70,000 

80,000 

Recorded 

in. 

to 
70,000 

to 
85,000 

min. 

to 
70.000 

to 
85.000 

min. 

only 

Yield  point,  min.,  lb.  per  sq. 
in. 

33,000 

40,000 

50,000 

33,000 

40,000 

50,000 

55,000 

Elongation  in  8  in.  min.  %' 

1,400,000 

1,300,000 

1,200,000 

1,250,000 

1.125,000 

1,000,000 

5 

Tens.  str. 

Tens.  str. 

Tens.  str. 

Tens.  str. 

Tens.  str. 

Tens.  str. 

1  See  Sect.  9. 


(b)  The  yield  point  shall  be  determined  by  the  drop  of  the  beam  of  the  testing  machine. 

9.  (a)  For  plain  and  deformed  bars  over  in.  in  thickness  or  diameter,  a  deduction  of  1  from  the  percent- 
ages of  elongation  specified  in  Sect.  8(o)  shall  be  made  for  each  increase  of  }i  in.  in  thickness  or  diameter  above 
Vi  in. 

(b)  For  plain  and  deformed  bars  under  Yie  in.  in  thickness  or  diameter,  a  deduction  of  1  from  the  percentages 
of  elongation  specified  in  Sect.  8(a)  shall  be  made  for  each  decrease  of  Mo  in-  in  thickness  or  diameter  below  lie  in. 

10.  The  test  specimen  shall  bend  cold  around  a  pin  without  cracking  on  the  outside  of  the  bent  portion,  as 
follows : 


Thickness  or  diameter  of 
bar 

Plain  bars 

Deformed  bars 

Cold- 
twisted 
bars 

Structural- 
steel 
grade 

Inter- 
mediate 
grade 

Hard 
grade 

Structural- 
steel 
grade 

Inter- 
mediate 
grade 

Hard 
grade 

180  deg. 

d  =  t 
180  deg 

d  =  t 

180  deg. 
d  =  2t 
90  deg. 
d  =  2t 

180  deg. 
d  =  3t 
90  deg. 

d  =  3t 

180  deg. 

d  =  t 
180  deg. 

d  =  2t 

180  deg. 
d  =  Zt 
90  deg. 

d  =  3t 

180  deg. 
d  =  U 
90  deg. 
d  =  \t 

180  deg. 
d  =  2t 
ISO  deg. 

d  =  3< 

d  =  diameter  of  pin  about  which  the  specimen  is  bent. 
t  =  thickness  or  diameter  of  specimen. 


11.  (a)  Tension  and  bend  test  specimens  for  plain  and  deformed  bars  shall  be  taken  from  the  finished  bars, 
and  shall  be  of  the  full  thickness  or  diameter  of  bars  as  rolled;  except  that  the  specimens  for  deformed  bars  may  be 
machined  for  a  length  of  at  least  9  in.,  if  deemed  necessary  by  the  maiiufacturer  to  obtain  uniform  cross-section. 

(6)  Tension  and  bend  test  specimens  for  cold-twisted  bars  shall  be  taken  from  the  finished  bars,  without 
further  treatment;  except  as  specified  in  Sect.  2(6). 

12.  (a)  One  tension  and  one  bend  test  shall  be  made  from  each  melt  of  open-hearth  steel,  and  from  each  melt, 
or  lot  of  10  tons,  of  Bessemer  steel;  except  that  if  material  from  one  melt  differs  %  in.  or  more  in  thickness  or  diam- 
eter, one  tension  and  one  bend  test  shall  be  made  from  both  the  thickest  and  the  thinnest  material  rolled. 

(6)  If  any  test  specimen  shows  defective  machining  or  develops  flaws,  it  may  be  discarded  and  another  soeci- 
men  substituted. 


40 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-59 


(c)  If  the  percentage  of  elongation  of  any  tension  test  specimen  is  less  than  that  specified  in  Sect.  8(a)  and  any 
part  of  the  fracture  is  outside  the  middle  third  of  the  gage  length,  as  indicated  by  scribe  scratches  marked  on  the 
specimen  before  testing,  a  retest  shall  be  allowed. 

Permissible  Variations  in  Weight. — 13.  The  weight  of  any  lot  of  bars  shall  not  vary  more  than  5%  from  the 
theoretical  weight  of  that  lot. 

Finish. — 14.    The  finished  bars  shall  be  free  from  injurious  defects  and  shall  have  a  workmanlike  finish. 

Inspection  and  Rejection. — 15.  The  inspector  representing  the  purchaser  shall  have  free  entry,  at  all  times 
while  work  on  the  contract  of  the  purchaser  is  being  performed,  to  all  parts  of  the  manufacturer's  works  which  con- 
cern the  manufacture  of  the  bars  ordered.  The  manufacturer  shall  afford  the  inspector,  free  of  cost,  all  reasonable 
facilities  to  satisfy  him  that  the  bars  are  being  furnished  in  accordance  with  these  specifications.  All  tests  (except 
check  analyses')  and  inspection  shall  be  made  at  the  place  of  manufacture  prior  to  shipment,  unless  otherwise  speci- 
fied, and  shall  be  so  conducted  as  not  to  interfere  unnecessarily  with  the  operation  of  the  works. 

16.  (a)  Unless  otherwise  specified,  any  rejection  based  on  tests  made  in  accordance  with  Sect.  7  shall  be  re- 
ported within  5  working  days  from  the  receipt  of  the  samples. 

(6)  Bars  which  show  injurious  defects  subsequent  to  their  acceptance  at  the  manufacturer's  works  will  be 
rejected,  and  the  manufacturer  shall  be  notified. 

17.  Samples  tested  in  accordance  with  Sect.  7,  which  represent  rejected  bars,  shall  be  preserved  for  2  weeks 
from  the  date  of  the  test  report.  In  case  of  dissatisfaction  with  the  results  of  the  tests,  the  manufacturer  may  make 
claim  for  a  rehearing  within  that  time. 

Reinforcing  bars  rolled  from  old  rails  are  being  used  tc  a  considerable  extent  in  reinforced- 
concrete  work  and  seem  to  be  giving  satisfaction,  especially  for  unimportant  work  such  as 
footings,  retaining  walls,  and  possibly  in  slabs  where  the  failure  of  one  rod  could  not  wreck 
the  structure.  The  specifications  for  rail-steel  concrete  reinforcement  bars  adopted  by  the 
Association  of  American  Steel  Manufacturers  April  20,  1912  (revised  April  21,  1914)  are  as 
follows : 


Manufacturers'  Standard  Specifications  for  Rail-steel  Concrete  Reinforcement  Bars 

1.  Manufacture. — All  steel  shall  be  rolled  from  standard  section  Tee  rails. 

2.  Physical  Properties. — The  physical  properties  shall  conform  to  the  following  limits: 

3.  Yield  Point. — For  the  purposes  of 
these  specifications,  the  yield  point  shall 
be  determined  by  careful  observation  of 
the  drop  of  the  beam  of  the  testing  ma- 
chine, or  by  other  equally  accurate  method. 

4.  Form  of  Specimens. —  (a)  Tensile 
and  bending  test  specimens  may  be  cut 
from  the  bars  as  rolled,  but  tensile  and 
bending  test  specimens  of  deformed  bars 
may  be  planed  or  turned  for  a  length  of 
at  least  9  in.  if  deemed  necessary  by  the 
manufacturer  in  order  to  obtain  uniform 
cross-section. 

(6)  Tensile  and  bending  test  speci- 
mens of  hot-twisted  bars  shall  be  cut  from 
the  bars  after  twisting,  and  shall  be  tested 
in  full  size  without  further  treatment,  un- 
less otherwise  specified. 

5.  Number  of  Tests. — (a)  One  ten- 
sile and  one  bending  test  shall  be  made 
from  each  lot  of  10  tons  or  less  of  each 

size  of  bar  rolled  from  rails  varying  not  more  than  10  lb.  per  yd.  in  nominal  weight.  Should  a  test  specimen 
develop  flaws,  or  should  the  tensile  test  specimen  break  outside  of  the  middle  third  of  its  gaged  length,  it  may 
be  discarded  and  another  test  specimen  substituted  therefore.  In  case  a  tensile  specimen  does  not  meet  the 
specifications,  an  additional  test  may  be  made. 

(b)  The  bending  test  may  be  made  by  pressure  or  by  light  blows. 

6.  Modtfications  in  Elongation  for  Thin  and  Thick  Material. — For  bars  less  than  ^ie  in.  and  more  than  ^4 
in.  nominal  diameter  or  thickness,  the  following  modifications  shall  be  made  in  the  requirements  for  elongation: 

(a)  For  each  increase  of  3^^  in.  in  diameter  or  thickness  above  ?4  in.,  a  deduction  of  1  shall  be  made  from 
the  specified  percentage  of  elongation. 

(6)  For  each  decrease  of  Me  in.  in  diameter  or  thickness  below  Yif,  in.,  a  deduction  of  1  shall  be  made 
from  the  specified  percentage  of  elongation. 

7.  Number  of  Twists. — Hot-twisted  bars  of  rail  carbon  steel  shall  be  twisted  with  one  complete  twist  in  a 
length  equal  to  not  more  than  12  times  the  thickness  of  the  bar. 


Rail-steel  grade 

Properties  considered 

Plain 
bars 

Deformed 
and  hot- 
twisted  bars 

Ultimate  tensile  strength,  minimum,  lb. 

per  sq.  in. 
Yield  point,  minimum,  lb.  per  sq.  in. .  .  . 

Elongation,  %  in  8-in.  minimum  

80,000 

50,000 
1,200,000 

80,000 

50,000 
1,000,000 

Tens.  str. 

Tens.  str. 

Cold  bend  without  fracture:  Bars  under 
H  in.  diameter  or  thickness. 

180  deg. 
d  =  3t 

180  deg. 
d  =  U 

Bars   H  in.  diameter  or  thickness  and 
over. 

90  deg. 

d  =  3t 

90  deg. 
d  =  'it 

Sec.  1-59] 


MATERIALS 


41 


8.  Finish. — Material  must  be  free  from  injurious  seams,  flaws  or  cracks,  and  have  a  workmanlike  finish. 

9.  Variation  in  Weight. — Bars  for  reinforcement  are  subject  to  rejection  if  the  actual  weight  of  any  lot 
varies  more  than  5%  over  or  under  the  theoretical  weight  of  that  lot. 


Properties  considered 

Plain  bars 

Deformed 
and  hot- 
twisted  bars 

Tensile  strength,  lb.  per  sq.  in  

80.000 
50,000 
1.200,000 

80.000 
50.000 
1.000,000 

Tens.  str. 

Tens.  str. 

1  See  Sect. 


ReroUed  bar  specifications  have  also  been  adopted  by  the  American  Society  for  Testing 
Materials  after  an  extended  series  of  tests.    The  specifications  follow: 

Standard  Specifications  for  Rail-steel  Concrete  Reinforcement  Bars 

(American  Society  for  Testing  Materials') 

1.  The  specifications  cover  three  classes  of  rail-steel  concrete  reinforcement  bars,  namely:  plain,  deformed, 
and  hot-twisted. 

Manufacture. — 2.  The  bars  shall  be  rolled  from  standard  section  Tee  rails. 

3.  Hot-twisted  bars  shall  have  one  complete  twist  in  a  length  not  over  12  times  the  thickness  of  the  bar. 

Physical  Properties  and  Tests. — 4.  (a)  The  bars  shall  conform  to  the  following  minimum  requirements  as 
to  tensile  properties: 

{h)  The  yield  point  shall  be  deter- 
mined by  the  drop  of  the  beam  of  the  test- 
ing machine. 

5.  (a)  For  bars  over  Yi  in.  in  thick- 
ness or  diameter,  a  deduction  of  1  from  the 
percentages  of  elongation  specified  in  Sect. 
4(a)  shall  be  made  for  each  increase  of 
in.  in  thickness  or  diameter  above  ?4  in. 

(6)  For  bars  under  Jle  in.  in  thickness 
or  diameter,  a  deduction  of  1  from  the  per- 
centages of  elongation  specified  in  Sect.  4(a) 
shall  be  made  for  each  decrease  of  Me  in. 
in  thickness  or  diameter  below  Ha  in. 

6.  The  test  specimen  shall  bend  cold  around  a  pin  without  cracking  on  the  outside  of  the  bent  portion,  as 
follows: 

7.  (a)  Tension  and  bend  test  speci- 
mens for  plain  and  deformed  bars  shall  be 
taken  from  the  finished  bars,  and  shall  be  of 
the  full  thickness  or  diameter  of  bars  as 
rolled;  except  that  the  specimens  for  de- 
formed bars  may  be  machined  for  a  length 
of  at  least  9  in.,  if  deemed  necessary  by  the 
manufacturer  to  obtain  uniform  cross- 
section. 

(6)  Tension  and  bend  test  speci- 
mens for  hot-twisted  bars  shall  be  taken 
from  the  finished  bars,  without  further 
treatment. 

8.  (o)  One  tension  and  one  bend  test 
shall  be  made  from  each  lot  of  10  tons  or  less  of  each  size  of  bar  rolled  from  rails  varying  not  more  than  101b.  per 
yd.  in  nominal  weight. 

(fe)  If  any  test  specimen  shows  defective  machining  or  develops  flaws,  it  may  be  discarded  and  another  speci- 
men substituted. 

(c)  If  the  percentage  of  elongation  of  any  tension  test  specimen  is  less  than  that  specified  in  Sect.  4  (a)  and  any 
part  of  the  fracture  is  outside  the  middle  third  of  the  gage  length,  as  indicated  by  scribe  scratches  marked  on  the 
specimen  before  testing,  a  retest  shall  be  allowed. 

Permissible  Variations  in  Weight. — 9.  The  weight  of  any  lot  of  bars  shall  not  vary  more  than  5%  from  the 
theoretical  weight  of  that  lot. 

Finish. — 10.  The  finished  bars  shall  be  free  from  injurious  defects  and  shall  have  a  workmanlike  finish. 

Inspection  and  Rejection. — 11.  The  inspector  representing  the  purchaser  phall  have  free  entry,  at  all  times  while 
work  on  the  contract  of  the  purchaser  is  being  performed,  to  all  parts  of  the  manufacturer's  works  which  concern 
the  manufacture  of  the  bars  ordered.  The  manufacturer  shall  aff'ord  the  inspector,  free  of  cost,  all  reasonable  facili- 
ties to  satisfy  him  that  the  bars  are  being  furnished  in  accordance  with  these  specifications.  All  tests  and  inspec- 
tion shall  be  made  at  the  place  of  manufacture  prior  to  shipment,  unless  otherwise  specified,  and  shall  be  so  con- 
ducted as  not  to  interfere  unnecessarily  with  the  operation  of  the  works. 

12.  Bars  which  show  injurious  defects  subsequent  to  their  acceptance  at  the  manufacturer's  works  will  be 
rejected,  and  the  manufacturer  shall  be  notified. 


Thickness  or  diameter  of  bar 

Plain  bars 

Deformed 
and  hot- 
twisted  bars 

180  deg. 
d  =  3t 
90  deg. 

d  =  3t 

180  deg. 
d  ^  At 
90  deg. 

d  =  it 

d  =  diameter  of  pin  about  which  the  specimen  is  bent. 
t  =  thickness  or  diameter  of  the  specimen. 


42 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-60 


60.  Factors  Affecting  Cost  of  Reinforcing  Bars.— In  order  to  insure  minimum  cost  and 
prompt  delivery  of  steel  reinforcing  bars,  the  steel  schedule  for  a  reinforced-concrete  structure 
should  call  for  bars  of  as  few  different  sizes  and  lengths  as  possible.  Bars  of  odd  16th  sizes 
are  seldom  to  be  found  in  stock  (except  the  ^e-in.  size  which  is  frequently  used  for  slab  rein- 
forcement) and  shipments  from  the  mill  on  such  sizes  are  likely  to  be  very  slow.  Designers 
should  always  bear  in  mind  this  fact  and  arrange  to  use  either  round  or  square  bars  in  3^^-in. 
sizes.  Wherever  possible,  steel  lengths  that  do  not  vary  greatly  on  the  schedule  should  all  be 
made  equal  since  an  order  calling  for  only  a  few  different  lengths  will  be  put  through  the  mill 
much  faster  than  one  calling  for  many  different  lengths. 

The  following  size  extras  for  bars  less  than  ^^-in.  are  standard  with  all  mills  and  are  the 
same  for  either  round  or  square  bars: 

Size  Extras  for  Rounds  and  Squares  in  Cents  per  100  Lb. 

^-in.  and  larger   Base 

to  1  He-ill   5  cts.  extra 

M  to  ^le-in   10  cts.  extra 

]^G-in   20  cts.  extra 

^^-in  4  25  cts.  extra 

^6 -in   35  cts.  extra 

3'^-in   50  cts.  extra 

It  should  be  noticed  that  a  higher  size  extra  must  be  paid  for  an  odd  16th  size  below  ^:^-in. 
than  for  the  next  larger  J-^-in.  size.  This  fact  alone  offsets  any  advantage  in  saving  steel 
by  always  calling  for  the  nearest  theoretical  size  whether  odd  or  even. 

Where  the  character  of  the  work  requires  small  bars  a  saving  in  cost  is  obtained  by  using 
round  bars  owing  to  the  difference  in  size  extras  between  rounds  and  squares  of  equivalent  area. 

Lengths  less  than  5  ft.  should  be  avoided,  if  possible,  as  they  are  subject  to  the  following 
cutting  extras,  whether  sheared  or  hot-sawed: 

Lengths  over  24  in.  and  less  than  60  in   5  cts.  per  100  lb. 

Lengths  12  in.  to  24  in.  inclusive   10  cts.  per  100  lb. 

Lengths  under  12  in   15  cts.  per  100  lb. 

All  orders  calling  for  less  than  2000  lb.  of  the  same  size  and  shape  are  subject  to  the  follow- 
ing extras: 

Quantities  less  than  2000  lb.  but  not  less  than  1000  lb   15  cts.  per  100  lb. 

Quantities  less  than  1000  lb   35  cts.  per  100  lb. 

61.  Deformed  Bars. — The  following  deformed  bars  are  in  common  use: 

61a.  Diamond  Bar  (Fig.  18). — Furnished  by  Concrete-Steel  Engineering  Co., 
New  York  City.    The  standard  sizes  are  as  follows: 

Diamond  Bars 


Size  in  inches 

Vl6 

5/8 

H 

1 

VA 

IH 

Area  in  square  inches.  .  .  . 

0.0625 

0.1406 

0.19 

0.25 

0.39 

0.56 

0.76 

1.00 

1.26 

1.56 

Weight  per  foot  in  pounds. 

0.213 

0.478 

0.65 

0.85 

1.33 

1.91 

2.60 

3.40 

4.30 

5.31 

Fig.  18. — Diamond  bar. 

It  should  be  noted  that  the  weights  and  areas  of  Diamond  bars  are  equal  to  those  of  plain 
square  bars  of  like  denominations. 


Sec.  1-616]  MATERIALS  43 


616.  Corrugated  Bars  (Fig.  19).— Furnished  by  Corrugated  Bar  Co.,  Buffalo, 
N.  Y.    The  standard  sizes  are  as  follows: 

Corrugated  Rounds 


Size  in  inches 

H 

H 

ri6 

^/^ 

H 

1 

11^ 

IH 

Net  area  in  square  inches  

Weight  per  foot  in  pounds  

0.11 
0.38 

0.19 
0.66 

0.25 
0.86 

0.30 
1.05 

0.44 
1.52 

0.60 
2.06 

0.78 
2.69 

0.99 
3.41 

1.22 
4.21 

Corrugated  Squares 

Size  in  inches 

Vi 

H 

H 

H 

H 

1 

IH 

VA 

Weight  per  foot  in  pounds  

0.06 
0.22 

0.14 
0.49 

0.25 
0.86 

0.39 
1.35 

0.56 
1.94 

0.76 

2.64 

1.00 

3.43 

1.26 
4.34 

1 . 55 
5.35 

Fig.  19. — Corrugated  bars. 


61c.  Havermeyer  Bars  (Fig.  20). — Furnished  by  Concrete  Steel  Co.,  New  York 
City.    The  following  table  gives  the  weights  and  areas  of  the  standard  Havermeyer  bars: 


Havermeyer  Bars 


Squares 

Rounds 

Flats 

Size  in  inches 

Area  in 

Weight 

Area  in 

Weight 

Size  in 

Area  in 

Weight 

square 

per  foot  in 

square 

per 

foot  in 

square 

per  foot  in 

inches 

pounds 

inches 

pounds 

inches 

inches 

pounds 

H 

0 . 0625 

0.212 

0.0491 

0 

167 

ixH 

0.2500 

0.850 

He 

0.9770 

0.332 

0.3750 

1.280 

H 

0.1406 

0.478 

0.1104 

0 

375 

\\ix% 

0.4690 

1.590 

0.2500 

0.850 

0.1963 

0 

667 

0 . 4688 

1.590 

H 

0.3906 

1.328 

0.3068 

1 

.043 

0.5625 

1.913 

% 

0.5625 

1.913 

0.4418 

1 

502 

WixM 

0.7500 

2.550 

% 

0.7656 

2.603 

0.6013 

2 

044 

mxH 

0 . 6563 

2.230 

1 

1.0000 

3.400 

0.7854 

2 

670 

mxviG 

0.7656 

2.600 

1.2656 

4.303 

0.9940 

3 

379 

ly^xM 

0.8750 

2.980 

1.5625 

5.312 

1.2272 

4 

173 

44 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  l-6ld 


Special  sizes  of  1^^-in.  and  l3>2-in.  square  Havermeyer  bars  can  be  rolled  by  special  arrange- 
ment, but  are  not  carried  in  stock.  A  size  extra  of  10  cts.  applies  against  1  by  ^-^-in.  and  13-2 
by  ^{Q-in.  flats;  all  other  sizes  tabulated  take  the  base  price. 

Qld.  Rib  Bar  (Fig.  21). — Furnished  by  Trussed  Concrete  Steel  Co.,  of  Youngs- 
town,  Ohio  and  Detroit,  Mich.    The  following  sizes  are  standard: 


Rib  Bar 


Size  in 
inches 

Area  in 
square  inches 

Weight  per 
linear  foot 
in  pounds 

Size  in 
inches 

Area  in 
square  inchSs 

Weight  per 
linear  foot 
in  pounds 

ys 

0.1406 

0.48 

0.7656 

2.65 

0.2500 

0.86 

1 

1.0000 

3.46 

% 

0.3906 

1.35 

1.2656 

4.38 

0.5625 

1.95 

Fig.  21.— Rib  bar. 


60e.  Inland  Bar  (Fig.  22).— Furnished  by  Inland  Steel  Co.,  Chicago. 
Sizes     in.  to      in.  inclusive  with  single  row  of  stars  on  each  side. 
Sizes      in.  to  IJ^  in.  inclusive  with  double  row  of  stars  on  each  side. 

Lengths  may  be  obtained  up  to  85  ft.  Supplied  in  both  open-hearth  steel  and  rail  carbon 
steel. 

Standard  sizes  are  as  follows: 


Inland  Bar 


Size  in  inches 

% 

K2 

% 

1 

IH 

Area  in  square  inches .... 
Weight  per  foot  in  pounds. 

0.140 
0.485 

0.250 
0.862 

0.390 
1.341 

0.562 
1.932 

0.765 
2.630 

1.000 
3.434 

1.265 
4.349 

1.562 
5.365 

Fig.  22.— Inland  bar. 


Rail  carbon  steel  bars  not  rolled  larger  than  1  in. 

61/.  American  Bars  (Fig.  23). — Furnished  by  American  System  of  Reinforcing, 
Chicago.    The  following  sizes  are  standard: 


Sec.  1-62]  MATERIALS  45 


American  Bars 


Squares 

Rounds 

Size  in  inches 

Net  area  in  square 
inches 

Weight  per  foot  in 
pounds 

Net  area  in  square 
inches 

Weight  per  foot  in 
pounds 

H 

0.141 

0.48 

0  110 

U  .  00 

0.250 

0.85 

0.196 

0.68 

/8 

0.391 

1.33 

0.307 

1.05 

0.563 

1.92 

0.442 

1.51 

0.766 

2.61 

0.602 

2.05 

1 

1.000 

3.40 

0.786 

2.68 

1.270 

4.31 

0.994 

3.38 

1.560 

5.32 

1.230 

4.19 

Fig.  23. — American  bars. 


62.  Wire  Fabric. — This  material  is  used  to  a  considerable  extent  for  floors,  roofs,  walls, 
vaults,  pavement,  etc.,  and  has  been  found  to  possess  many  valuable  quaUties.  Wire  fabric 
is  made  of  steel  wires  crossing  generally  at  right  angles  and  secured  at  the  intersections.  The 
heavier  wires  run  lengthwise  and  are  called  carrying  wires;  the  lighter  ones  cross  these  and  are 
called  distributing  or  tie  wires.  One  distinct  advantage  in  the  use  of  fabric  is  that  it  preserves 
uniform  spacing  of  the  steel. 

The  steel  wire  gage  adopted  as  standard  for  all  steel  wire  upon  recommendation  of  the 
United  States  Bureau  of  Standards  is  given  in  the  following  table: 


Steel  Wire  Gage 


Diameter, 
inches 

Steel  wire 
gagei 

Diameter, 
inches 

Area,  square 
inches 

Pounds  per 
foot 

Pounds  per 
mile 

Feet  per 
pound 

0 

5000 

0 

19635 

0 

.6668 

3,521.0 

1 

.500 

7/0  . 

0 

4900 

0 

18857 

0 

6404 

3,381.0 

1 

.562 

0 

46875 

0 

17257 

0 

5861 

3,094.0 

1 

.706 

6/0 

0 

4615 

0 

16728 

0 

5681 

2,999.0 

1 

760 

Ke 

0 

4375 

0 

15033 

0 

5105 

2,696.0 

1 

959 

5/0 

0 

4305 

0 

14556 

0 

4943 

2,610.0 

2 

023 

0 

40625 

0 

12962 

0 

4402 

2,324.0 

2 

272 

4/0 

0 

3938 

0 

12180 

0 

4136 

2,184.0 

2 

418 

H 

0 

3750 

0 

11045 

0 

3751 

1,980.0 

2 

666 

3/0 

0 

3625 

0 

10321 

0 

3505 

1,851.0 

2 

853 

0 

34375 

0 

092806 

0 

3152 

1,664.0 

3 

173 

2/0 

0 

3310 

0 

086049 

0 

2922 

1,543.0 

3 

422 

1  Formerly  called  the  "American  Steel  &  Wire  Go's.  Gage." 


46  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  l-62a 


Steel  Wire  Gage. — {Continued.) 


Diameter, 
inches 

Steel  wire 
gage 

Diameter, 
inches 

Area,  square 
inches 

Pounds  per 
foot 

Pounds  per 
mile 

Feet  per 
pound 

Vi 

0.3125 

0.076699 

0.2605 

1,375.0 

3.839 

0 

0.3065 

0.073782 

0.2506 

1,323.0 

3.991 

1 

X 

n  2R'^n 

0  062Q02 

n  91  "^fi 

1  128  0 

%2 

0.28125 

0.062126 

0.2110 

1,114.0 

4.74 

2 

0.2625 

0.054119 

0.1838 

970.4 

5.441 

\4 
74 

0  2500 

0  04Q087 

0. 1667 

880.2 

5  QQQ 

3 

0.2437 

0.046645 

0.1584 

836.4 

6.313 

4 

0.2253 

0.039867 

0.1354 

714.8 

7.386 

/3  2 

0  21875 

0  037583 

0. 1276 

673.9 

7. 835 

5 

0.2070 

0.033654 

0.1143 

603.4 

8.750 

6 

0.1920 

0.028953 

0.09832 

519.2 

10.17 

/16 

0. 1875 

0  027612 

0  0Q377 

495. 1 

10  66 

7 

0.1770 

0.024606 

0.08356 

441.2 

11.97 

8 

0.1620 

0.020612 

0.07000 

369.6 

14.29 

/3  2 

0  15625 

0  01 91 75 

0  06512 

343. 8 

15. 36 

9 

0.1483 

0.017273 

0.05866 

309.7 

17.05 

10 

0.1350 

0.014314 

0.04861 

256.7 

20.57 

0.125 

0  012272 

0  04168 

220.0 

24.00 

0. 1205 

0  01 1 404 

0  03873 

204.5 

25. 82 

12 

0  0087417 

0  02Q6Q 

156. 7 

33. 69 

0.09375 

0.0069029 

0 . 02344 

123.8 

42.66 

13 

0.0915 

0.0065755 

0.02233 

117.9 

44.78 

14 

0.0800 

0.0050266 

0.01707 

90.13 

58.58 

15 

0.0720 

0.0040715 

0.01383 

73.01 

72.32 

16 

0.0625 

0.0030680 

0.01042 

55.01 

95.98 

17 

0.0540 

0.0022902 

0.007778 

41.07 

128.60 

The  manner  of  securing  the  intersections  of  wire  fabric  has  given  rise  to  a  number  of 
different  types,  several  of  the  principal  ones  of  which  are  given 
n  f]  below. 

K       '  ■     . '   ^  62a.  Welded  Wire  Fabric. — Welded  wire  fabric, 

■  Fig.  24,  manufactured  by  the  CHnton  Wire  Cloth  Co.,  is  a  gal- 

"       '  vanized  wire  mesh  made  up  of  a  series  of  parallel  longitudinal 

 wires,  spaced  a  certain  distance  apart  and  held  at  intervals  by 

'    '  '    ■      "  means  of  transverse  wires,  arranged  at  right  angles  to  the  longi- 

^  — — — tudinal  ones,  and  welded  to  them  at  the  points  of  intersection 
[J  — — ^  ^  ^  patented  electrical  process.    Longitudinal  wires  can  be 

Fig.  24.— Welded  wire  fabric,    spaced  on  centers  of  2  or  more  in.,  in  steps  of  3^  in.    Transverse  i 

wires  can  be  spaced  on  centers  of  1  to  18  in,  inclusive,  in  steps  | 
of  1  in.  and  on  centers  of  10  to  18  in.  inclusive,  in  steps  of  2  in.    The  following  table  shows 


Sec.  1-626] 


MATERIALS 


47 


the  sizes  and  areas  of  the  wire  used.  Rolls  kept  in  stock  vary  in  length  between  150  and  200 
ft.  and  between  56  and  100  in.  in  width.  The  wire  will  develop  an  average  ultimate  strength 
of  70,000  to  80,000  lb.  per  sq.  in. 


Welded  Wire  Fabric 


Area  per 

foot  of  width 

in  longitudinal  wires  only 

Diameter  of 
longitudinal 
wires 
(inches) 

Area  of  one 
longitudinal 
wire  (square 
inches) 

Spacing  of 
transverse 
wires 
(inches) 

G&gG  of 
longitud- 
inal wires 

Gage  of 
transverse 
wires 

Spacing  of  longitudina 

wires 

2  in. 

3  in. 

4 

in. 

5  in. 

6  in. 

0000 

0 

394 

0 

122 

3 

16 

0 

735 

0 

490 

0 

367 

0 

294 

0.245 

r\r\r\ 
OOU 

0 

363 

0 

103 

1  A 
ID 

0 

619 

0 

413 

0 

310 

0 

248 

n  9nA 

00 

0 

331 

0 

086 

4 

16 

0 

516 

0 

344 

0 

258 

0 

207 

n  1 79 

0 

n 
u 

n 
U 

ri7A 
\j(  ^ 

6 

16 

0 

443 

0 

295 

0 

221 

0 

177 

0.148 

1 

0 

283 

0 

063 

O 

1  A 

lo 

0 

377 

0 

252 

0 

189 

0 

151 

n  1 0A 

2 

0 

263 

0 

054 

8 

16 

0 

325 

0 

217 

0 

162 

0 

130 

0.108 

3 

0 

244 

0 

047 

8 

16 

0 

280 

0 

187 

0 

140 

0 

112 

0.093 

4 

0 

225 

0 

040 

9 

16 

0 

239 

0 

160 

0 

120 

0 

096 

0.080 

5 

0 

207 

0 

034 

9 

16 

0 

202 

0 

135 

0 

101 

0 

081 

0.067 

6 

0 

192 

0 

029 

10 

16 

0 

174 

0 

116 

0 

087 

0 

069 

0.058 

7 

0 

177 

0 

025 

10 

16 

0 

148 

0 

098 

0 

074 

0 

059 

0.049 

8 

0 

162 

0 

021 

10 

12 

0 

124 

0 

082 

0 

062 

0 

049 

0.041 

9 

0 

148 

0 

017 

11 

12 

0 

104 

0 

069 

0 

052 

0 

041 

0.035 

10 

0 

135 

0 

014 

12 

12 

0 

086 

0 

057 

0 

043 

0 

034 

0.029 

626.  Triangle-mesh  Wire  Fabric. — Triangle-mesh  steel-wire  fabric,  manu- 
factured by  the  American  Steel  &  Wire  Co.,  is  made  with  both  single  and  stranded  longitudinal 
or  tension  members.  That  with  the  single  wire  longitudinal  is  made  with  one  wire  varying  in 
size  from  a  No.  12  gage  up  to  and  including  a  3'^-in.  diameter,  and  that  with  the  stranded  longi- 


FiG.  25. — Triangle-mesh  wire  fabric. 


tudinal  is  composed  of  two  or  three  wires  varying  from  No.  12  gage  up  to  and  including  No.  4 
wires  stranded  or  twisted  together  with  a  long  lay.  These  longitudinals  either  solid  or  stranded 
are  invariably  spaced  4-in.  centers,  the  sizes  being  varied  in  order  to  obtain  the  desired  cross- 
sectional  area  of  steel  per  foot  of  width  (see  Fig.  25). 

The  transverse  or  diagonal  cross  wires  are  so  woven  between  the  longitudinals  that  triangles 


48 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  l-62c 


are  formed  by  their  arrangement.  These  diagonal  cross  wires  are  woven  either  2  or  4  in.  apart, 
as  is  desired.  Triangle-mesh  wire  reinforcement  is  made  in  lengths  of  150,  200,  and  300  ft. 
and  in  widths  from  18  to  58  in.  (4-in.  steps).  The  table  following  shows  the  number  and  gage 
of  wires  and  the  areas  per  foot  width  when  the  longitudinals  and  cross  wires  are  spaced  4  in. 
on  centers. 


Triangle-mesh  Wire  Fabric 


Style 
number 

Number  of 
long. 

Gage  of 
wire,  G3<ch. 
long. 

Gage  of 
cross  wires 

Sectional 
square  inches 

bectional 
area,  cross 
wires, 
square  inches 

Cross-sec- 
tional area 

per  foot 

width 

Approximate 
per  100  sq.  ft. 

A  1 

4^ 

a 
D 

1  A 

14 

0 . 087 

A    AO  C 

0 .  Ozo 

A    1  AO 

0 .  lOz 

A  0 

43 

C  1 

Q 
O 

1  A 

14 

U .  ObZ 

A    AO  K 

0 .  Ozo 

A  A'TT 

0.0// 

0  A 

34 

61 

10 

14 

0.043 

0.025 

0.058 

27 

/  ^ 

1  A 

14 

U .  yjZb 

A    AO  K. 

0 .  Uzo 

A  nA  1 
0 . 041 

0 1 
zl 

1  O  1  / 

0 . 14/ 

A  AOO 

0. 038 

A    1  TA 
0  .  170 

TO 

7z 

24 

4 

mi 

0.119 

0.038 

0.142 

62 

o 

U .  iUi 

A  AQQ 

A    1  OA 

U .  Iz4 

00 

D 

101/ 

n  AC? 
U .  08/ 

A  AOO 

0 . 038 

A    1  1  A 

0. 110 

K  A 

50 

271 

8 

mi 

0.062 

0.038 

0.085 

41 

OQ  1 

10 

1  O  1  / 

12>^ 

0 . 04d 

A  AOO 

0 . 008 

A  A£!£! 
0  .  OOD 

0  A 

34 

1  o 
IZ 

0 .  UZb 

A  AOO 

0 . 038 

A  r\  A  Pi 

0 . 04y 

OQ 

z8 

311 

2 

4 

mi 

0.238 

0.038 

0.261 

106 

o 

z 

r 
0 

101/ 

0  .  ZOZ 

A  AOO 

0 . 008 

A    00  K 

0 .  zzo 

00 
9z 

33 

2 

6 

m'2 

0.174 

0.038 

0.196 

82 

34 

2 

8 

m^i 

0.124 

0.038 

0.146 

63 

35 

2 

10 

123^ 

0.086 

0.038 

0.109 

50 

36 

2 

12 

mi 

0.052 

0.038 

0.075 

37 

38' 

3 

4 

mi 

0.358 

0.038 

0.380 

151 

39 

3 

5 

123^ 

0.303 

0.038 

0.325 

130 

401 

3 

6 

123^ 

0.260 

0.038 

0.283 

114 

41 

3 

8 

123^ 

0.185 

0.038 

0.208 

87 

421 

3 

10 

mi 

0.129 

0.038 

0.151 

66 

43 

3 

12 

mi 

0.078 

0.038 

0.101 

47 

Elastic  limit  of  regular  stock  is  from  50,000  to  60,000  lb.  per  sq.  in.  Ultimate  strength  is 
85,000  lb.  per  sq.  in.  or  over.  Higher  elastic  limits  and  breaking  strengths  are  furnished  when 
required.  Material  may  be  obtained  either  plain  or  galvanized.  Unless  otherwise  specified, 
shipments  are  made  of  material  not  galvanized. 

62c.  Unit  Wire  Fabric. — A  rectangular-mesh  staple-locked  fabric  (Fig.  26)  is 
furnished  by  the  American  System  of  Reinforcing.    The  wire  used  is  of  high  tensile  steel  and 


1  Styles  usually  carried  in  stock. 


Sec.  1-Q2d] 


MATERIALS 


49 


is  secured  at  the  intersections  by  No.  14  wire.  Standard  sizes  are  shown  in  the  following  table. 
The  fabric  is  galvanized  and  comes  in  standard  widths  of  3,  4,  and  5  ft.,  200  lin.  ft.  in  a  roll. 


Fig.  26. — Unit  wire  fabric. 


Unit  Wire  Fabric 


Gage  of  longitud- 
inal wires 

Gage  of  cross  wires 

Distance  center  t 
Longitudinal  wires 

3  center  in  inches 
Cross  wires 

Sectional  area  in  sq. 
in.,  foot  width 

11 

11 

6 

6 

0 

023 

10 

10 

6 

6 

0 

028 

9 

6 

6 

0 

035 

9 

4 

12 

0 

05 

9 

3 

12 

0 

07 

8 

4 

12 

0 

062 

7 

4 

12 

0 

074 

6 

4 

12 

0 

087 

5 

4 

12 

0 

10 

4 

4 

12 

0 

12 

3 

4 

12 

0 

14 

Q2d.  Lock-woven  Steel  Fabric. — Lock-woven  steel  fabric  (Fig.  27)  is  also  known 
as  Page  Special  Process  fabric.    It  is  manufactured  by  the  Page  Woven  Wire  Fence  C'o.,  of 


Fig.  27. — Lock-woven  steel  fabric. 


Monessen,  Pa.  and  is  controlled  by  W.  W.  Wight  &  Co.  of  New  York  City.  This  fabric  is 
usually  made  54  in.  wide  with  special  widths  from  18  to  54  in.  The  longitudinal  wires  are  made 
by  a  special  process  which  gives  them  an  ultimate  tensile  strength  of  180,000  lb.  per  sq.  in. 
with  an  elastic  hmit  of  about  70%  of  the  ultimate.  The  material  is  galvanized  and  is  furnished 
in  rolls  of  150,  300,  450  and  600  ft.  in  length.  The  table  on  page  50  gives  the  characteristics 
of  the  different  styles. 
4 


50  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  l-62e 


Lock-woven  Steel  Fabric 


Style 

Gage 

Spacing 

in  inches 

Sectional 
area  in  sq.  in. 
per  foot  width 

Ultimate 
strength  in 
pounds  per 
foot  width 

Weight  per 
100  sq.  ft. 

Long. 

Trans. 

Long. 

Trans. 

14P 

14 

14 

3 

12 

0.0201 

3,621  ■ 

11.04 

13P 

13 

14 

3 

12 

0 . 0265 

4,790 

12.91 

12P 

12 

14 

3 

12 

0 . 0350 

6,300 

15.85 

IIP 

11 

14 

3 

12 

0.0452 

8,140 

17.47" 

9P 

9 

14 

3 

12 

0 . 0680 

12,390 

28.62 

8P 

8 

14 

3 

12 

0.0824 

14,280 

34.82 

7P 

7 

14 

3 

12 

0.0984 

17,720 

39.48 

14D 

14 

14 

12 

0 . 0402 

7,242 

22.08 

13D 

13 

14 

•IK 

12 

0.0532 

9,580 

25.82 

12D 

12 

14 

IK 

12 

0 . 0700 

12,600 

31.70 

11^ 

14 

IK 

12 

0.0795 

14,313 

33.25 

1 1  "n 

11 

14 

1 1^ 

1X2 

1  9 

0  0004. 

1  a  900 

o'k . 

93^D 

93^ 

14 

12 

0.12498 

22,450 

53.43 

9D 

■  9 

14 

12 

0.1376 

24,780 

57.20 

8D 

8 

14 

IK 

12 

0.1648 

29,640 

69.64 

7D 

7 

14 

IK 

12 

0.1968 

35,440 

78.96 

62e.  Wisco  Reinforcing  Mesh. — Wisco  mesh  is  manufactured  by  the  Witherow 
Steel  Co.,  Pittsburgh,  Pa.  It  is  made  from  the  best  grade  of  open-hearth  steel  and  has  a  high 
tensile  strength.  All  longitudinals  are  spaced  3  in.  c.  to  c.  and  cross  wires  12  in.  c.  to  c.  Stand- 
ard rolls  are  150  and  300  ft.  in  length.  Width  of  rolls  are  furnished  in  any  multiple  of  3  in. 
from  18  to  54  in.    Properties  of  the  Wisco  mesh  are  given  in  the  following  table: 


Wisco  Mesh 


.  Style 

Sectional 
area  per 
foot  width 

Weight  per 
square  foot 

Style 

Sectional 
area  per 
foot  width 

Weight  per 
square  foot 

style 

Sectional 
area  per 
foot  width 

Weight  per 
square  foot 

14 

0.020 

0.110 

9K 

0.062 

0.277 

6 

0.116 

0.465 

12 

0.035 

0.158 

9 

0.069 

0.286 

29 

0.138 

0.556 

11 

0.046 

0.175 

8 

0.083 

0.341 

27 

0.197 

0.775 

10 

0.058 

0.223 

7 

0.098 

0.395 

26 

0.230 

1.036 

panded  metal  (Fig.  28)  is  one  of  the  oldest  forms  of  sheet  rein- 
forcement. It  is  formed  by  slitting  a  sheet  of  soft  steel  and 
then  expanding  the  metal  in  a  direction  normal  to  the  axis  of 
the  sheet.  The  principal  advantages  claimed  for  this  type  of 
reinforcement  are  the  following:  (!)  An  increased  ultimate 
strength  and  high  elastic  limit  for  low-carbon  steel  when  the 
diamond-shaped  meshes  are  formed  by  cold  drawing  the  metal; 
(2)  a  mechanical  bond  with  the  surrounding  concrete;  (3)  great 
efficiency  in  the  carrying  of  concentrated  loads  due  to  the  ob- 


63.  Expanded  Metal.—: 


Fig.  28. — Expanded  metal. 


Sec.  l-63a] 


MATERIALS 


51 


liquity  of  the  strands;  (4)  an  increased  ductility  because  of  the  fact  that  the  diamonds  or  quad- 
rilaterals tend  to  close  under  severe  loading;  (5)  a  greater  slab  strength  as  the  effect  of  closing 
up  of  the  diamonds  is  to  introduce  a  compression  into  the  concrete  at  the  lower  part  of  the 
slab.  Expanded  metal  and  other  sheet  metal  is  made  according  to  the  U.  S.  Standard  gago 
which  differs  but  slightly  from  the  Steel  Wire  gage  given  on  page  45. 

63a.  Steelcrete. — Manufactured  by  the  ConsoUdated  Expanded  Metal  Cos., 
Rankin,  Pa.  The  designation  of  the  material  gives  the  width  of  the  diamond,  the  gage  of  the 
plate  and  the  cross-section  per  foot  of  width.  Size  3-9-15  means  that  it  is  a  3-in.  diamond, 
made  out  of  No.  9  plate,  having  a  sectional  area  per  foot  of  width  of  0.15  sq.  in.  All  standard 
meshes  have  a  diamond  3  by  8  in.  The  standard  sizes  and  gages  are  given  in  the  following 
table: 


"Steelcrete"  Expanded  Metal 


Designation 
of  mesh 

Width  of 
diamond 
in  incliGS 

Size  of  mes] 

Length  of 
diamond 
in  inches 

1 

Section  in 
sq.  in.  per 
ft.  of 
width 

wt.  per 
sq.  ft. 

in 
pounds 

No.  of 

sheets 

in  a 
bundle 

Size  of  standard 
sheets 

No.  of 
sq.  ft. 

in  a 
bundle 

Wt.  pet 
bundle 
in  lb. 

3-13-075 

3 

8 

0.075 

0.27 

10 

6'0"  X  8'0" 

480 

129.6 

6  0    X  12'0 

720 

194.4 

3-13-10 

3 

8 

0.10 

0.37 

7 

6'9"  X  8'0" 

378 

139.9 

^  6'9"  X  12'0" 

567 

209.8 

3-13-125 

3 

8 

0.125 

0.46 

7 

5'3"  X  8'0" 

294 

135.2 

^  5'3"  X  12'0" 

441 

202.9 

3-9-15 

3 

8 

0.15 

0.55 

5 

'  7'0"  X  8'0" 

280 

154.0 

^  7'0''  X.  12'0'' 

420 

231.0 

3-9-20 

3 

8 

0.20 

0.73 

5 

'  5'3"  X  8'0" 

210 

153.3 

5'3"  X  12'0" 

315 

230.0 

3-9-25 

3 

8 

0.25 

0.92 

5 

*  4'0"  X  8'0" 

160 

147.2 

4'0"  X  12'0" 

240 

220.8 

3-9-30 

3 

8 

0.30 

1.10 

2 

7'0"  X  8'0" 

112 

123.2 

^  7'0"  X  12'0'' 

168 

184.8 

3-9-35 

3 

8 

0.35 

1.28 

2 

^  6'0"  X  8'0" 

96 

122.9 

6'0"  X  12'0" 

144 

184.3 

3-6-40 

3 

8 

0.40 

1.46 

2 

'  7'0"  X  8'0'' 

112 

163.5 

7'0"  X  12'0'' 

168 

245.3 

3-6-45 

3 

8 

0.45 

1.65 

2 

6'3"  X  8'0" 

100 

165.0 

6'3"  X  12'0" 

150 

247.5 

3-6-50 

3 

8 

0.50 

1.83 

2 

5'9"  X  8'0'' 

92 

168.4 

5'9"  X  12'0" 

138 

252.5 

3-6-55 

3 

8 

0.55 

2.01 

2 

5'3"  X  8'0" 

84 

168.8 

5'3"  X  12'0" 

126 

253.3 

3-6-60 

3 

8 

0.60 

2.19 

2 

j 

4'9"  X  8'0" 

76 

166.4 

4'9"  X  12'0" 

114 

249.7 

The  Consolidated  Expanded  Metal  Cos.  also  make  to  order  a  6-in.  mesh,  the  size  of  the 
diamond  being  6  by  16  in.  The  gage  of  plate  used  is  No.  4,  or  nearly  K  in.  thick.  Any  cross- 
sectional  area  desired  up  to  and  including  0.4  sq.  in.  can  be  obtained.  The  width  of  the  sheets 
depend  on  the  sectional  area.  These  companies  also  make  a  4-in.  mesh  from  No.  16  plate 
which  is  unexpanded.    Any  length  can  be  obtained  up  to  16  ft.    The  cross-sectional  area  per 


52 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-635 


foot  of  width  is  0.093  sq.  in.  Special  meshes  can  be  obtained  having  diamonds  of  in.,  13^ 
in.,  and  2  in. 

636.  Kahn  Mesh. — Manufactured  by  the  Trussed  Concrete  Steel  Co.,  of 
Youngstown,  Ohio,  and  Detroit,  Mich.  The  standard  sizes  and  gages  are  the  same  as  for 
"Steelcrete."  The  Kahn  Mesh  may  also  be  obtained  with  larger  diamonds  for  reinforcing 
concrete  pavements.    The  sizes  of  the  Kahn  Road  Mesh  follow: 


Kahn  Road  Mesh 


Decimal 
designation 

Size  of  mesh 

Sectional 

Size  No. 

Width  of  diamond 
in  inches 

Length  of  diamond 
in  inches 

area 
in  square  inches 

15 

6-13-042 

6 

12 

0.042 

20 

6-13-053 

6 

12 

0.053 

22 

6-13-058 

6 

12 

0.058 

25 

6-13-066 

6 

12 

0.066 

28 

6-13-074 

6 

12 

0.074 

30 

6-9-079 

6 

12 

0.079 

32 

6-9-085 

6 

12 

0.085 

No.  of  sheets  in  bundle,  10.  Standard  width  of  sheets,  5  ft.  Standard  lengths  of  sheets,  8  ft.,  10  ft.,  12  ft.,  or 
any  equal  divisions  of  these  lengths. 


63c.  Corr-X-Metal. — Furnished  by  the  Corrugated  Bar  Co.,  Buffalo,  N.  Y. 
The  weights,  sectional  areas  and  standard  sizes  of  sheets  are  given  in  the  following  table: 


Corr-X-Metal 


Style 

Size  of  mesh, 
short  way 
(inches) 

Nominal  thickness 
of  metal 
(gage) 

Approximate  weight 
per  square  foot, 
(pounds) 

Net  sec.  area  per  foot 
of  width 
(square  inches) 

F 

3 

10 

0.51 

0.150 

G 

3 

10 

0.6 

0.176 

H 

3 

10 

0.9 

0.265 

J 

3 

10 

1.2 

0.353 

K 

3 

16 

0.278 

0.082 

L 

16 

0.4 

0.118 

M 

12 

0.56 

0.164 

R 

12 

0.66 

0.194 

S 

H 

13 

0.84 

0.246 

Sec.  l-63c^]  MATERIALS  53 


Standard  Size  Sheets 


Style 

Long  way  of  diamond 

Short  way  of  diamond 

F 

6',  8',  9'  and  10' 

8" 

3', 

4',  5'  and  6' 

G 

0,8,9  and  10 

o// 

8 

3', 

4',  5'  and  6' 

H 

6',  8',  9'  and  10' 

8" 

4'      and  5'  4" 

T 
J 

6',  8',  9'  and  10' 

8" 

3', 

4'      and  6' 

K 

6'  and  8'  and  10' 

8" 

3', 

4',  5'  and  6' 

L 

6'  and  8'  and  10' 

6" 

3', 

4',  5'  and  6' 

M 

6'  and  8'  and  10' 

6" 

4'      and  5'  4" 

R 

6' 

3', 

4',  5'  and  6' 

S 

6' 

3', 

4',  5'  and  6' 

63c?.  Econo. — Furnished  by  the  North  Western  Expanded  Metal  Co.,  Chicago, 
111.    Standard  sizes  and  weights  are  as  follows: 


Econo  Expanded  Metal 


No. 

Weight  per 
square  foot, 
pounds 

Mesh  and  gage 

Widths,  feet 

Lengths,  feet 

06-3 

0.20 

3"— 16  ga. 

3,  4,  6 

8  and  12 

10-3 

0.34 

3" — 12  ga. 

3,  4,  6 

8  and  12 

15-3 

0.51 

3"— 10  ga. 

3,  4,6 

8',  10'  6"  and  12' 

16-3 

0.55 

3"— 10  ga. 

3,  4,  6 

8',  10'  6"  and  12' 

20-3 

0.68 

3"— 10  ga. 

3,  4,  6 

8',  10'  6"  and  12' 

25-3 

0.85 

3"— 10  ga. 

3,  4,  6 

8',  10'  6"  and  12' 

30-3 

1.02 

3"— 10  ga. 

3,  4,  6 

8',  10'  6"  and  12' 

35-3 

1.19 

3"— 10  ga. 

3,  4,6 

8',  10'  6"  and  12' 

40-3 

1.36 

3"—  7  ga. 

3'  6",  7'  0" 

8  and  12 

10-2M 

0.34 

2}i"—m  ga. 

3,  4,  6 

8  and  12 

15-2K 

0.51 

234"— 12  ga. 

3,  4,  6 

8  and  12 

20-234 

0.68 

234"— 10  ga. 

3,  4,  6 

8  and  12 

40-2M 

1.36 

234"—  7  ga. 

3'  6",  7'  0" 

8  and  12 

10-1 H 

JO. 34 
\0.34 

13^"— 18  ga. 
11^"— 16  ga. 

3,  4,  6 
3,  4,  6 

8  only 
8  and  12 

20-13^ 

0.68 

1>^"— 12  ga. 

3,  4,  6 

8  and  12 

0.51 

^i"— 16  ga. 

3,  4,  6 

8  and  12 

25-^ 

0.85 

M"— 12  ga. 

3,  4,  6 

8  and  12 

20-1^ 

0.68 

3^"— 18  ga. 

3,  4,  7 

8  only 

24-3^ 

0.82 

3^"— 16  ga. 

2,4 

8  only 

The  first  two  figures  in  the  first  column  give  the  area  of  steel  and  the  last  figure  gives  the  short 
dimensions  of  mesh.  Thus  No.  30-3  has  an  area  of  0.30  sq.  in.  per  12  in.  of  width  and  has  a 
mesh  3  in.  wide. 

63e.  GF  Expanded  Metal— Manufactured  by  the  General  Fireproofing  Co., 
Youngstown,  Ohio.    Standard  sizes  are  given  in  the  table  on  page  54, 


54  CONCRETE  ENGINEERS'  HANDBOOK  [Sec. 


GF  Expanded  Metal 


Standard  size  sheets 

Style 

Approx.  weight  per 
sq.  ft.  in  pounds 

Deliveries 

Lengths 

Widths 

Long  w£ty  of  diRmonci 

Short  wsy  of  di^dnoncl 

3-10-176 
3-10-265 
3-10-353 

3-12-150 

13^-12-194 

M-12-246 

0.60 
0.90 
1.20 

0.51 
0.66 
0.84 

Carried  in  stock 
in  standard  sheets 

6',  8',  9',  10'-8" 
6',  8',  9',  10'-8" 
6',  8',  9',  10'-8" 

6',  8',  9',  10'-8" 
6',  8' 
6',  8' 

3',  4',  5',  6' 
4',  5'-4" 
3',  4',  6' 

3',  4',  6' 
3',  4',  6' 
3',  4',  6' 

3-10-324 

3-10-25 

3-10-20 

1.10 

0.85 
0.68 

6',  8',  9',  10'-8" 
6',  8',  9',  10-8" 
6',  8',  9',  10'-8" 

4'-4" 
5-8" 
5'-6" 

3-10-162 

3-10-15 

3-12-125 

0.55 
0.51 
0.425 

6',  8',  9',  10'-8" 
6',  8',  9',  10'-8" 
6',  8',  9',  10'-8" 

3',  4'-6" 
3',  6' 
4'-4",  6'-6" 

3-12-10 

3-16-082 

3-16-059 

0.34 

0.278 

0.20 

Five  days 

6',  8',  9',  10'-8" 
6',  8',  10'-8" 
6',  8',  10'-8" 

4',  6'-4" 
3',  4',  5',  6' 
3',  4',  6' 

2^^-12-164 
23^-16-118 
23^-16-10 

2-12-161 
2-16-103 
1>^-12-181 

13-^-16-105 
13^-18-088 
1-12-234 

0.56 
0.40 
0.34 

0.547 
0.351 
0.61 

0.36 

0.308 

0.796 

to  two 
weeks 
dependent 
on  size 
order 
and 
unfilled 
business  on 
books 

6',  8',  10'-6" 
6',  8',  10-6" 
6',  8',  10'-6" 

6',  8' 
6',  8' 
6',  8' 

6',  8' 
6',  8' 
6',  8' 

4',  5' 
3',  4'  6' 
4',  5' 

4',  5' 
4',  5' 
4'-3" 

4',  5' 
3',  6' 
4'-8" 

1-16-175 
1-18-125 
^^-1 6-1 54 

0.597 
0.425 
0.525 

6',  8' 
6',  8' 
6',  8' 

3',  4',  6' 
4'-4" 
4'-4" 

H-IS-U7 
>^-l 8-220 

0.50 
0.75 

6'  8' 
6',  8' 

3'-8" 
4' 

3-7-609 
3-6-550 
3-6-500 

2.00 
1.87 
1.70 

Mill 
shipment 

6',  8',  9',  10'-8' 
6',  8',  9',  i0'-8" 
6',  8',  9',  10'-8" 

5' 

3',  4',  6' 
4'-4" 

3-6-450 
3-7-400 

1.53 
1.36 

only 

6',  8',  9',  10'-8" 
6',  8',  9',  10'-8" 

4'-8" 
5' 

Note. — Interpret  styles  as  follows:  For  example  3-10-176.  3  equals  short  dimension  of 
diamond  in  inches;  10  equals  approximate  gage;  176  equals  0.176  sq.  in.  sectional  area  per  foot 
of  width. 


Sec.  1-64] 


MATERIALS 


55 


64.  Rib  Metal. — Rib  metal  is  manufactured  by  the  Trussed  Concrete  Steel  Co.,  and  con- 
sists of  nine  longitudinal  ribs  rigidly  connected  by  light  cross  members.  It  is  made  from  a 
sheet  of  metal,  fiat  on  one  side  and  corrugated  on  the  other.  Strips  of  the  metal  adjacent  to 
the  ribs  are  stamped  out,  and  the  sheet  is  drawn  out  into  square  meshes  (Fig.  29).  The  standard 
sheets  are  manufactured  with  meshes  of  from  2  to  8  in.  and  in  all  lengths  up  to  18  ft.  The  prop- 
erties of  rib  metal  are  given  in  the  table  which  follows: 


Fig.  29. — Rib  metal. 


Rib  Metal 


Size 
No. 

Width  of 
standard  sheet, 
inches 

Sq.  ft.  per 
linear  foot  of 
standard  sheet 

Area  per  ft. 
width,  sq.  in. 

Ult.  tensile 
strength  per  foot 
of  width 

Safe  tensile 
strength  per 
foot  of  width, 
pounds 

2 

16 

1.33 

0.54 

38,880 

9,720 

3 

24 

2.00 

0.36 

25,920 

6,480 

4 

32 

2.67 

0.27 

19,440 

4,860 

5 

40 

3.33 

0.216 

15,552 

3,888 

6 

48 

4.00 

0.18 

12,960 

3,240 

7 

56 

4.67 

0.154 

11,088 

2,772 

8 

64 

5.33 

0.135 

9,720 

2,430 

Area  of  one  rib  =  0.09  sq.  in. 
Ultimate  tensile  strength  =  6480  lb. 
Safe  tensile  strength  =  1620  lb. 

65.  Self-centering  Fabrics. — Permanent  centering  fabrics  (used  mostly  for  reinforcement 
in  concrete  floor  slabs  resting  on  steel  beams)  are  stiffened  by  rigid,  deep  ribs  which  do  away 
with  the  use  of  slab  forms.  The  mesh  is  made  small  enough  to  prevent  ordinary  concrete  from 
passing  through.  The  centering  fabric  is  laid  over  the  supports,  the  concrete  is  poured  on  top 
and  the  under  side  plastered.  A  simple  brace  along  the  middle  of  the  slab  span  is  sometimes 
required  to  give  sufficient  strength  to  the  ribs  until  the  concrete  has  set.  The  permanent  cen- 
tering fabrics  may  be  obtained  either  in  flat  or  segmental  form. 

A  serious  disadvantage  in  this  type  of  construction  is  the  difficulty  of  providing  efficient 
fire-protection  on  the  under  side  of  the  fabric.  Bond  with  the  concrete  is  also  likely  to  be 
insufficient. 


56 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  l-65a 


65a.  Hy-Rib. — Hy-Rib  (Fig.  30)  is  a  steel  sheathing,  stiffened  by  deep  ribs 
formed  from  a  single  sheet  of  steel.  It  is  controlled  by  the  Trussed  Concrete  Steel  Co.  of 
Youngstown,  Ohio,  and  Detroit,  Mich. 


Fig.  30— Hy-rib. 

Hy-Rib 


Type  of  Hy-Rib 

Formerly  called 

Height  of 

ribs 
(inches) 

Spacing 
of  ribs 
(inches) 

Width  of 
sheets 
(inches) 

Gage  Nos.  U.  S. 
Standard 

l>^-in.  Hy-Rib 

Deep-Rib 

m 

7 

14 

22,  24,  26 

i^l6-in.  Hy-Rib 

7-Rib 

4 

24 

22,  24,  26,  28 

i^e-in.  Hy-Rib 

3-Rib 

8 

16 

24,  26,  28 

^^-in.  Hy-Rib 

6-Rib 

Vs 

4 

20 

24,  26,  28 

Standard  lengths,  6,  8,  and  12  ft. 

Other  lengths  are  cut  from  standard  lengths  without  charge  except  for  waste. 
1^-in.  and  ^^{Q-'m.  Hy-Rib  are  shipped  in  bundles  of  eight  sheets;  '^^{Q-'m.  and  ^^-in. 
Hy-Rib  in  bundles  of  sixteen  sheets. 

656.  Corr-Mesh. — Corr-Mesh  (Fig.  31)  is  furnished  by  the  Corrugated  Bar  Co., 
Buffalo,  N.  Y.    It  is  a  stiff-ribbed  expanded  metal,  the  ribs  being  spaced  3^^  2  in.  c.  to  c.  The 


Fig.  31. — Corr-mesh. 


height  of  the  ribs  is  in.  and  the  width  of  the  sheets  is  12  %  in.  c.  to  c.  of  outside  ribs.  The 
standard  gages  are  No.  24,  No.  26,  and  No.  28,  although  other  gages  can  be  obtained  if  required. 
The  standard  lengths  are  6,  8,  10  and  12  ft.  The  sheets  are  furnished  either  fiat  or  in  various 
types  of  curves.    All  metal  is  shipped  painted  unless  specifically  ordered  otherwise. 

65c.  Self-Sentering. — Self-Sentering  (Fig.  32)  is  manufactured  by  the  General 
Fireproofing  Co.,  Youngstown,  Ohio.  It  is  made  up  of  a  series  of  heavy,  cold-drawn  ribs, 
6  in.  high,  always  spaced  3^^  in.  c.  to  c,  connected  by  a  form  of  expanded  metal — all  cut 
and  drawn  from  one  sheet  of  steel.  Size  of  sheets — 29  in.  wide  by  lengths  of  4,  5,  6,  7,  8,  9, 
10,  11  and  12  ft.  Longer  lengths  up  to  14  ft.  furnished  on  special  order.  Self-Sentering  is 
made  of  No.  24,  26  and  28-gage  metal. 

Q5d.  Chanelath.— Chanelath  (Fig.  33),  furnished  by  the  North  Western  Ex- 
panded Metal  Co.,  Chicago,  111.,  is  a  type  of  expanded  metal  composed  of  a  series  of  heavy 


Sec.  l-65el 


MATERIALS 


57 


cold-formed  steel  T-ribs  connected  together  by  a  mesh  known  as  "Kno-Burn"  metal  lath. 
The  T-ribs  are  }i  in.  high  and  spaced  4  in.  c.  to  c.  The  flange  of  the  T  is  3^  in.  wide.  Ghane- 
lath  is  manufactured  and  carried  in  stock  ready  for  immediate  shipment  in  the  following  sizes 
of  sheets:  Lengths— 3,  4,  5,  6,  7,  8,  9,  10,  11  and  12  ft.;  width?— 4,  8,  12,  16,  20,  24,  28,  32, 
36,  40,  44  and  48  in. 

65e.  Ribplex. — Ribplex  manufactured  by  the  Berger  Mfg.  Co.,  Canton,  Ohio, 
is  an  expanded  metal  with  ribs  4.8  in.  on  centers  and      in.  high.    Standard  sheets  are  24  in. 


Fig.  32. — Self-sentering. 


wide  and  are  carried  in  Stock  in  4,  5,  6,  7,  8,  9,  10,  11  and  12-ft.  lengths.  Sheets  are  made 
in  28,  26  and  24  gages. 

65/.  Dovetailed  Corrugated  Sheets. — Sheets  of  thin  steel  corrugated  so  as  to 
form  dovetailed  grooves  are  manufactured  by  the  Brown  Hoisting  Machinery  Co.,  Cleveland, 
Ohio,  and  by  the  Berger  Mfg.  Co.,  Canton,  Ohio.  The  first-mentioned  company  manufacture 
a  plate  known  as  Ferroinclave  and  the  latter  company  furnish  two  types  of  plates  known  as 


Fig.  33. — Chanelath. 

Ferro-Lithic  and  Multiple  Steel.  The  dovetailing  in  these  plates  serve  to  unite  the  plates  to 
the  concrete. 

66.  Reinforcing  Systems  for  Beams,  Girders  and  Columns. 

66a.  Kahn  System.— The  Kahn  trussed  bar  (Fig.  34),  named  for  its  inventor, 
is  rolled  with  flanges,  which  are  bent  up  to  resist  the  shear  in  the  beam.  For  continuous  beams, 
inverted  bars  are  placed  over  the  supports  in  the  upper  part  of  the  beam,  extending  over  the 
region  of  tension.    Properties  of  Kahn  trussed  bars  are  shown  in  the  following  table: 


58  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  1-666 


Kahn  Trussed  Bars 


Size  in 
inches 
a  Xb 

Weight 
in 

pounds 
per 
foot 

Area 

Length  of  diagonals 
in  inches 

Standard 

Special 

Square  Section  Bars 

y2  X  m 

y4  X  23^6 

1.4 
2.7 

0.41 
0.79 

12 

12,  24,  36 

6,    8,  18 
8,  18,  30 

New  Section  Bars 

iy2  X  2H 

m  X  2H 
2   X  sy2 

4.8 
6.8 
10.2 

1.4.1 
2.00 
3.00 

12,  24,  36 
36 
36 

8,  18,  30 
24,  30,  48 
24,  30,  48 

Note. — 8,  12,  18,  24,  30,  36,  and  48-in.  diagonals  are  sheared  alternately.  Six-in.  diagonals 
only  are  sheared  opposite. 


Fig.  34. — Kahn  trussed  bars. 


What  might  be  called  the  Kahn  system  is  illustrated  in  Fig.  35.  The  collapsible  column 
hooping  is  shown  more  in  detail  in  Fig.  36.  The  hooping  is  shipped  in  the  form  of  flat,  circular 
coils  of  exact  diameter  and  accurately  spaced  by  means  of  special  spacing  bars.  These  coils 
spring  automatically  into  a  complete  hooped  column  on  cutting  the  small  fastening  wires.  Rib 
bars  (see  Art.  Qld)  are  ordinarily  used  as  vertical  reinforcement  in  conjunction  with  the  hooping. 

The  collapsible  column  hooping  is  shipped  complete  with  two  spacing  bars.  Sizes  of  wire 
for  hooping:  y,  ^{q,  %^  J-^e?  and  3^-in.  diameter.  Diameter  of  coils:  9  to  30  in.  Pitch: 
ly  to  12  in.  Hooping,  where  desired,  can  also  be  obtained  in  bundles,  coiled  to  the  correct 
diameter,  and  with  separate  spacing  bars,  ready  for  assembling  in  the  field. 

666.  Cummings  System. — The  Cummings  system  is  shown  in  Fig.  37.  U- 
shaped  stirrups  are  used  on  the  girder  frame  shown.  They  are  shipped  flat  with  the  longitudinal 
reinforcement,  but  are  bent  up  to  an  inclined  position  on  the  work.  The  rods  are  held  together 
by  means  of  a  patented  chair.  In  the  Cummings  hooped  column,  each  hoop  is  securely  attached 
to  the  upright  rods.  ■  The  hoops  are  made  of  flat  steel,  bent  to  a  circle,  with  the  ends  riveted 
or  welded  together  in  such  a  manner  that  the  ends  of  the  hoops  protrude  at  right  angles  to 
keep  them  the  proper  distance  from  the  mold.  Reinforcement  of  the  Cummings  system  is 
manufactured  and  sold  by  the  Electric  Welding  Co.,  Pittsburg,  Pa. 

66c.  Unit  System. — Figs.  38  and  39  show  the  unit  system  of  reinforcing  con- 
trolled by  the  American  System  of  Reinforcing,  Chicago,  III.    The  girder  frames  are  not  stock 


Sec.  l-66c] 


MATERIALS 


59 


60 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  l-66d 


frames  but  are  built  to  meet  the  engineer's  or  architect's  plans.  Unit  girder  frames  are  pro- 
vided with  overlapping  rods  for  continuous  beams  to  reinforce  against  negative  moment. 

666?.  Corr  System. — Corr-bar  girder  frames  (Fig.  40)  and  shop  fabricated  spirals 
(Fig.  41)  are  furnished  by  the  Corrugated  Bar  Co.,  Buffalo,  N.  Y.  As  with  the  unit  system, 
the  girder  frames  are  built  to  meet  the  engineer's  or  architect's  plans.  In  the  spiral  reinforce- 
ment the  spacing  bars  consist  of  two  or — in  large  columns — four  spacers  made  of  T-section 
bars  notched  to  receive  the  spiral.  The  spirals  are  made  of  cold-drawn  wire  and  are  furnished 
in  any  length,  in  diameters  of  10  to  36  in.,  pitch  1  to  4  in.,  and  of  the  following  sizes  of  wire: 


Gage 

Dia.  of 
wire 
(inch) 

Wt.  of 
wire  (lb. 
per  foot) 

Practical 
equivalent 
(inch) 

Gage 

Dia.  of 
wire 
(inch) 

wt.  of 
wire  (lb. 
per  foot) 

Practical 
equivalent 
(inch) 

7/0 

0.4900 

0.6404 

}/2  round 

0 

0.3065 

0.2506 

^{q  round 

5/0 

0.4305 

0.4943 

}{q  round 

3 

0.2437 

0.0466 

round 

3/0 

0.3625 

0.3505 

%  round 

Fig.  38.— "Unit"  frames.  FtG.  39. — "  Unit"  spirals. 


66e.  Hennebique  System. — One  of  the  pioneers  in  concrete  construction  in 
Europe  is  Mr.  Hennebique,  in  France,  and  the  system  which  still  bears  his  name  is  shown  in 
Fig.  42. 

66/.  Pin-connected  System. — Reinforcement  in  the  pin-connected  system  con- 
sists of  bars  made  into  a  truss  and  ready  for  placing  in  the  forms  (see  Fig.  43). 

QQg.  Luten  Truss. — The  Luten  truss  is  shown  in  Fig.  44.  The  bars  are  rigidly 
locked  together  to  form  the  truss  by  a  clamp,  with  a  wedge  that  is  self-locking  when  driven 
home.  The  truss  is  especially  adapted  to  highway  culverts  and  bridges  and  is  put  out  by  the 
National  Concrete  Co. 

66/i.  Xpantruss  System. — The  truss  by  this  name  is  shown  in  Fig.  45,  and  is 
applicable  chiefly  to  beams,  girders,  and  heavy  slabs.  This  system  is  patented  by  The  Con- 
solidated Expanded  Metal  Cos. 

66i.  Shop  Fabricated  Reinforcement  System. — In  this  system  (Fig.  46)  manu- 
factured by  the  Lackawanna  Steel  Co.,  Lackawanna,  N.  Y.,  the  standard  bar  is  a  troughed 


Sec.  l-66^] 


Fig.  40. — Corr-bar  girder  frame. 


Fig.  41. — Corrugated  Bar  Co.'s  spirals. 


Fig.  42. — Hennebique  system. 


Fig.  43. — Pin-connected  system. 


Fig.  44. — Luten  truss. 


62 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  1-m 


section  and  the  auxiliary  reinforcing  members,  such  as  diagonal  tension  members,  tie  rods  for 
columns,  walls,  etc.,  are  flat  bars  {}i  by  ^{q  in.)  with  knobs  on  each  edge.    Fabrication  is 


Fig.  45. — Xpantruss  system. 


effected  by  placing  a  portion  of  the  auxiliary  flat,  properly  bent,  within  the  trough  and  with  a 
bulldozer  or  other  pressure  machine  squeezing  the  wings  of  the  main  bar  and  also  gripping  the 
knobs  of  the  flat.    The  upper  or  troughed  part  of  the  main  bar  is  a  constant.    Increased  area  is 


Fig.  46. — Shop  fabricated  reinforcement  system. 


developed  by  making  the  section  deeper  as  required.  Tests  have  shown  that  the  rivet  grip,  as 
it  is  called,  is  greater  than  the  strength  of  the  auxiliary  member. 


SECTION  2 


GENERAL  METHODS  OF  CONSTRUCTION 
PROPORTIONING  CONCRETE 

1.  Properties  of  Concrete  Dependent  upon  Properties  and  Relative  Proportions  of  Con- 
stituent Materials. — Despite  prevalence  of  careless  measurement  of  materials  and  arbitrary 
specifying  of  proportions  for  concrete,  it  does  not  follow,  as  many  infer,  that  such  procedures 
are  right,  either  in  practice  or  in  theory,  or  that  they  should  be  continued.  On  the  contrary, 
such  procedures  are  wasteful  and  inefficient  and  to  meet  their  effects,  the  allowable  stresses  on  con- 
crete have  been  fixed  at  a  standard  so  low  that  actual  failure  or  disintegration  can  result  only 
from  flagrant  abuses  of  these  lax  and  undesirable  methods.  All  consideration  of  possible  per- 
fection aside,  it  is  known  beyond  question  that  proper  proportioning  of  selected  materials  is  a 
prerequisite  to  success,  for  concrete  is  wholly  dependent  for  its  properties  upon  the  properties 
and  proportions  of  its  constituent  materials,  both  severally  and  in  combination. 

2.  Theory  of  Proportioning. — Considering  the  composite  nature  of  concrete  as  revealed 
by  a  fractured  section  (Fig.  1),  it  will  be  seen  at  a  glance  that  this  substance  is  a  pudding  of 
large  stone  particles  set  in  a  mass,  or  ''matrix,"  of  other  substances,  which  matrix  is  a  mortar 
of  cement  and  sand.  If  this  matrix  be  magnified,  it  will  be  seen  to 
be  similar  to  the  gross  section,  with  sand  grains  as  large  par- 
ticles held  in  a  matrix  of  more-or-less  hydrated  cement.  Theo- 
retically, the  large  stone  particles  and  also  the  sand  grains  should 
lie  as  closely  together  as  possible,  so  that  if  all  fragments  (sand 
included)  had  come  from  crushing  a  solid  cube  of  stone,  their 
reassembly  would  approach  the  cube's  original  volume,  density, 
and  stress  resistance.  The  aim  in  proportioning,  therefore,  is 
efficient  recombination. 

It  is  impossible  in  practice  to  obtain  the  close  rearrange- 
'  ment  and  interlocking  of  the  particles  that  is,  on  all  counts, 

desirable.    There  must  and  do  remain  between  them,  as  is  ^  x  i^-^v^^^xw^-oi-v/iic 

visually  evident,  inter-particle  spaces  or  voids.    To  fill  spaces  or  structure  of  concrete, 

voids  between  large  particles,  finer  materials  of  like  nature  and 

origin  are  chosen ;  and  on  theoretical  grounds,  it  should  be  possible  by  measuring  these  inter- 
particle  spaces — as,  for  instance,  by  pouring  measured  quantities  of  water  into  a  given  con- 
tainer filled  with  stone  particles  until  the  container  can  hold  no  more — to  add  a  quantity  of 
sand  to  the  stone  of  a  volume  equivalent  to  the  added  volume  of  water,  so  as  to  render  the 
measure  almost  solidly  full  of  sand  and  stone  particles,  or  rather,  of  stone  particles  since  sand 
is  itself  disintegrated  rock. 

It  is  to  be  expected,  however,  as  is  evidenced  by  visual  magnification,  that  between  the 
sand  grains  must  lie  other  and  smaller  inter-particle  spaces  in  great  number;  and  on  the  theo- 
retical basis  of  proportioning,  these  should  be  filled  by  cement,  so  that  the  entire  measure 
might  be  solidly  full  of  a  composite  which  would  closely  approximate  natural  stone  in  texture, 
density,  and  strength.  But  this  ideal  is  not  attained,  partly  because  in  this  hypothesis  the  water 
necessary  for  reaction  with  cement  is  not  allotted  space,  and  partly  because  no  allowance  is 
made  for  the  necessary  surface  coating  of  sand  and  stone  by  cement  and  water,  with  consequent 
dispersion  of  particles.    The  water  is  assumed  either  to  lie  in  inter-particle  spaces  not  filled 

63 


64 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-3 


by  cement  or  in  inter-particle  spaces  in  the  cement  itself,  or  else  to  be  negligible  in  quantity  and 
volume. 

The  foregoing  are  the  assumptions  on  which  the  void  theory  of  proportioning  is  based. 
There  is  hardly  one  of  these  assumptions  that  does  not  rely  on  false  premises,  so  that  the  whole 
void  theory  must  be  and  is  found  at  variance  with  practice,  particularly  when  subjected  to 
comparison  with  results  obtained  by  rough  field  procedure.  Yet  the  idea  behind  the  theory 
is  right,  for  it  suggests  by  inference  that  density  of  natural  stone  is  the  ideal  to  be  striven  for 
and  that  it  may  be  obtained:  (1)  by  using  a  maximum  quantity  of  natural  stone  in  fragments 
large  enough  to  possess  unimpaired  its  inherent  properties;  and  (2)  by  filling  in  the  inter- 
fragment  spaces  with  maximum  quantities  of  like  mineral  materials.  The  error  lies  not  so 
much  in  the  standard  thus  chosen  as  in  neglect  to  give  proper  consideration  to  the  individual 
and  combinative  properties  of  the  several  substances  included  in  concrete,  not  the  least  impor- 
tant of  which  is  water,  both  as  a  space  occupier  as  well  as  in  its  chemical  and  physical  actions 
with  cement  and  with  inert  aggregate.^  It  is  always  to  be  remembered  that  concrete  is  not 
concrete  without  water;  that  its  proportioning  is  equally  important  with  the  proportioning 
of  cement,  stone,  or  sand;  and  that  it  affects  by  its  quantity  the  proportions  of  the  other 
ingredients  that  may  be  placed  in  any  given  volume. 

3.  The  Strength  Elements  of  Concrete. — Any  concrete  will  have  as  an  upper  limit  of 
stress  resistance  the  properties  of  the  most  resistant  of  the  materials  entering  into  it.  These 
materials  are  usually  stone  and  sand,  with  some  strength  preference  in  favor  of  sand,  as  most 
sand  particles  are  individual  crystal  units  without  cementing  substance  between  them,  while 
natural  stone  is  an  aggregation  of  similar  particles,  built  up  in  one  way  or  another.  Since 
natural  stone  is  formed  under  the  most  advantageous  conditions  as  to  arrangement  of  particles, 
pressure,  etc.,  and  since  in  its  composite  nature,  it  is  closely  analagous  to  concrete,  it  may  be 
taken  as  the  ultimate  ideal  in  artificial  stone  made  by  the  admixture  of  sand,  stone,  and  water, 
with  Portland  cement.  Furthermore,  in  natural  stone  as  in  concrete,  the  weakest  element 
is  the  cementing  substance  which  lies  between  the  inert  grains,  for  in  each  material  this  is 
alterable  by  various  agents  and  is  at  the  same  time  of  less  inherent  strength  than  the  mineral 
particles  which  it  unites. 

4.  Proportioning  for  High-strength  Concretes. — From  the  above,  it  follows  that  the 
greater  the  proportion  of  mineral  grains  in  any  stone,  brought  about  through  compacting  and 
the  exclusion  of  all  but  a  film  of  cementing  material  (as  in  a  very  compact  sandstone),  the 
higher  will  be  its  strength.  In  the  same  way,  in  artificial  concretes,  the  greater  the  proportion 
of  natural  stone  (or  of  analogous  mineral  matter)  and  the  less  the  quantity  of  cement,  consistent 
with  proper  coating  of  the  inert  materials,  the  greater  will  be  the  resulting  strength,  for  Portland 
cement  in  combination  with  water  is  the  weakest  element  of  this  cement-sand-stone  combina- 
tion. In  this  connection  it  should  be  further  remembered,  that  while  ground  Portland-cement 
clinker  (commercial  powdered  cement)  is  extremely  hard  and  of  great  inherent  strength,  the 
same  substance  in  combination  with  water  results  in  an  entirely  different  product  of  different 
chemical  nature  and  composition,  having  relatively  low  strength.  It  is,  therefore,  actually 
true  that  down  to  a  certain  limit,  the  less  cement  there  is  in  any  concrete  the  more  enduring 
and,  at  the  same  time,  the  cheaper  will  be  that  concrete.  It  becomes,  then,  of  vital  importance 
not  only  to  so  select  inert  materials  that  they  shall  by  their  properties  be  able  to  endow 
the  concrete  with  high  strength,  but  also  to  so  choose  their  proportions  that  they  shall  be  a 
quantitative  maximum  in  the  mixture,  the  cement  functioning  in  minimum  quantities,  as 
an  adhesive  surface  coverer  and  as  a  void  filler. 

6.  Weakness  Due  to  Poor  Proportioning. — By  reason  of  the  remarkable  properties  of 
Portland  cement,  carelessness  in  proportioning  concrete  has  become  tacitly  accepted,  if  not 
permitted  and  sanctioned  practice.  Fairly  good  results  have  been  obtained  in  spite  of  gross 
carelessness;  and  this  has  brought  about  a  belief  in  the  minds  of  perhaps  a  majority  of  con- 
structors, that  practically  any  materials  in  any  proportions  in  combination  with  any  cement 

1  See  chapter  on  "Water"  in  Sect.  1. 


Sec.  2-6] 


GENERAL  METHODS  OF  CONSTRUCTION 


.65 


will  give  the  desired  results.    It  is  also  unfortunately  true,  that  in  first  results  and  appearance, 
Portland-cement  concrete,  even  when  of  inferior  materials  and  in  improper  proportions,  appears 
equal  to  that  properly  made;  but  the  rapidly  increasing  number  of  defective  constructions 
which  are  being  brought  to  hght  with  the  passage  of  time  is  bringing  about  an  awakening 
in  regard  to  the  causes  of  such  disintegrations.    Such  apparently  easy  successes  have  given 
rise  to  the  so-called  "arbitrary"  proportions  in  widespread  present  use,  but  in  probably  a 
majority  of  cases,  not  the  least  important  of  the  causes  which  result  in  ultimate  failure  is  the 
use  of  these  same  arbitrary,  "practical"  proportions,  which  actually  are  not  practical  in  one 
case  out  of  ten,  so  far  as  results  achieved  in  making  a  good  product  are  concerned. 
I        6.  Unit  of  Proportioning. — In  specifying  concrete  or  mortar  mixtures  a  unit  quantity  of 
1  cement  is  taken  as  a  base.    The  cubic  foot  is  the  usual  unit  of  quantity.    On  large  work  where 
overhead  bins  and  measuring-hoppers  are  provided,  the  cubic  yard  may  be  chosen.    In  general 
the  assumption  is  made  that  1  sack  of  cement  weighs  94  lb.;  that  it  is  3^1  bbl.;  and  that  it 
I  occupies  1  cu.  ft.^ 

7.  Arbitrary  Proportions. — Despite  their  inadvisabihty  and  incorrectness,  arbitrary 
proportions  cannot  be  ignored.  With  the  cubic  foot  of  cement  as  a  unit,  these  proportions 
are  commonly  described  as  1  :  2  :  4  or  1  :  3  :  6  or  1  :  4  :  8  or  some  other  easily  remembered  ratio, 
expressed  in  terms  of  volumes  of  sand  and  stone  respectively,  to  the  unit  volume  of  cement. 

Evil  as  is  such  arbitrary  choosing  of  proportions,  when  such  proportions  are  rendered 
still  further  indefinite  by  inaccurate  measurement  of  materials,  the  composition  of  the  resulting 
concrete  is  indefinite  and  uncertain  to  an  extent  that  gives  a  new  respect  for  the  abilities  of 
Portland  cement.  It  has  been  shown  repeatedly  on  test,  and  confirmed  by  examination  of 
the  resulting  concrete,  that  measurement  of  materials  in  the  usual  manner  by  wheelbarrows  or 
shovelfuls,  may  bring  about  variations  of  from  100  to  200%  in  actual  proportion  of  material 
delivered  to  the  concrete  batch.  This  is  particularly  true  with  regard  to  sand.  Since  sand 
occupies  at  least  one-third  of  the  volume  of  any  concrete,  and  as  the  density  and  stress  resistance 
of  the  mixture  is  so  largely  dependent  on  the  quantity  of  sand  present,  the  variations  introduced 
through  change  of  grading  attendant  on  supplies  from  different  localities,  or  through  change 
in  moisture  content,  will  be  seen  to  be  very  serious.  It  is  all  too  true  that  in  commercial  work, 
a  supposedly  1:2:4  concrete  is  quite  as  likely  to  be  1  :  4  :  8  or  1  :  5  : 9  or  even  worse,  or  on  the 
other  hand  it  may  be  1  : 1  :  2,  or  other  combinations  in  indefinite  number,  with  a  corresponding 
increase  of  unreliability  and  cement  cost. 

It  should  always  be  remembered  that  each  of  the  inert  materials  of  concrete  has  surfaces 
and  voids  peculiar  to  itself,  and  the  combination  of  any  two  is  peculiar  to  them  alone.  A  change 
in  either  material  must,  therefore,  result  in  new  relations,  with  change  in  the  burden  imposed 
on  the  cement,  which  (in  combination  with  water)  must  function  both  as  an  adhesive,  as  a 
surface  cover,  and  as  a  void  filler.  Regardless  of  the  apparent  sanction  generally  given  to  the 
use  of  arbitrary  proportions  in  making  concrete  and  to  the  apparent  expediting  of  work  by 
slap-dash  measurement,  this  practice  should  be  prohibited  on  all  work  above  that  of  the  most 
ordinary  grade. 

H.  C.  Johnson  in  "What  is  a  1:2:4  Concrete ?"2  states  that  with  maintenance  of  strict 
proportions  with  different  materials,  the  cement  demanded  will  range  from  100  to  130  bags — 
a  variation  of  4.5%  in  a  definite  quantity  of  concrete.  The  table  on  page  66  summarizes  the 
results  of  his  experiments. 

8.  Proportioning  by  Void  Determinations. — For  reasons  given  in  Art.  2  proportioning 
materials  by  void  determinations  is  obsolescent  practice,  not  to  be  more  countenanced  than 
that  of  arbitrary  proportions,  which  it  resembles.  The  determination  of  voids  may  give  a  rough 
indication  as  to  the  inter-particle  spaces  existing  in  any  fine  or  coarse  aggregate,  but  it  does  not 

1  A  number  of  authorities  have  approved  the  adoption  of  3.8  cu.  ft.  of  cement  to  the  barrel.  This  value  is 
more  nearly  exact  and  gives  100  lb.  of  cement  to  the  cubic  foot  or  0.95  cu.  ft.  per  sack.  One  standard  sack,  however, 
may  be  and  usually  is  considered  as  1  cu.  ft. 

2  Concrete  and  Constructional  Engineerimj  (London),  Feb.,  1915. 
5 


CONCRETE  ENGINEERS'  HANDBOOK 


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Sec.  2-81  GENERAL  METHODS  OF  CONSTRUCTION  67 

afford  a  basis  on  which  to  proportion  the  materials.  If  a  cubic  foot  of  broken  stone  contains 
40%  of  voids,  the  void  basis  of  proportioning  is  based  on  the  assumption  that  cu.  ft.  of  sand 
should  be  added  in  order  to  fill  these  spaces,  i.e.,  to  bring  the  mass  up  to  approximate  solidity 
and  that  if  this  quantity  of  sand  in  turn  contains  35%  of  voids,  that  ^^qo  X  Viq  cu.  ft.  of 
cement  should  be  added  (plus  a  certain  arbitrary  percentage  for  coating  sand  and  stone  sur- 
faces) to  give  to  the  mass  actual  solidity. 

The  inaccuracy  of  this  method  is  partially  due  to  the  variation  in  voids  in  sand  under  differ- 
ent conditions,  this  variation  being  sometimes  sufficient  to  make  a  difference  of  30%  in  the 
amount  of  cement  required.  The  following  table  shows  variation  in  voids  due  to  difference 
in  moisture  alone.  The  figures  in  this  table  are  for  sand  in  a  loose  condition  and  the  differences 
would  be  still  greater  if  the  dry  sand  had  been  shaken  and  tamped.  It  is  evident  that  the 
method  of  proportioning  by  voids  is  valueless  unless  the  sand  is  in  the  same  state  of  compact- 
ness when  mixed  in  concrete  as  it  is  when  the  void  test  is  made. 

Physical  Characteristics  of  Concrete  Aggregates^ 


(For  aggregates  in  loose  condition) 


Voids  (aggre- 
gate contain- 
ing natural 
moisture) 

Voids 
(aggre- 
gate 
dry, 

% 

Weight    (lb.  per 
cu.  ft.,  aggregate 
containing  natural 
moisture) 

Weight  (lb.  per 
cu.  ft.,  aggre- 
gate dry) 

%  moisture 
in  moist 
aggregate 

Specific 
grav- 
ity of 
stone 

Average  of  4  good  concrete 

53 

43 

82 

95 

5 

2.65 

sands. 

Long  Island  washed  gravel 

36 

106 

2.65 

graded  %  in.  to  1^^  in. 

Commercial    ^-in.  lime- 

44 

97 

2.80 

stone. 

Commercial    l3^-in.  lime- 

46 

95 

2.80 

stone. 

Trap  rock,  graded  %  in.  to 

44 

103 

2.95 

l^in. 

In  practice,  therefore,  the  proportions  obtained  by  void  determinations  do  not  hold.  As 
soon  as  water  is  added  to  sand,  stone,  and  cement,  very  different  physical  relations  are  effective 
from  those  that  previously  existed.  The  particles  of  cement  and  the  finer  particles  of  sand  are 
necessarily  dispersed  by  the  water  which  coats  and  lies  between  them;  the  larger  particles  of 
sand  are  dispersed  by  this  thin  mortar  of  cement,  fine  sand,  and  water;  and  the  finer  and  larger 
stones  in  turn  are  dispersed  in  a  similar  manner  by  a  like  combination  of  the  finer  materials. 
As  pointed  out  in  Art.  2,  this  fact  is  made  very  evident  by  the  examination  of  the  fractured  sur- 
face of  any  concrete.  No  matter  whether  the  surface  examined  is  in  the  gross,  showing  large 
particles  of  stone,  or  whether  it  is  magnified  to  make  visible  the  very  fine  particles  of  sand 
and  cement,  the  same  dispersion  will  be  found  to  obtain,  offering  visual  evidence,  confirmed 
by  test,  as  to  the  necessary  inaccuracy  of  void  determinations  as  a  basis  of  proportioning. 

This  may  be  made  evident  by  a  simple  illustration.  Assume  a  vessel  containing  a  given 
number  of  small  spheres  of  varying  sizes  which  may  be  considered  as  so  many  sand  and  cement 
grains.  It  is  evident  that  if  these  spheres  fill  the  measure,  a  certain  quantity  of  water  may  be 
added  without  disturbing  their  inter-relations.  That  is  to  say,  it  is  assumed  that  these  spheres 
will  remain  in  surface  contact  one  with  another  even  after  the  addition  of  water.  If,  however, 
the  same  spheres  be  put  into  a  larger  vessel  and  an  additional  quantity  of  water  added,  filling 


1  R.  E.  Goodwin  in  Concrete,  Nov.,  1915. 


68 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-9 


this  vessel,  then,  if  the  mixture  is  uniform  (which  is  the  condition  assumed  to  exist  in  mortar 
and  in  concrete),  these  spheres  must  be  dispersed  and  be  out  of  surface  contact  one  with  another. 
This  represents  in  exaggerated  illustration,  but  not  in  exaggerated  degree  the  conditions  as 
they  exist  in  commercial  concretes,  dispersion  therein  being  progressive  from  the  finest  particles 
to  the  largest,  each  successive  grade  assisting  in  the  dispersion  of  the  size  next  larger,  with 
resultant  increased  demand  for  cement  and  corresponding  weakening  of  the  mass. 

Rather  than  proportion  strictly  on  the  basis  of  voids,  therefore,  a  better  way  is  first  to 
grade  the  aggregates,  both  coarse  and  fine,  by  sieve  analyses.  In  this  way,  the  voids  are  taken 
cognizance  of,  though  in  a  different  way.  A  combination  of  materials  may  then  be  made  such 
as  to  give  a  mixture  containing  these  materials  in  greatest  quantities.  The  proportions  of 
aggregates  in  this  mixture  having  been  determined,  the  amount  of  cement  required  will  then 
depend  very  largely  upon  the  strength  needed  or  the  degree  of  imperviousness  required  of  the 
concrete.  It  can  be  approximately  estimated  by  determining  the  percentage  of  voids  in  the 
mass,  but  on  account  of  the  errors  introduced  through  the  establishment  of  new  conditions  by 
the  introduction  of  water,  this  latter  assumption  is  not  to  be  recommended  unless  checked  on 
actual  mixtures. 

9.  Proportioning  by  Mechanical  Analysis. — Although  the  foregoing  recognizes  the  exist- 
ence of  inter-particle  spaces  or  voids,  it  properly  should  be  termed  ''proportioning  by  mechanical 
analysis."  Such  proportioning  is  recombination  after  analyses  are  made  by  passing  representa- 
tive samples  of  the  inert  materials  through  successive  sizes  of  standard-mesh  screens;  noting 
the  quantity  passing  and  the  quantity  retained  on  each  screen;  and  plotting  these  as  a  curve, 
with  sizes  of  screen  openings  as  abscissae  and  percentages  of  material  passing  as  ordinates 
(see  Art.  32,  Sect.  1).  By  this  procedure  a  more  or  less  regular  curve  will  be  obtained  for 
the  sand  and  for  the  stone;  and  its  variation  from  a  predetermined  curve,  such  as  that  of  Wil- 
liam F.  Fuller,^  or  that  advocated  by  the  Bureau  of  Standards  at  Washington,^  may  be  deter- 
mined. The  deficiencies  of  one  material,  therefore,  can  be  balanced  against  the  advantages  of 
another;  and  by  proper  combination  of  the  two,  as  determined  from  this  curve,  a  determina- 
tion may  be  had  as  to  the  proper  proportions  of  the  several  materials.  A  few  trials  will  give  a 
very  close  approximation;  and  if  the  qualities  of  the  several  materials  are  maintained  to  sample 
throughout  the  work,  these  proportions  may  be  safely  followed.  It  is  probable,  however,  that 
the  character  of  the  materials  will  change  more  or  less  throughout  the  job,  so  that  it  is  usually 
necessary  to  continuously  check  the  several  shipments  of  materials  as  they  go  into  the  work; 
and  if  they  vary  seriously  from  the  established  standard,  to  alter  the  proportions  of  the  concrete 
in  accordance  with  variations  noted  by  repetitions  of  the  processes  before  noted. 

10.  Proportioning  by  Maximum  Density  Tests. — A  direct  test  which  reproduces  actual 
conditions  is  always  preferable  to  an  indirect  test  based  on  assumptions  subject  to  variation. 
The  result  desired  in  proportioning  concrete  is  a  mixture  of  maximum  density,  and  the  most 
direct  means  to  this  end  is  the  testing  of  trial  mixtures.  These  are  best  made  with  concrete, 
or  the  coarse  aggregate  may  be  omitted  and  the  mortar  alone  used.  The  latter  method,  how- 
ever, is  not  always  representative,  as  in  this  case  the  voids  in  the  coarse  aggregate  must  be 
determined  and  the  concrete  so  proportioned  that  the  mortar  will  fill  the  voids  in  the  gravel 
or  the  stone,  with  a  certain  arbitrary  excess,  thus  introducing  an  element  of  error.  As  a  factor 
of  safety,  the  amount  of  mortar  should  exceed  the  voids  in  the  gravel  or  stone  about  10%. 
Nevertheless,  this  method  has  some  justification  as  the  percentage  of  voids  in  coarse  aggregate 
is  less  variable  than  in  sand,  and  also  because  an  error  in  determining  them  has  less  effect  on  the 
quantitj^  of  cement  used. 

In  proportioning  by  trial  mixtures,  definite  quantities  of  the  materials  in  proportions  first 
determined  by  mechanical  analysis  are  mixed  with  a  requisite  quantity  of  water  and  are  put  in 
a  metal  cylinder  about  1  ft.  long  by  about  1}4  in.  in  diameter,  and  tamped.  The  volume  they 
occupy  is  then  determined  by  measuring  from  the  top  of  the  cylinder.    When  this  has  been 

1  See  "Concrete,  Plain  and  Reinforced,"  by  Taylor  and  Thompson. 
-  See  Bull.  58,  Bureau  of  Standards,  Washington,  D.  C. 


Sec.  2-11] 


GENERAL  METHODS  OF  CONSTRUCTION 


determined  the  mixture  is  removed  from  the  cyhnder,  the  latter  cleaned  and  a  new  mixture  made 
and  tried  out  in  the  same  way,  with  a  slight  variation  of  the  proportions  of  sand,  stone  and  ce- 
ment, but  with  the  quantity  of  water  constant.  Very  soon  a  mixture  which  will  give  the  least 
volume  for  any  given  quantity  of  materials  will  be  found  and  this  mixture  will  give  the  densest, 
most  impervious  and  strongest  concrete  with  those  materials. 

This  is  known  as  a  mixhire  of  maximum  density,  but  it  is  apt  to  be  inconvenient  for  use 
in  ordinary  concrete  work,  inasmuch  as  it  contains  so  large  a  proportion  of  stone  that  it  is  ex- 
tremely harsh  and  difficult  to  work.  To  make  it  freer-working,  more  sand  is  generally  added; 
and,  although  something  of  strength  and  density  is  sacrificed  by  so  doing,  the  advantages  of 
easy  working  and  increased  compactness  in  forms  probably  compensates  for  disadvantages 
arising  directly  from  any  impropriety  of  proportions. 

Proportioning  by  maximum  density  is  very  readily  applied  in  the  field,  all  that  is  necessary 
being  an  iron  pail  and  a  pair  of  scales.  Proportions  can  be  determined  for  the  concrete,  without 
the  use  of  a  laboratory  apparatus  or  any  unusual  equipment,  by  weighing  out  the  materials, 
having  due  care  that  the  sand  is  reasonably  dry  so  that  too  great  volumetric  errors  may  not  be 
introduced,  and  then  mixing  them  in  the  pail  until  a  mixture  of  maximum  density  is  obtained. 
All  tests  are  useless,  however,  unless  the  determined  proportions  apply  to  every  batch  mixed 
and  placed  in  forms. 

11.  Checking  Materials  on  the  Job  J — When  the  materials  used  on  the  job  are  from  the 
same  sources  as  those  tested  and  from  which  tests  the  proportions  to  be  used  were  determined, 
it  is  a  simple  matter  to  check  up  their  qualities.  Sand  and  stone 
from  the  same  source  do  not  vary  much  in  quality,  except  in  so  far 
as  quality  is  influenced  by  size  of  particles.  Having  once  established 
by  test  the  suitability  of  sand  and  stone  for  any  grade  of  concrete 
and  having  determined  the  proper  proportions  in  which  to  use 
them  to  attain  a  certain  desired  result,  it  is  only  necessary  there- 
after to  see  that  the  size,  grading,  and  proportions  of  these  ma- 
terials are  reasonably  constant  to  insure  uniform  quality  of  con- 
crete. Such  a  check  on  size  and  grading  should  be  had  on  each 
and  every  shipment  of  material  and  is  easily  obtained  with  a  small 
set  of  sieves,  or  in  the  case  of  sand,  which  is  by  far  the  more  impor- 
tant material,  by  means  of  a  self-contained  sand  tester  (see  Fig.  2). 

The  regular  and  systematic  testing  of  the  size  of  the  aggregates 
gives  data  which  will  permit  the  engineer  to  tell  without  further 
tests,  whether  the  aggregates  will  produce  a  better  or  poorer  con- 
crete than  that  produced  by  the  original  or  standard  sample.  This 
fact  is  based  on  the  well-established  principle  that,  other  things 
being  equal,  the  aggregate  whose  granulometric-analysis  curve 
most  nearly  approaches  the  line  of  maximum  density  will  pro- 
duce the  best  concrete.    This  makes  it  possible  to  determine  with 

reasonable  certainty  which  of  two  sands  of  the  same  kind  and  from  the  same  source,  but 
differing  only  in  fineness,  will  make  the  better  concrete. 

To  illustrate :  Concrete  is  to  be  placed  in  a  certain  locali  ty.  There  are  to  be  heavy  machin- 
ery foundations  and  thick  building  foundation  walls  and  footings  below  grade,  with  rein- 
forced superstructure.  The  engineer  in  charge  secures  samples  of  the  available  concrete  aggre- 
gates, both  fine  and  coarse,  and  sends  them  to  the  laboratory  for  test.  The  tests  show  that 
although  the  best  available  sand  has  a  strength  in  1  :  3  mortar  only  70%  of  that  of  standard 
Ottawa  sand,  yet  mixed  in  the  proportions  of  1  :  1^^  :  3^^  with  the  cement  and  coarse  aggregates 
to  be  used,  the  resulting  concrete  has  a  compressive  strength  of  2600  lb.  per  sq.  in.  at  28  days. 
Other  proportions  give  higher  and  lower  strengths,  depending  on  their  richness,  but  as  the 

1  Chapman  and  Johnson:  Eng.  Rec,  June  12,  19,  26,  1915. 
2Kolesch  &  Co.,  Fulton  St.,  New  York. 


Fig.  2. — Universal  Sand 
Tester — portable  instrument  for 
making  mechanical  analyses  of 
sands.- 


70 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-12 


design  of  the  structure  requires  concrete  having  an  ultimate  strength  of  2500  lb.  per  sq.  in. 
the  1:1^^:  3^^  proportion  is  used.  For  the  foundations  and  footings,  the  designs  being  based 
on  an  ultimate  strength  of  1500  lb.  per  sq.  in.  in  the  concrete,  the  proportion  of  1  :  2}^  :  A}^, 
which  gave  in  the  test  a  compressive  strength  of  1550  lb.  per  sq.  in.,  is  chosen.  Under  the 
present  standard  method  of  specifying  sand,  this  particular  sand  could  not  have  been  used  in 
concrete. 

Among  the  tests  advantageously  made  in  the  field  on  a  sand  are  granulometric-analysis 
charts  made  with  the  sand  tester  (Fig.  2).  This  sand  tester  has  five  screens  having  6,  10, 
20,  35,  and  65  meshes  per  in.  Each  screen  in  succession  has  openings  one-half  the  width  of 
the  openings  in  the  preceding  screen.  The  charts  are  averaged  and  a  special  guide  chart  is 
prepared  for  the  use  of  the  inspector  on  the  job.  In  making  up  this  guide  chart  a  permissible 
variation  of  about  2.5%  each  way  from  the  mean  of  the  tests  made  on  the  sample,  is  allowed. 
A  copy  of  this  chart  is  sent  to  the  job  and  a  copy  kept  in  the  office  files. 

As  the  sand  arrives  on  the  job  the  inspector,  or  some  one  designated  by  the  superintendent, 
makes  tests  with  the  sand  tester  and  compares  the  resulting  chart  with  the  guide  chart.  If  the 
results  show  greater  variation  than  is  permissible — particularly  if  they  show  the  sand  to  be 
finer  than  shown  on  the  guide  chart — then  the  matter  is  taken  up  with  the  one  who  supplies 
the  sand. 

By  this  method  the  quality  of  the  aggregates  is  recognized  and  provided  for  in  the  selection 
of  proportions  for  the  concrete,  and  enough  cement  is  used  to  produce  the  desired  quality. 
In  this  way  the  uncertainty  which  is  attendant  upon  separately  testing  each  of  the  three 
materials,  and  predicting  therefrom  the  quality  of  the  concrete  resulting  from  their  combina- 
tion, is  eliminated.  The  time  required  for  testing  the  combination  is  no  greater  than  that 
required  for  testing  any  one  of  the  materials.  ^ 

12.  Proportions  and  the  Measurement  of  Materials. — Proportioning  always  involves 
measurement  of  materials.  Even  with  the  most  exact  determinations  of  proportions,  if  measure- 
ment of  materials  in  the  field  is  inexact  and  variable,  concrete  so  made  will  necessarily  be  a 
substance  of  extremely  uncertain  value.  Furthermore,  so  long  as  there  is  prevalent  a  tendency 
to  use  excess  water,  even  the  most  exact  measurement  of  stone,  sand,  and  cement  may  be 
nullified.  Those  who  seek  the  best  results  must  use  the  utmost  care  not  only  in  the  initial 
determination  of  the  proper  proportions,  but  also  in  the  measurement  of  the  quantities  of 
each  material  employed,  and  in  checking  the  qualities  of  the  materials  that  come  on  the 
work.  There  will  be  a  proportionate  improvement  in  the  general  quality  of  concrete  as  at- 
tention is  more  generally  paid  to  these  matters. 

13.  Proportioning  Bank-run  Gravel. — It  is  often  questioned  whether  or  not  a  natural 
mixture  of  sand  and  gravel  as  taken  from  the  bank  is  suitable  for  concrete  work.  Inherently 
there  should  be  no  objection  to  this  material,  provided  it  is  not  contaminated  by  impurities, 
but  the  proportions  of  the  several  grades  of  sand  and  gravel  in  any  bank  are  extremely  uncertain 
and  variable.  Taking  bank-run  gravel  and  mixing  it  with  cement  in  the  proportions  of  1  part 
of  cement  to  6  of  gravel  is  not  in  any  sense  equivalent  to  1  part  of  cement,  2  of  sand  and  4  of 
screened  gravel,  or  to  1  of  cement,  l}i  of  sand  or  4}^  of  screened  gravel,  or  any  other  equivalent 
summation. 

Gravel  of  itself,  if  of  proper  quality,  makes  a  most  excellent  concrete,  equal  to  that  pro- 
duced by  the  use  of  crushed  stone.  Sand  in  bank-run  gravel  is  often  of  excellent  qualities  equal 
in  every  way  to  that  taken  from  large  deposits  of  exclusively  fine  material.  However,  if  bank- 
run  gravel  is  to  be  used,  the  relative  proportions  of  sand  and  gravel  must  first  be  determined 
by  a  series  of  tests  on  representative  samples  in  sufficient  number  so  that  the  average  of  the  bank 
may  be  determined  with  fair  accuracy.  These  materials  may  then  be  combined  with  cement, 
preferably  by  proportioning  for  maximum  density.  After  proportions  are  determined  in  this 
way,  it  may  be  found  possible  to  use  a  bank-run  gravel  as  it  comes.    On  the  other  hand,  it  may 

1  See  C.  M.  Chapman:  "Specifications  for  Concrete  Aggregates."    Procs.  Am.  See.  Test.  Mat.,  1916. 


Sec.  2-14] 


GENERAL  METHODS  OF  CONSTRUCTION 


71 


be  found  necessary  in  some  cases  to  screen  out  the  finer  materials  from  the  coarse  and  recomhinc^ 
them  in  proper  proportions,  the  defining  limits  between  gravel,  sand,  and  other  grades  of 
materials  being  as  stated  in  Art.  16,  Sect.  1. 

This  method  of  screening  and  recombination  is  always  cumbersome  and  except  on  ex- 
perimental or  very  large  scales,  impossible  of  putting  into  effective  practice.  In  other  cases, 
after  existing  proportions  of  the  several  grades  have  been  determined  as  above,  a  measured 
quantity  of  sand,  or  of  gravel,  or  of  broken  stone  of  a  size  or  sizes  lacking  in  the  bank  may  be 
added  to  the  pit-run  gravel,  the  quantities  to  be  added  having  been  determined  by  test.  In 
this  way,  the  deficiencies  of  pit-run  can  be  overcome  by  addition  of  other  substances  readily  at 
hand,  or  of  certain  of  the  screened-out  portions  of  the  bank  itself.  Only  in  these  ways,  how- 
ever, can  certainty  as  to  proportions  be  secured;  and  it  must  further  be  borne  in  mind  that 
frequent  tests  should  be  made  during  progress  of  the  work  to  insure  uniformity. 

Furthermore,  great  care  should  be  exercised  to  make  certain  that  silt  in  detrimental 
quantities,  or  loam,  are  not  present  in  bank-run  gravel.  Sand  pits  are  less  likely  to  contain 
injurious  quantities  of  silty  materials  than  are  gravel  pits,  by  reason  of  the  latter  being  the 
bottom  of  an  old  stream  bed  or  a  like  deposit,  with  all  materials  held  therein,  just  as  they  chanced 
to  be  when  the  waters  receded.  Furthermore,  natural  disintegration  at  the  surface,  with  organic 
additions,  affects  the  quality  of  the  material.    Stripping  away  top  layers  is  too  often  omitted. 

14.  Proportioning  Crusher-run  Stone. — The  statements  made  with  respect  to  pit-run 
gravel  apply  in  lesser  degree  to  crusher-run  stone.  Different  stones  crush  in  different  ways 
with  consequent  variation  in  the  character  and  quantity  of  the  fine  material  incident  to  the 
process.  The  softer  stones  give  a  larger  yield  of  fine  materials  than  the  harder  ones;  and  often 
much  of  the  very  fine  material  is  of  a  character  unsuited  to  use  in  concrete.  This  applies  es- 
pecially to  limestone,  inasmuch  as  limestone  has  a  flaky  fracture  in  its  fine  particles,  making  the 
particles  very  friable  and  rendering  the  adhesion  of  cement  difficult,  so  that  concrete  made  with 
such  material  is  pervious  and  of  low  strength. 

Furthermore,  where  there  are  excessive  fines  in  crushed  rock  materials,  some  of  these  fines 
are  merely  impalpable  dust.  It  is  almost  impossible  for  cement  to  properly  coat  particles  of 
this  size,  as  the  dust  particles  then  approach  in  fineness  the  cement  particles.  With  this  very 
fine  material  in  large  proportions,  a  considerable  source  of  weakness  is  thus  introduced  into 
concrete,  inasmuch  as  these  materials  cannot  be  covered  by  cement. 

The  use  of  crusher-run  materials  of  undetermined  size  and  grading,  therefore,  introduces 
an  element  of  uncertainty  in  the  making  of  concrete,  which  should  not  be  permitted.  The 
course  to  pursue  is  similar  to  that  indicated  for  the  use  of  bank-run  gravel — i.e.,  adequate 
samples  of  the  crushed  materials  should  be  taken;  the  proportions  and  size  of  fine  and  coarse 
materials  determined  by  mechanical  analyses;  the  mixture  of  maximum  density  obtained;  and 
the  proportions  noted  of  each  of  the  several  materials  required  to  produce  this  mixture.  Then, 
either  by  screening  or  by  diluting  the  crusher  run  with  screened  materials  or  with  extraneous 
materials,  concrete  of  proper  quality  can  be  more  nearly  assured. 

15.  Proportioning  Blast-furnace  Slag  and  Cinders. — It  is  difficult  to  proportion  for 
maximum  density  when  blast-furnace  slag  or  cinders  are  used  as  aggregate.  This  difficulty 
arises  largely  because  of  the  porosity  of  these  two  materials,  cinders  being  especially  absorptive 
of  water.  A  rough  approximation  as  to  proportions  can  be  had  with  blast-furnace  slag  but  with 
cinders  it  is  probably  better  not  to  attempt  to  secure  accurate  proportioning,  inasmuch  as  the 
use  of  cinder  concretes  is  so  restricted  and  their  strength  and  impermeability  are  so  low,  as  to 
render  any  increase  obtainable  by  refinement  of  methods  of  secondary  importance.  Further 
reference  as  to  the  quality  of  these  two  materials  will  also  be  found  in  the  chapter  on  "Aggre- 
gates" in  Sect.  1. 

16.  Proportioning  Water.— Last  but  not  least  is  the  question  of  proportioning  water  in 
concrete.  This  is  often  given  so  Httle  thought  as  to  make  it  considered  of  either  minor  or  no 
importance  but  it  can  be  authoritatively  stated  that  the  strength  of  any  concrete  mixture  is  as 


72 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-17 


dependent  upon  the  proportion  of  water  contained  as  it  is  upon  the  proportions  of  any  or  all  of 
the  other  materials. 

Unfortunately,  little  is  definitely  known  at  the  present  time  as  to  the  proper  proportions 
of  water.  It  is  known,  however,  that  the  quantity  depends  both  upon  the  demands  of  the 
cement  and  also  upon  the  character  of  aggregate  employed,  upon  the  surfaces  to  be  covered,  and 
the  voids  to  be  filled.  Research  has  been  recently  directed  to  these  lines  with  highly  important 
results. 

17.  Success  in  Proportioning. — For  success  in  proportioning,  not  only  must  the  original 
test  determinations  be  right,  and  the  specifications  provide  proper  authority  for  their  enforce- 
ment, but  these  powers  must  be  exercised  and  a  rigid  compliance  compelled.  Otherwise  there 
is  no  use  in  tests,  and  specifications  are  empty  words. 

MIXING,  TRANSPORTING,  AND  PLACING  CONCRETE 

18.  Mixing  Concrete. — Although  with  careful  superintendence  hand-mixing  will  give  good 
results,  machine-mixed  concrete  is  usually  of  more  uniform  quality  than  that  mixed  by  hand, 
and  is  less  expensive — except,  of  course,  where  the  quantity  of  concrete  is  so  small  as  to  pro- 
hibit the  expense  of  purchasing  or  renting  a  mixer.  The  engineer  should  preferably  reserve  the 
right  to  permit  hand-mixing  if  practically  unavoidable,  but  this  method  of  mixing  should  be 
resorted  to  only  when  machinery  is  unobtainable  or  where  it  is  necessary  to  start  work  on  a 
large  job  before  the  machinery  has  arrived. 

Some  contractors  mix  the  materials  dry  until  a  uniform  color  is  secured  and  then  add  the 
water.  Others  put  the  material  and  the  water  into  the  mixer  at  once.  Either  way  can  pro- 
duce good  results,  except  in  hand-mixing,  where  the  mixing  of  the  cement  and  the  sand  in  the 
dry  state  is  the  general  and  better  practice. 

The  strength  of  concrete  is  very  largely  dependent  upon  the  thoroughness  of  mixing,  and 
much  care  is  needed  in  this  part  of  the  work.  No  matter  how  suitable  for  the  purpose  the 
materials  and  proportions  of  the  same  may  be,  insufficient  mixing  will  result  in  inferior  con- 
crete.   Time  of  mixing  is  treated  in  Art.  236,  Sect.  3,  and  in  Art.  12,  Sect.  5. 

The  greatest  care  should  also  be  exercised  to  make  sure  that  the  specified  amounts  of  the 
materials  go  into  each  batch  of  concrete.  For  measuring  concrete  aggregates,  it  is  not  good 
practice  to  use  the  common  form  of  contractor's  wheelbarrow  because  the  loads  vary  consider- 
ably with  the  variation  in  the  heaping  of  the  barrow.  Special  barrows  constructed  with  sides 
nearly  vertical  can  be  obtained  which  will  give  the  required  amount  when  level  full.  The 
proper  measuring  of  materials  is  discussed  in  Art.  23e,  Sect.  3. 

19.  Amount  of  Water  to  be  Used  in  Mixing  Concrete. — Sufficient  water  should  be  used 
in  mixing  to  obtain  a  concrete  of  sufficiently  mushy  consistency  to  be  readily  puddled.  In  re- 
inforced work  the  amount  of  water  should  be  such  as  to  make  the  mixed  concrete  into  a  flowing 
paste  that  will  flow  readily  around  the  reinforcing  steel  and  require  only  light  tamping  or  pud- 
dling to  bring  the  mass  to  a  homogeneous  condition.  A  slight  excess  of  water  is  preferable  to 
not  enough,  but  there  should  not  be  any  appreciable  quantity  of  free  water  present.  Concrete 
is  mixed  with  an  excess  of  water  if  pools  are  immediately  formed  on  top  of  the  concrete  when 
deposited  in  the  forms.  Although  the  quantity  of  water  needed  in  different  batches  will  vary 
occasionally  because  of  the  condition  of  the  materials,  the  amount  to  use  can  be  regulated  best 
by  measurement.  A  tank  with  a  float  fastened  to  an  indicator  on  the  outside  is  easily  con- 
structed in  connection  with  a  concrete  mixer.  The  effect  of  consistency  on  strength  of  concrete 
is  discussed  in  Art.  9,  Sect.  5.  For  harmful  effects  from  the  use  of  excess  water,  see  chapter  on 
"Water"  in  Sect.  1. 

The  general  types  of  mixers  are  described  in  Art.  22,  Sect.  3. 

20.  Transporting  Concrete. — The  transportation  of  concrete  is  not  only  an  engineering 
problem,  often  of  first  magnitude,  but  as  a  physical  operation  it  is  of  prime  importance  in  its 
effect  on  the  qualities  of  material  in  the  manufacture  of  which  transportation  and  transporta- 


Sec.  2-21] 


GENERAL  METHODS  OF  CONSTRUCTION 


73 


tion  equipment  are  an  incident.  Briefly,  the  transportation  system  nmst  be  such:  (1)  that  the 
time  interval  elapsed  between  reception  of  concrete  and  its  deUvery  to  forms  will  not  cause  it 
■  to  dry,  or  to  take  initial  set;  (2)  that  the  system  shall  be  tight,  so  that  more  fluid  portions  may 
not  be  lost  in  transit;  (3)  that  the  mode  of  transit  shall  not  promote  separation  of  ingredients; 
(4)  that  the  delivery  shall  be  approximately  continuous,  so  that  mixtures  of  varying  composition 
may  not  be  caused  by  stoppage  and  settling;  (5)  that  it  shall  be  efficient,  rapid  and  economical. 
In  this  summary  of  principles,  the  order  of  importance  is  such  as  to  emphasize  quality  of  pro- 
duct delivered,  as  well  as  cheapness. 

The  varied  and  various  appliances  for  the  delivery  of  mixed  concrete  to  forms  are  dis- 
cussed and  illustrated  in  Sect,  3  on  ''Construction  Plant."  To  each  individual  need  must  be 
applied  such  means  as  careful  analysis  and  study  indicate,  so  correlated  and  systematized 
that  the  ends  desired  will  best  be  served.  In  the  proper  selection  of  transportation  plant,  per- 
sonal experience  and  judgment  enter  as  factors  of  such  importance  that,  on  large  operations  in 
particular,  profit  or  loss  may  depend  wholly  on  them.  In  default  of  these,  a  safe  rule  is  to  study 
methods  and  equipment  used  on  operations  of  like  character,  either  by  first-hand  inspection 
or  in  printed  reports;  to  supplement  information  so  obtained  by  advice  from  those  who  have 
had  direct  experience;  and  to  so  adjust  and  modify  the  ways  and  means  indicated  by  the  fore- 
going as  to  suit  them  to  the  needs  of  a  particular  situation. 

21.  Depositing  Concrete  in  Forms. — Responsibility  for  the  character  and  quality  of  con- 
crete does  not  end  with  its  arrival  at  the  forms.  Depositing,  or  placement  in  forms  is  also  an 
operation  of  prime  importance  and  its  conduct  is  governed  by  elementary  principles  which  are 
similar  to  those  that  govern  the  transporting  of  concrete.  These  principles,  directed  toward 
securing  quality  with  economy,  are:  (1)  that  the  concrete  shall  be  continuously  and  evenly 
placed  in  forms;  (2)  that  it  shall  not  be  deposited  continuously  in  one  spot,  with  lateral  flow 
and  (in  wet  concretes)  gravity  separation  of  lighter,  more  fluid  portions  from  those  that  are 
heavier;  (3)  that  it  shall  not  be  deposited  in  forms  in  a  manner  tending  to  promote  dissociation 
or  segregation  of  the  component  materials;^  (4)  that  so  far  as  possible,  forms  shall  be  continu- 
ously filled  without  stoppage,  to  prevent  laitance,  or  stoppage  planes;  (5)  that  before  new  concrete 
is  deposited  on  concrete  which  has  set,  special  precautions  shall  be  taken  to  secure  union  between 
the  two;  (6)  that  concrete  shall  be  so  deposited  as  to  minimize  the  entraining  of  air;  (7)  that  con- 
crete shall  be  joggled  in  the  forms  or  that  forms  shall  be  tapped  on  the  outside  after  fiUing,  suffi- 
ciently to  expel  a  considerable  portion  of  entrained  air;  (8)  that  puddling  and  tamping  shall 
be  done  sufficient  to  bring  about  close  filling  of  forms,  and  close  contact  with  reinforcement; 
(9)  that  larger  aggregate  shall  be  spaded  away  from  forms  at  the  concrete  rises,  permitting  a 
dense  mortar  coat  and  smooth  finish  at  the  exterior  surface  of  the  casting;  (10)  that  uncombined 
concrete  shall  not  be  deposited  through  water;  (11)  that  concrete  remixed  or  retempered  after 
initial  set  shall  not  be  deposited  in  forms;  and  (12)  that  no  concrete  shall  be  deposited  in  cold 
or  very  hot  weather  unless  special  and  adequate  precautions  are  taken. 

22.  Continuous  and  Even  Depositing  in  Forms. — The  temptation  is  very  great  to  locahzc 
delivery  of  concrete  at  one  point,  with  reliance  on  gravity  or  hoeing  for  distribution  to  other 
parts  of  a  form.  By  such  indulgence,  one  set-up  of  spout  or  barrow  runways  only  is  needed; 
and  by  adding  excess  water,  the  form  gets  filled  with  less  labor  than  where  movement  of  the 
spout,  or  movable  or  multiplication  of  runways  are  required.  There  are,  of  course,  forms  of 
such  section  and  dimensions  that  localized  delivery  is  both  permissible  and  advisable,  but  where 
the  form  is  long  and  high,  localized  delivery  brings  about  a  stratification  or  banding  that  not 
only  mars  the  appearance  of  the  wall,  but  also  provides  fault  planes  along  which  seepage  and 
disintegration  may  proceed. 

Furthermore,  bearing  in  mind  the  harsh  nature  and  heavy  weight  of  concrete,  the  difficulty 
of  manual  spreading  in  forms  of  concrete  dumped  on  one  spot  creates  a  tendency  to  the  use  of 
freer-flowing  mixtures,  and  the  ease  with  which  a  certain  degree  of  flow  may  be  brought  about 

1  See  N.  C.  Johnson:  Ena.  Rec,  Dec.  4,  11  :ind  IS,  lOlo. 


74 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-23 


by  the  addition  of  water  gives  rise  to  the  use  of  water  in  excess  quantities  in  an  attempt  to 
further  accelerate  the  placing  operations.  (The  consequences  of  such  additions  are  treated  at 
length  in  chapter  on  "Water"  in  Sect.  1.)  With  such  sloppy,  or  overwet  concretes,  but  little 
imagination  is  needed  to  conceive  what  actually  happens  in  the  forms.  The  more  fluid  por- 
tions flowing  off  from  the  delivery  mound  carry  with  them  much  of  the  cement,  together  with 
the  lighter  portions  of  sand,  and  fill  the  lower  unoccupied  parts  of  the  form,  there  to  solidify 


Fig,  3. — "Soup"  in  forms.  Fig.  4. — Loose  stone  section — the  top  of  the 

depositing  heap. 

in  a  chalky  mass  of  "laitance"  in  which  is  embedded  much  cement  needed  by  the  stripped  ag- 
gregate left  higher  up.  If  materials  are  subsequently  dumped  into  this  "soup"  before  it  sets, 
segregations  result  by  reason  of  the  several  materials  settling  through  this  fluid  in  the  order  of 
their  gravity. 

Cause  and  effect  are  shown  in  Figs.  3  and  4.  The  cause  in  Fig.  3  is  a  knee-deep  puddle  of 
these  light  materials.    The  effect,  in  Fig.  4,  is  a  reservoir  wall  section  almost  devoid  of  cement 

and  sand — the  top  of  the  heap — while  adjacent  to  it  is  a 
lower  section  that  can  be  chopped  like  chalk. ^ 

Knowing  the  procedures  to  be  avoided,  substitute  pro- 
cedures suited  to  individual  needs  may  be  evolved.  Local- 
ized delivery  brings  a  chain  of  evil  consequences.  Distributed 
delivery  avoids  these,  at  an  expense  only  slightly  greater. 
The  gain  in  quality,  endurance  and  value  is  worth  the  differ- 
ence in  first  cost. 

23.  Continuous  Depositing  to  Avoid  Stoppage  Planes. 
— Even  in  concretes  mixed  only  to  a  plastic  consistency, 
there  is  tendency  for  a  scum  of  light,  chalky  material  C'lait- 
ance")  to  rise.  The  greater  the  quantity  of  water,  the 
thicker  this  deposit,  which  also  is  aggravated  by  silty  sand 
or  dusty  stone.  Such  a  deposit  at  the  top  of  a  foundation 
foundation  slab.  block  is  shown  in  Fig.  5.    The  scrolls  were  traced  by  a  lath, 

the  depth  of  deposit  being  about  in.  and  the  thickness  of 
block  about  4  ft.  Concrete  was  subsequently  deposited  directly  on  this  layer,  as  it  is  in  thousands 
of  other  instances  daily,  but  in  all  of  them,  this  will  remain  as  a  plane  of  weakness,  ready  to  yield 
when  stress  of  proper  character  is  imposed.  Visual  evidence  of  such  yielding  is  furnished  by 
seepage  of  water  and  disintegrations  starting  at  like  planes  in  concretes  on  every  hand. 

1  See  N.  C.  Johnson:  Eng.  Rec,  Dec.  30,  1916. 

D.  A.  Abrams:  Concrete,  April,  1917.    Proc.  Am.  W.  Wks.  Assoc.,  1916. 
Carl  Gaylor:  Proc.  Am.  Soc.  C.  E.,  April,  1917,  p.  669. 


Sec.  2-24] 


GENERAL  METHODS  OF  CONSTRUCTION 


75 


24.  Bonding  Set  and  New  Concrete.— The  foregoing  is  closely  related  to  the  problem  of 
bonding  new  and  old  concrete  or,  more  properly,  set  concrete  and  concrete  subsequently  cast 
upon  it.  Recognizing  that  at  least  on  the  majority  of  concretes,  a  top  film  or  deposit  of  lait- 
ance  exists;  that  this  deposit  is  loose  in  texture  and  non-coherent;  and  that  a  portion  of  it  is 
hydrolized  cement,  it  is  not  to  be  expected  that  concrete  subsequently  placed  in  contact  with  it 
shall  adhere.  It  is  known  and  recognized  that  a  dust  film  on  stone  or  gravel  will  prevent  adhe- 
sion of  cement  and  it  must  no  less  be  expected  that  a  like  film  on  solid  concrete,  often  multi- 
plied many  times  in  thickness,  will  have  like  effect.  Other  and  more  complicated  conditions 
also  affect  the  procurement  of  bond,  but  those  above  given  are  of  themselves  sufficient  to  ac- 

;  count  for  the  failure  of  many  attempts  (see  Art.  50,  Sect.  1). 

■  A  first  essential,  therefore,  in  procuring  bond  is  to  remove  this  separating  laitance  film, 
whether  the  set  concrete  is  hours  old,  or  years  old.  It  is  best  to  remove  at  least  in.  and  pos- 
sibly it  may  be  necessary  to  remove  several  inches  before  clean,  sound  concrete  and  aggregates 
are  exposed.  This  surface  should  then  be  well  washed  and  preferably  soaked  with  clean  water, 
all  loose  material  being  removed.  A  wash  of  rich  neat  grout  well  scrubbed  in  with  clean  brushes 
will  provide  a  good  bedment;  and  before  this  has  set  or  dried,  the  new  concrete  should  be  depos- 
ited, a  first  thin  layer  being  tamped  into  place,  followed  by  the  full  deposition.  The  foregoing 
gives  better  guaranty  of  success  than  methods  usually  followed,  but  it  should  be  borne  in  mind 
that  drying  out  of  the  fresh  concrete  surface,  or  drying  or  setting  of  the  cement  wash  previous 
to  applying  and  ramming  the  first  layer  of  concrete,  or  failure  to  deposit  the  remainder  of  the 
concrete  before  this  latter  has  taken  set,  will  each  be  sufficient  to  cause  failure  to  bond,  as  each 
can  and  will  duplicate  in  greater  or  less  degree  the  separating  film  which  first  caused  trouble. 

Bonding  fluids  and  compounds  are  marketed  under  various  trade  names,  but  these  cannot 
be  successful  unless  conditions  suitable  for  bond,  as  outlined  above,  are  first  established. 
Hydrochloric  acid  is  advocated  by  some  as  a  wash  preparatory  to  bonding,  but  the  amount  that 
would  be  required  if  unassisted  by  picks  or  chisels  in  removing  the  usual  laitance  coat  to  a 
sufficient  depth  makes  its  use  prohibitive,  both  in  cost  and  in  time  and  labor  required.  Its  use, 
even  when  considerable  effort  is  made  to  wash  it  away  after  use,  is  not  to  be  recommended,  as 
concrete  by  its  porosity,  is  capable  of  absorbing  harmful  quantities. 

25.  Removal  of  Entrained  Air. — The  customary  mixing  and  depositing  processes  entrain 
quantities  of  air.  Even  when  the  volumetric  air  content  of  a  concrete  appears  low,  a  con- 
siderable portion  of  the  aggregate  may  actually  be  isolated  by  air,  with  little  or  no  attachment 
to  cement.^  It  is  doubtful  if  the  weaknesses  produced  in  concrete  by  the  occlusion  of  air  are 
appreciated.  The  evils  of  existing  practices  in  this  particular  are  to  be  deplored.  In  particular, 
spouting  unconfined  from  a  height,  or  dumping  from  barrows  in  like  manner  probably  do  maxi- 
mum damage  in  this  particular.  The  present  type  of  mixers  work  further  evil  in  this  regard. 
But  since  many  present  fixed  practices  and  equipment  entail  the  occlusion  of  air,  with  no  like- 
lihood of  an  immediate  change,  the  removal  of  as  much  as  possible  is  logical  progress. 

To  this  end,  vibrating  rammers  applied  to  the  plastic  concrete,  or  air  hammers  rapping  the 
outside  of  forms,  or  even  sledge  or  maul  blows^  have  been  used  with  good  effect.  In  concrete- 
products  plants,  vibrated  molds  have  been  used  to  obtain  superior  density;  and  in  road  work, 
vibration  by  motor,  appHed  to  mats  on  the  fresh-laid  concrete  are  said  to  produce  superior 
wearing  qualities.  ^  Certainly  if  the  introduction  of  an  objectionable  impurity  in  a  structural 
material  cannot  be  prevented,  but  its  removal  can  be  later  effected,  it  is  the  part  of  constructive 
engineering  to  overcome  the  undesirable  effects  while  seeking  to  remove  the  cause. 

26.  Spading,  Puddling  and  Tamping.— Forms  should  be  closely  filled,  and,  so  far  as  pos- 
sible, close  contacting  of  form  surfaces  with  smooth,  plastic  material  should  be  brought  about. 
Since  large  aggregates  tend  to  bridge  over,  or  jam,  leaving  unsightly  surface  pockets,  they  should, 

1  See  N.  C.  Johnson:  Eng.  Rec,  Jan.  23,  1915. 

C.  B.  McCullough:  Concrete,  April,  1917. 

2  See  H.  S.  Carpenter;  Eng.  Rec,  March  31,  1917. 

8  The  Vibrolithio  Pavement  of  R.  S.  Stubbs  Co.,  Austin,  Tex. 


76 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-27 


as  the  form  is  filled,  be  spaded  back  from  form  surfaces  so  that  a  dense,  smooth 
mortar  may  lie  at  exposed  surfaces.  Furthermore,  since  it  is  essential  for  structural 
strength  and  for  preservation  of  steel  that  the  embedment  of  reinforcement  be  adequate  with 
close  contacting  of  mortar,  puddling  of  concrete  should  be  progressively  carried  on  as  forms  are 
filled. 

The  temptation  to  use  excessively  wet  concretes  to  lessen  labor  in  the  two  foregoing  opera- 
tions is  prevalent.  For  intricate  reinforcement,  a  free-flowing  concrete  must  be  used,  but  it 
is  better  to  obtain  the  requisite  flow  by  sufficient  mixing,  by  the  use  of  finer  ballast  and  by  pud- 
dling than  by  indulging  in  excess  water,  which  so  generally  defeats  the  intent  of  its  use. 

27.  Depositing  Concrete  Through  Water. — Care  should  be  taken  in  depositing  concrete 
under  water  that  it  is  not  deposited  through  water,  unless  confined. 

Underwater  concretes  are  usually  deposited  by  means  of  a  tremie — a  tube  of  about  1  ft. 
diameter  at  the  top,  slightly  flaring  at  the  bottom  and  at  the  start  of  a  length  sufficient  to  reach 
to  the  bottom.  As  deposition  proceeds,  the  delivery  end  may  be  raised,  but  not  out  of  the  soft 
deposited  concrete,  else  water  will  enter,  causing  washing  of  concrete  subsequently  deposited. 
The  tremie  must  be  kept  full  of  concrete  at  all  times;  and  deposition  is  assisted  by  moving  the 
bottom  of  the  pipe  slowly  about,  permitting  gradual  discharge.  If  the  charge  is  lost,  and  the 
tremie  becomes  filled  with  water,  it  is  wise  to  add  extra  cement  to  the  next  charge,  in  order  to 
compensate  for  that  which  will  be  lost  through  washing  away.  Necessarily,  a  tremie  is  heavy, 
so  that  scow,  derrick  or  other  handling  arrangements  must  be  provided.  Care  also  must  be 
exercised  in  order  that  waves  from  passing  boats  may  not  lift  the  tremie  as  well  as  the  scow, 
causing  loss  of  charge. 

Underwater  buckets,  which  are  substantially  boxes  with  bottom-dumping  doors,  have  been 
used  in  some  underwater  concreting,  but  their  use  is  more  costly  than  that  of  tremies  and 
possibly  less  satisfactory.  Tilting  buckets  are  not  suited  to  underwater  work,  inasmuch  as 
their  dumping  subjects  the  concrete  to  washing. 

Depositing  in  cloth  bags  of  greater  or  less  size  to  hold  together  the  mixed  concrete  in  pass- 
ing through  the  water,  has  been  successfully  accomphshed.^  Paper  bags  are  less  successful 
than  are  those  of  jute  or  burlap.  The  adhesion  of  successive  bags  is  dependent  upon  trans- 
fusion between  and  saturation  of  the  bags  with  dissolved  cementitious  products,  but  in  view  of 
the  great  mass  in  which  the  concrete  is  used  in  such  operations,  and  its  gravity  functioning,  lack 
of  strength  at  joining  planes  is  of  little  moment. 

28.  Remixed  and  Retempered  Concrete. — It  is  erring  on  the  side  of  safety  to  reject  all 
concrete  or  mortar  which  has  taken  pronounced  set,  whether  initial  or  final,  or  which  requires 
the  addition  of  water  and  reworking  to  have  requisite  plasticity.  The  exact  actions  which  take 
place  during  initial  set  are  not  precisely  known,  but  it  is  probable  that  in  this  process  is  begun  an 
interlacing  crystallization  which  is  later  augmented  by  other  crystallizations  and  depositions 
of  colloidal  (amorphous  or  non-crystalline)  material  in  the  processes  of  final  set  and  the  sub- 
sequent hardening.  But  whatever  the  exact  process,  it  is  known  that  retempering  and  re- 
working of  Portland-cement  mixtures  after  initial  set  is  decidedly  disadvantageous  at  best, 
resulting  in  a  loose,  unresistant  product  of  inferior  strength  and  coherence.  This  practice, 
therefore,  is  to  be  avoided;  and  the  operations  of  transporting  and  placing  should  never  be  of 
such  duration  as  to  permit  initial  set,  even  in  hot  weather. 

29.  Concreting  in  Hot  Weather  and  in  Cold  Weather. — The  basis  of  all  concrete  is  the 
union  of  inert  materials  by  substances  produced  through  chemical  reaction  between  Portland 
cement  and  water.  Any  acceleration  or  retardation  of  this  chemical  process  affects  the  quan- 
tity and  quality  of  binder  resultant  from  this  reaction;  and  any  such  alteration  affects  critically 
the  quality,  strength,  and  endurance  of  concrete  formed  by  admixture  of  this  binding  product 
with  sand  and  stone. 

Temperature  is  known  to  control  the  rate  of  all  chemical  reactions.    In  general,  heat 

1  Proc.  Am.  Soo.  C.  E.,  vol.  39,  p.  120;  and  vol.  47,  p.  101. 


Sec.  2-29a]  GENERAL  METHODS  OF  CONSTRUCTION 


77 


accelerates  and  cold  retards  chemical  union. ^  Furthermore,  solution  of  some  products,  such  as 
gypsum  (CaS04)  contained  in  Portland  cement,  is  active  at  relatively  low  temperatures  and 
inactive  at  higher  temperatures,  while  solution  of  other  products  takes  place  in  reverse  order. 
Relative  evaporation  speeds  at  different  temperatures  are  also  to  be  considered,  with  correlative 
effect  on  the  strength  of  concrete  produced  at  any  given  time.  It  is  reasonable  to  expect, 
therefore,  as  is  borne  out  in  fact,  that  hot  (weather)  concretes  are  quick-setting  and  of  early 
strength  and  that  cold  (weather)  concretes  are  slow-setting  and  of  low  strength;  and  on  forget- 
fulness  of  these  obvious  but  inescapable  facts  rests  responsibility  for  many  a  failure. 

Particularly  is  this  true  of  cold-weather  concreting.  At  40°F.  concrete  requires  four 
times  as  long  a  period  to  attain  a  given  strength  as  the  same  concrete  at  50°F.;  and  at  40°F. 
about  nine  times  as  long  as  at  70°F.  Below  40°F.  the  ratio  still  further  increases.  Many  so- 
called  "mysterious"  failures,  in  which  the  concrete  is  obviously  not  frozen,  are  to  be  explained 
by  delayed  set  and  hardening,  due  to  low  temperatures  alone.  Below  40°F.  the  set  is  so 
delayed  down  to  and  including  32°F.  where  rupture  by  ice  formation  occurs  (requiring  a 
later  extra  period  at  elevated  temperatures  to  induce  reconsolidation  in  addition  to  that 
normally  required  for  setting  at  the  average  temperature  prevailing)  that  computation  must 
be  made  for  each  instance  to  insure  safety. 

Using  Portland  cement  of  normal  hardening  rate,  the  following  periods  before  removal  of 
forms  in  summer  weather  are  suggested  as  representative  of  correct  practice: 


For  concrete  in  mass  work  24  to  48  hr. 

For  concrete  in  thin  sections  48  to  60  hr. 

For  concrete  columns  48  to  60  hr. 

For  concrete  in  beams  and  girders  12  to  21  days 

For  concrete  in  long  span  slabs  14  to  21  days 


The  period  required  in  cold  weather  will  be  more  or  less  protracted  according  to  the 
average  temperature  prevailing2  both  prior  to  and  during  the  setting  period,  inasmuch  as  tem- 
peratures prior  to  mixing  and  placing  will  hold  for  the  aggregates,  even  though  in  many  cases 
attempts  at  preheating  have  been  made. 

29a.  Preheating  Aggregates  and  Water. — Preheating  sand,  stone,  and  water 
previous  to  admixture  is  an  operation  difficult  adequately  to  perform.  Each  cubic  yard  of 
materials  will  require  approximately  1000  B.t.u.  per  degree  rise  in  temperature.  With  an 
indeterminate  factor  of  heat  transference,  the  fuel  required  on  a  day's  operations  may  be  com- 
puted or,  better  still,  such  computation  may  be  neglected  and  fuel  added  until  the  temperature 
of  the  materials  has  been  sufficiently  raised.  It  is  erring  on  the  side  of  safety  to  have  this 
temperature  judged  by  an  unsensitive,  calloused  hand,  rather  than  by  a  thermometer.  Water 
may  more  easily  be  made  too  hot,  inducing  flash  set  when  mixed  with  cement. 

296.  Means  for  Heating  Aggregates. — An  old  smokestack  section,  buried  in 
sand  or  stone,  and  fired  with  wood,  is  perhaps  the  best  construction-job  means  of  heating  ag- 
gregates. Steam  jets  are  the  least  efficient.  Water  may  be  heated  by  either  immersed  steam 
coils,  or  by  steam  jets,  or  by  externally  applied  heat.  A  gasoline  torch  playing  directly  into  the 
mixer  drum  is  sold  as  a  concrete  heater. 

29c.  Enclosure  and  Heating  of  Forms.— In  cold-weather  building  operations 
in  particular,  enclosure  by  canvas  is  desirable.  Salamanders,  or  other  heating  units  are  kept 
burning  within  to  keep  the  temperatures  somewhat  elevated.  It  must  be  borne  m  mmd, 
however,  that  at  best  the  temperature  of  the  enclosure  is  low;  and  that  heat  transference 
through  wooden  forms  to  the  concrete  is  slow.  Such  precautions,  therefore,  do  not  admit  of 
dispensing  with  preheating  of  aggregates  and  water,  or  of  leaving  forms  in  place  for  a  requisite 
time. 

1  The  speed  of  chemical  reactions  is  approximately  as  the  sixth  power  of  the  absolute  temperature. 

2  See  A.  B.  McDaniel:  Proc.  Am.  Con.  Inst.,  1915;  also  Art.  16,  Sect.  5. 


78 


CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  2-29d 


29c?.  Proteccion  Against  Frost. — The  employment  of  manure  in  contact  with 
concrete  is  seriously  objectionable.  The  heat  of  manure  is  derived  from  the  decomposition  of 
its  organic  portions  and  in  this  process,  compounds  destructive  of  concrete  are  formed.  Clean 
straw,  clean  sawdust,  or  canvas  will  assist  in  protection  against  frost,  but  in  addition,  artificial 
heat  must  be  employed  for  temperatures  below  35°F.  if  assurance  of  safety  is  desired. 

29e.  Freezing  of  Concrete. — If  frozen  before  initial  set,  concrete  will  reconsoli- 
date  on  later  elevation  of  temperature  with  seemingly  no  impairment  of  strength.  This  holds 
particularly  for  sections  where  there  is  sufficient  hydrostatic  head  to  recompact  the  mass  as 
the  expansively  disrupting  ice  is  thawed,  chemical  reactions,  in  the  interval,  having  been  sus- 
pended.   It  is  better,  however,  to  prevent  freezing  than  to  take  chances. 

29/.  Use  of  Anti -freezing  Mixtures. — Common  salt  (NaCl),  or  calcium  chloride, 
(CaCU),  is  the  basis  of  most  anti-freezing  mixtures.  Glycerine  and  alcohol  also  have  been  tried, 
but  both  tend  to  lower  the  strength  and  there  is  also  question  as  to  the  propriety  of  using  gly- 
cerine, because  of  possible  organic  decomposition  and  injury  to  the  concrete.  Calcium  chlo- 
ride or  salt  added  to  water  will  lower  its  freezing  point,  and  in  proportions  of  CaCl2  not  to  exceed 
2%  of  the  weight  of  cement  or  proportions  of  salt  from  2  to  10%  of  the  weight  of  water,  have 
been  recommended  and  used,  but  the  ill  effects  of  salt  so  far  outweighs  its  benefits— as  for  in- 
stance, by  promoting  corrosion  of  steel — that  it  is  better  omitted.  No  anti-freezing  compound 
is  better  than  salt;  and  none  is  equal  to  adequate  heating  of  materials  with  proper  maintenance 
of  temperature  during  the  setting  period. 

29g.  Protection  Against  Heat. — Aside  from  slab  and  thin  wall  construction, 
protection  of  concrete  against  heat  is  rarely  needed.  For  such  purposes,  protecting  coverings 
of  straw,  sawdust,  sand,  or  canvas^  are  usually  sufficient.  Evaporation  must  be  guarded 
against,  as  must  also  working  after  initial  set,  as  in  floating  floor  or  sidewalk  surfaces.  Hot- 
weather  evils,  however,  are  less  troublesome  than  are  those  incident  to  cold-weather  concreting 
and  are  provided  against  with  corresponding  ease. 

FIELD  TESTS  OF  CONCRETE 

30.  Object  of  Field  Tests. — The  primary  object  of  making  field  tests  of  concrete  is  either 
to  obtain  information  as  to  the  strength  of  field  concretes  or  assurance  as  to  the  strength  and 
integrity  of  a  commercial  structure. 

31.  Limitations  Inherent  in  Field  Tests. — Necessarily,  field  tests  of  concrete  must  be  made 
on  specimens  of  such  section — usually  6-in.  cubes,  or  better,  6  by  12-in.  or  8  by  16-in.  cylinders 
— that  the  maximum  strength  to  be  anticipated  shall  not  exceed  the  capacity  of  testing  appa- 
ratus available.  This  limits  the  size  of  specimen  to  a  considerable  degree,  which  affects  the 
relationship  between  strength  of  test  specimen  and  strength  of  a  like  section  in  the  structure 
according  as  aggregates  of  greater  or  less  size  are  used. 

Necessarily,  also,  the  strength  of  test  specimens  has  dependence  upon  the  degree  of  compact- 
ing and  care  of  molding  employed  in  their  manufacture.  In  actual  structures,  quite  dissimilar 
internal  conditions  exist,  with  static  head  playing  a  more  or  less  important  part  in  consoli- 
dation, this  static  head  varying  continually  in  each  portion  of  the  structure.  It  is  therefore 
difficult,  if  not  impossible,  to  duplicate  in  test  specimens  pressure  conditions  obtaining  in  a 
structure. 

It  is  assumed,  furthermore,  that  the  materials  incorporated  in  a  small  test  specimen  are 
representative  of,  and  in  like  quantities  to,  those  making  up  concrete  in  the  structure.  It  is  a 
regretable  fact  that  a  concrete  mix  is  rarely  of  uniform  composition  in  its  several  parts;  and  that 
so  great  is  this  variation  found  to  be  that  relatively  small  portions  of  any  mix  may  or  may 
not  represent  in  their  constitution  and  properties  when  hardened  a  fair  average  of  the  con- 
cretes in  the  structure. 

Temperature  conditions  further  increase  discrepancies  between  test  specimens  and  struc- 

1  See  Sect.  4  on  "Concrete  Floors  and  Floor  Surfaces,  Sidewalks,  and  Pavements." 


Sec.  2-32] 


GENERAL  METHODS  OF  CONSTRUCTION 


79 


tural  concretes.  When  concrete  is  in  considerable  mass,  temperature  rise  due  to  chemical  re- 
actions between  cement  and  water  are  largely  retained,^  and  atmospheric  variations  exercise 
less  effect  on  the  proper  increase  of  strength.  In  small  specimens,  on  the  contrary,  moicture 
and  temperature  conditions  are  subject  to  abrupt  change  with  consequent  variation  of  proper- 
ties in  the  hardened  concrete. ^  The  mode  of  applying  stress  is  another  factor  tending  to  dis- 
similarity and  to  misleading  conclusions. 

32.  Comparative  Tests  on  Field-molded  and  Structural  Specimens. — Two  notable  series 
of  investigations  are  on  record  with  respect  to  the  value  of  field  tests  of  concrete.  Those  of  the 
Public  Service  Commission  of  New  York^  give  comparative  values  between  field-molded  speci- 
mens and  specimens  cut  from  the  actual  structure.  Those  of  Kansas  City,  Mo.,^  were  tests  on 
field-molded  specimens  alone,  without  comparative  tests  on  specimens  cut  from  the  structure. 

33.  Value  of  Tests  on  Field-molded  Test  Specimens. — The  indications  of  the  tests  above 
mentioned  are  not  favorable  so  far  as  consistency  between  laboratory  and  field  is  concerned, 
and  this  is  to  be  expected,  as  the  practice  of  sampling  concrete  from  a  mixer;  molding  such 
samples  more  or  less  inexpertly  into  small  specimens;  curing  them  under  conditions  dissimilar 
to  those  structurally  existing;  and  applying  a  breaking  stress,  must,  obviously,  give  results  of 
doubtful  value.  Then  again,  by  the  time  these  test  specimens  are  matured  and  broken,  tons 
upon  tons  of  concrete  have  been  piled  on  or  around  that  portion  of  the  structure  of  which  they 
might  have  been  part,  so  that  the  removal  of  this  concrete  would  be  next  to  impossible,  even 
though  test  results  should  be  adverse  and  indicate  a  low  strength.  The  best  that  might  be  done 
would  be  to  so  vary  mixtures  or  procedures  in  subsequent  parts  of  the  work  as  to  produce  more 
nearly  the  values  desired. 

34.  Transverse  Tests  on  Beam  Specimens. — A  variation  in  form  of  specimen  and  method  of 
testing  introduced  in  the  Welland  Canal  tests  is  of  interest,  though  subject  to  all  limitations 
above  set  forth.  In  these  tests^  the  test  specimen  is  a  beam  of  rectangular  section  4>^^  by  3}^ 
in.  and  3  ft.  long,  tested  transversely.  Such  tests  give  little  if  any  indication  as  to  the  ability  of 
a  concrete  to  withstand  applications  of  stress  other  than  exactly  similar  to  those  applied  in  the 
test. 

35.  Core  Drill  Test  Specimens  from  Actual  Structures. — In  certain  instances  core  borings 
to  secure  test  specimens  have  been  made  in  completed  structures.  Such  cores  are  more  rep- 
resentative of  mass  conditions  than  other  specimens.  In  taking  borings  at  the  Municipal 
Filter  Plant,  Cleveland,  Ohio,  both  6-in.  and  4-in.  cores  were  taken  with  a  diamond  drill  bit, 
the  cores  being  subjected  to  examination  and  tests  of  various  kinds.  Somewhat  similar  work 
but  with  a  shot  drill  was  done  at  the  Ashokan  Reservoir  of  the  New  York  City  water  supply 
system  in  1915. 

Either  a  shot  or  a  diamond  bit  may  be  used  in  core  borings.  The  shot  bit  is  slower,  cuts 
reinforcing  steel  more  readily,  but  gives  a  rough  core.  The  diamond  bit  cuts  rapidly,  gives  a 
smooth,  even  core,  but  the  diamond  loss  may  be  a  serious  item  of  expense,  particularly  where 
tie-wires  or  reinforcing  steel  is  encountered.  Either  bit  is  almost  helpless  where  segregated 
pockets  of  loose  material  are  encountered. 

36.  Suggested  Methods  for  Making  and  Testing  Field  Specimens  of  Concrete.— The  fol- 
lowing methods  for  making  and  testing  field  specimens  of  concrete  are  taken  by  permission 
from  the  report  of  Committee  C-9  of  the  Am.  Soc.  Test.  Mat.,  June,  1917. 

The  following  methods  are  presented  not  as  final  recommendations  but  as  an  outline  of  what  in  the  opinion 
of  the  committee  represents  the  best  practice  at  the  present  time.  The  necessity  for  greater  attention  to  testing 
concrete  in  construction,  and  for  the  adoption  of  a  proper  method  for  sampling  the  concrete  to  represent  the 
product  of  the  various  field  operations,  is  recognized  by  engineers  and  contractors,  eppecially  in  view  of  the  tend- 

1  Paul  and  Mayhew:  Trans.  Am.  Soc.  C.  E.,  1915,  pp.  1225-1267. 

2  A.  B.  McDaniel:  Bull.  47,  Univ.  of  111.,  1915. 
Withey:  Wise.  Engr.,  Feb.,  1915. 

3  Eng.  Rec,  Sept.  4,  1915. 

^  Eng.  News,  Sept.  10,  1914. 

6  Eng.  Rec,  July  24,  1915,  p.  112. 


i 


80 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-36 


ency  in  many  quarters  to  use  a  wet,  sloppy  concrete  which  may  give  a  final  strength  much  lower  than  that  upon 
which  the  design  is  based. 

The  tests  are  designed  to  provide  an  indication  of  the  quality  of  the  concrete  which  is  placed  in  the  structure 
and  character  of  workmanship  in  mixing.  By  providing  damp  sand  storage  for  the  test  specimens,  the  variable 
weather  conditions  are  purposely  disregarded  although  these  sometimes  greatly  affect  the  final  strength  of  the  con- 
crete.   In  comparing  the  results,  the  temperature  and  weather  conditions  must  be  taken  into  account. 

Size  and  Shape  of  Specimen. — The  test  specimen  should  be  of  cylindrical  form,  with  length  twice  the  diameter. 
When  the  coarse  aggregate  does  not  exceed  l^-^  in.  in  diameter,  a  6  by  12-in.  cylinder  may  be  used,  although  an  8 
by  16-in.  cylinder  gives  more  concordant  results.  For  larger-size  aggregate  a  mold  whose  diameter  is  not  less  than 
4  times  the  diameter  of  the  largest  size  aggregate  should  be  used. 


Side  view 


Top  view 
Stack:  6?i"0.D.  Cold-draivn  seamfesf 
steel  tubing;  ^e''¥valls.  Make  varrrw 
slit  along  One  element.  May  also 
use  6" steel  water  pipe,  machmed 
mside.  Slit  along  one  element,  so 
that  when  closed  will givg  ^"insia9 
^,^iam^ter. ,  • 


Top  view 


Side  view 


Fig.  6. 


Fig.  7. 


Molds  and  Apparatus. — Figs.  G  to  8  show  types  of  molds  which  should  be  used  in  the  field.  Figs.  G  and  7 
show  types  which  are  designed  for  repeated  use;  while  the  mold  shown  in  Fig.  7  is  destroyed  in  removing  test  piece, 
or  else  has  to  be  resoldered.  While  this  latter  mold  is  not  adapted  to  continuous  use  and  therefore  is  more  expensive 
in  actual  cost,  it  is  quite  convenient  to  use  where  but  few  tests  are  to  be  made  and  particularly  advantageous 
where  specimens  are  to  be  shipped  at  early  stages  as  the  specimens  can  be  left  in  the  molds  for  shipment.  "Various 
modifications  of  each  of  these  forms  will  suggest  themselves,  the  only  requirements  being  that  they  hold  their 
shape  during  the  molding  of  the  specimen  and  that  the  ends  remain  perpendicular  to  the  side. 

When  bottomless  forms  are  used,  it  will  be  necessary  to  provide  a  plane  surface  on  which  to  mold  the  specimens. 
Individual  plates  of  glass  M  to  H  in.  thick,  or  metal  plates  with  plain  surfaces  about  2  in.  larger  than  the  diameter 

of  the  mold,  may  be  used,  placing  one  under  each  test  piece. 
A  piece  of  wax  paper  should  be  provided  to  place  under  each 
test  specimen  to  prevent  the  concrete  from  adhering  to  the 
plate,  or  the  plate  may  be  oiled. 

A  central  place  should  be  selected  for  molding  the 
specimens,  and  a  sand  pile  provided  so  that  they  may  be 
kept  in  damp  sand  as  described  below,  to  prevent  undue 
evaporation  and  obtain  uniformity  of  storage  conditions. 

Sampling  the  Concrete. — Concrete  for  the  test  specimens 
should  be  taken  immediately  after  it  has  been  placed  in  the 
forms.  Each  sample  should  be  taken  from  one  place.  A 
sufficient  number  of  samples — each  large  enough  to  make 
one  test  specimen — should  be  taken  at  different  points  so 
that  the  specimens  made  from  them  will  give  a  fair  average 
of  the  work.  The  location  from  which  each  sample  is  taken 
should  be  clearly  noted  for  future  reference. 

In  securing  samples,  the  concrete  is  taken  up  irom  the 
mass  by  a  shovel  or  similar  implement  and  placed  in  a  large 
pail  or  in  some  other  receptacle  for  transporting  to  the  place 
Care  should  be  taken  to  see  that  each  specimen  represents  the  total  mixture 


Side  view 


Materia/: 
h/oZOSavge 
galvanized  sfaef. 
bj:^  lj- Bottom  tightly  soldered 


Fig.  8. 


where  the  specimens  are  molded, 
of  the  concrete  at  that  place. 

Molding  the  Specimen. — The  pails  containing  the  samples  of  concrete  should  be  taken  to  the  place  selected 
for  making  the  test  pieces  as  quickly  as  possible.  To  offset  segregation  of  materials  during  transportation,  each 
sample  should  then  be  dumped  out  of  the  pail  into  a  non-absorbent  water-tight  receptacle,  and  without  further 
mixing  immediately  placed  in  the  mold.  Different  samples  should  not  be  mixed  together,  but  each  sample  should 
make  one  specimen. 


Sec.  2-36] 


GENERAL  METHODS  OF  CONSTRUCTION 


81 


For  working  the  concrete  around  the  edges  of  the  sides  of  the  mold,  a  3-in.  round  steel  rod,  2  ft.  long,  should 
be  used. 

Ramming  should  be  avoided,  but  care  should  be  taken  to  remove  air  pockets.  The  freshly  made  specimen 
should  be  struck  off  and  troweled  level  with  the  top  of  the  form.  The  specimen  should  preferably  be  capped  in  the 
field  while  it  is  in  the  mold  so  as  to  be  ready  for  the  testing  machine.  After  the  concrete  has  stiffened  appreciably 
and  before  the  molds  are  removed,  neat  cement  or  a  rather  stiff  1  :  2  mortar  may  be  used  to  fill  the  molds  level  full 
A  piece  of  plate  glass  or  machined  metal  plate  should  then  be  worked  around  on  the  top  of  the  mortar  until  it  rests 
on  the  form.  This  plate  should  be  oiled  or  a  piece  of  wax  paper  be  placed  between  it  and  the  concrete.  If  the  forms 
are  carefully  made,  this  will  give  top  and  bottom  surfaces  perpendicular  to  the  sides  of  the  specimens.  To  prevent 
the  specimen  from  drying  out,  it  should  be  covered  or  otherwise  protected.  If  desired,  the  mold  itself  may  be 
buried  in  sand  while  the  specimen  is  being  molded. 

At  the  end  of  48  hr.  the  specimens  should  be  removed  from  the  mold  and  buried  in  damp  sand.  In  case  the 
molds  shown  in  Fig.  8  are  used,  specimens  may  be  buried  in  damp  sand  without  the  removal  of  the  forms,  thus 
permitting  shipment  of  the  specimens  in  the  molds.  Test  specimens  made  in  the  mold  shown  in  Fig.  8  may  be 
removed  by  opening  the  soldered  joint  with  a  sharp  tool. 

Testing. — Ten  days  prior  to  the  date  of  test,  specimens  should  be  well  packed  in  damp  sand  or  wet  shavings 
and  shipped  to  the  testing  laboratory,  where  they  should  be  stored  either  in  a  moist  room  or  in  damp  sand  until  the 
date  of  the  test.  It  is  assumed  that  ordinarily  a  28-day  test  will  be  made,  although  tests  at  7  and  14  days  will  give 
some  indications  of  the  results  to  be  expected  at  28  days.  In  case  7-day  tests  are  made,  the  test  pieces  should  re- 
main at  the  job  as  long  as  possible  to  harden,  and  should  be  shipped  so  as  to  arrive  at  the  laboratory  in  time  to 
make  the  test  on  the  required  date. 

The  foregoing  recommendations  of  the  Am.  Soc.  Test.  Mat.  are  subject  to  revision,  it 
being  recognized  that  they  are,  by  the  nature  and  cost  of  equipment  specified  and  require- 


5/ofe  of  mold  ■ 


Fbrraffineorgwuf- 
layer  to  level 
bo^l-om--, 


ments  for  curing  conditions,  more  nearly  allied  to  laboratory  procedures  than  to  testing  in 
the  field.  To  overcome  these  limitations,  the  author  has,  with  uniform  success,  used  stock 
cartons  of  paraffined  paper,  such  as  those  shown  in  Fig.  8 A  for  field  molds.  As  will  be 
seen,  they  are  simply  stout  cartons  with  caps  and  they  may 
be  had  in  quantities  at  prices  ranging  from  1^  cts.  for  3)^ 
by  7-in.,  to  6  cts.  for  6  by  12-in.  sizes. 

Molding  and  puddling  are  accomplished  in  the  usual 
manner,  the  mold  retaining  its  shape,  and  when  full,  capped, 
with  identifying  data  written  directly  on  the  cap.  When  the 
specimen  has  matured,  the  mold  is  slit  down  the  side  with  a 
sharp  knife,  as  in  Fig.  8j5,  and  the  shell  removed.  This  leaves 
a  perfect  specimen,  as  in  Fig.  8C,  whereon,  it  will  be  noted, 
the  top  and  bottom  cardboards  remain  as  cushions  for  the  testing  machine  heads. 

To  insure  even  bottoms,  it  is  well  to  set  the  empty  cartons  on  loose  sand  during  mold- 
ing and  until  set.  For  such  bottoms  as  are  sprung,  or  out  of  true,  a  little  melted  paraffin, 
or  of  cement  grout  (if  time  to  set  is  permitted)  poured  in  with  the  mold  vertical,  will  ensure 
a  bedment  so  even  as  to  make  plaster  preparation  unnecessary  (see  Fig.  8D). 

The  advantages  of  this  mold  for  field  work  are: 


Fig. 


5and  bedmenl- 

8D. — Leveling  distorted 
toms  of  waxed  ends. 


Disforfed^ 
..■pasretxxrrd 
boffoni' 


bot- 


82 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-37 


(if  5000 


^  4000 

o 


1.  It  is  readily  and  cheaply  procurable  anywhere. 

2.  Temperature  changes  excepted,  curing  conditions  for  all  specimens  are  always  uniform 
and  alike,  without  bedding  in  sand  or  immersing  in  water,  as  the  waxed  carton  retains  all 
water. 

3.  Shipment  of  specimens  from  job  (where  molded)  to  laboratory  (for  crushing)  maybe 
made  in  any  manner  convenient,  curing  proceeding  uniformly  throughout  this  period. 

4.  There  are  no  molds  to  clean  or  to  re-ship. 

37.  Pre-use  Tests  of  Materials.— It  is  to  be  observed  that  recognition  is  accorded  in  the 
above  recommendations  to  the  questionable  commercial  values  of  field  tests  of  concrete.  The 
art  is  at  present  in  a  transition  state. 

Some  field  tests,  however,  are  of  value.  One  of  these  is  as  follows:  It  seems  to  hold  true 
that  the  strength  of  concrete  is  directly  dependent  upon  the  size-grading  of  its  aggregate;  that 

this  is  particularly  true  as  respects  the  fine  ag- 
gregate; and  that  of  a  selection  of  sands,  con- 
crete will  be  strongest  when  made  with  that 
sand  whose  sum  of  percentage  passing  a  given 
series  of  screens  is  lowest. 

In  Fig.  9  is  shown  a  series  of  curves  pre- 
pared by  CM.  Chapman  illustrative  of  this 
point.  Percentages  passing  in  these  curves 
are  taken  from  record  cards  of  the  Universal 
Sand  Tester  and  illustrate  the  field  practice 
of  Westinghouse  Church  Kerr  &  Co.  in  the 
selection  of  sands.  It  is  obvious  from  this 
chart,  that  if  the  percentages  passing  is  known 
for  any  sand,  the  strength  of  a  mortar  made 
from  it  in  given  proportions  at  any  given  age 
(in  this  case,  28  days)  may  be  read  directly. 
Although  it  has  been  held  that  the  strength  of 
a  mortar  is  not  a  measure  of  the  strength  of  a 
like  mortar  in  concrete,  the  relationship  is  not 
entirely  misleading.  On  the  contrary,  it  now 
seems  probable  that  pre-use  tests  of  materials; 
the  establishment  and  maintenance  of  correct 
proportions;  and  refinement  of  processes  of 
mixing  and  placing  will  afford  the  greatest  de- 
velopments in  the  concrete  art.^ 


\ 

\ 

\ 

\ 

V 

N 

N 

\ 

\ 

\ 

N 

\ 

N 

K 

^- 

\ 

- 

100  125    150    175    200  2S5  £50  Z15    300  325   350  375  400 

Coefficienf  of  uniformity 
Sum  of''per  cents  passing'  screens  of  Universal  Sand  Tester 

Fia.  9. 


WATERPROOFING  CONCRETE 

38.  Meaning  of  "Waterproof." — ''Waterproof"  as  applied  to  concrete  may,  in  its  literal 
sense,  give  rise  to  confusion  and  misunderstanding.  "Water-resistant"  to  a  specified  degree, 
or  "impermeable"  might  more  nearly  define  and  delimit  the  abilities  of  concrete  to  withstand 
attack  from  or  permeation  by  water.  ^ 

39.  Resistance  of  Concretes  to  Water  Action. — Few  concretes  are  free  from  one  mani- 
festation or  another  of  water  action.  Except  for  minor  surface  attack,  such  action  follows 
water  penetration,  which  latter  may  result  from  an  actual  hydraulic  head,  as  in  a  dam,  sewer, 
aqueduct,  or  reservoir;  or  from  a  negative  head  induced  by  evaporation  from  an  exposed 
surface,  as  in  a  retaining  wall,  subaqueous  tunnel,  or  sidewalk;  or  it  may  be  caused  by  surface 
wetting  and  mass  absorption,  as  in  a  concrete  building,  or  in  stucco.    Chemical  attack  by  sol- 

1  See  R.  E.  Goodwin:  Concrete,  Nov.,  1915. 

*  See  M.  O.  Withey:  "Permeability  Test  of  Gravel  Concrete."    Proc.  Western  Soc.  Engr's.,  1914. 


Sec.  2-40] 


GENERAL  METHODS  OF  CONSTRUCTION 


83 


vents  excepted  (but  inclusive  of  secondary  frost  action)  the  effects  of  penetrant  water  on  con- 
cretes are  generally  alike,  though  differing  in  degree.  Water  penetration  is  directly  or  indirectly 
the  cause  of  the  majority  of  disintegrations  in  concrete  and  the  degree  to  which  water  pene- 
tration is  permitted  by  the  texture  of  any  concrete  is  a  direct  measure  of  its  strength  and 
endurance. 

40.  Resistance  of  Concretes  to  Water  Penetration. — Penetration  of  water  into  concrete  is 
readiest  by  an  actual  physical  passageway  or  passageways.  Obviously,  a  given  quantity  in  a  given 
time  may  enter  by  one  large  passageway,  or  by  a  multiplication  of  minute  passageways. 
Securing  resistance  to  penetration  is,  therefore,  to  be  ac- 
complished by  reduction  of  such  passageways  to  a  minimum, 
both  as  to  size  and  number,  or  by  sealing  them  off.  It 
follows,  therefore,  that  concretes  of  given  materials  arc 
water-tight  and  water-resistant,  as  well  as  strong  and  en- 
during, in  proportion  to  their  absolute  densities.  Con- 
versely, concretes  are  weak,  permeable,  and  of  low  endu- 
rance in  proportion  to  their  porosities. ^ 

41.  Degree  of  Impermeability  Attainable. — Absolute 
freedom  from  water  penetration  is  probably  impossible  of 
attainment  in  the  commercial  manufacture  of  concrete. 
Certainly,  the  average  results  of  present  practice  warrant 
that  belief.  An  improvement  in  present-day  work  is  not 
only  an  imperative  necessity,  but,  fortunately,  practicable  as  well. 

Illustrative  of  the  difficulty  of  obtaining  absolute  impermeability  in  artificial  concretes, 
the  structure  of  sandstone  (Fig.  10)  is  worthy  of  study.  This  has  before  been  cited^  as  an  ideal 
concrete  in  structure,  in  that  it  has  in  combination  silica  (sand)  particles  closely  compacted, 
with  a  minimum  of  cementitious  material  between  them.  Yet  sandstone  of  this  grade  is  known 
to  be  absorptive  of  water  and  to  weather  (disintegrate)  rapidly.  Arrows  (a)  and  (6)  indicate 
the  minute  passageways  in  the  cementing  material  between  the  silica  particles  through  which  water 
entrance  is  secured  and  at  which  disintegrations  center.    And  in  further  likeness  to  artificial 


Fig.  10.— Medina  sandstone  show- 
ing pores  which  render  the  stone  ab- 
sorbent.   (Magnified  20  diams.) 


Fig. 


11. — Pinholes  passageways  in  commercial 
concrete.    (Magnified  10  diams.) 


concretes,  the  more  cementing  material  in  any  sandstone,  the  higher  its  porosity  and  the  lower 
its  strength  and  endurance. 

42.  Porosity  of  Commercial  Concretes. — Necessarily,  because  of  limitations  imposed  in 
artificial  concretes  by  inadequate  compacting  and  consolidating  processes,  a  density  equal  even 
to  sandstone  cannot  be  obtained.  Dispersion  of  aggregates  in  concrete,  both  coarse  and  fine, 
with  corresponding  increase  of  cementing  material  between  and  around  them,  has  been  before 


1  See  chapter  on  "Proportioning  Concrete,"  Sect.  2,  and  on  "Properties  of  Plain  Concrete,"  Sect.  5. 
*  See  chapter  on  "Aggregates"  in  Sect.  1. 


84 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-43 


noted.  Isolation  of  aggregates  by  water^  and  occlusion  of  air  by  mixing  and  placing  methods 
in  current  vogue^  have  been  pointed  out  at  various  times.  The  value  of  proper  proportioning 
as  an  aid  to  water-tightness  has  been  the  subject  of  frequent  papers,  discussions,  and  writings. 
Field  methods,  however,  provocative  of  undesirable  conditions,  have  remained  unchanged. 
This  argues  either  an  apathy  not  creditable  to  the  engineering  profession  and  inimical  to  con- 
crete, or  else  a  confession  of  inability  to  remedy  recognized  evils.  A  present  lack  of  adequate 
presentation  of  the  problem  of  impermeable  concrete  may  be  one  reason  for  this  state  of 
the  art. 

Search  in  commercial  concretes  for  passageways  capable  of  conveying  water  need  not  be 
protracted  to  meet  with  reward.  Such  passageways  vary  in  size  from  "pinholes,"  indicated 
by  the  surface  shown  in  Fig.  11,  to  those  of  finger  size  in  Fig.  12.  "A  wall  you  could  throw  a 
cat  through"  is  verbatim  repetition  of  a  field  characterization  which  is  not  infrequently  ap- 
plicable. It  is  often  objected  that  "pinhole"  passageways  are  not  continuous,  but  no  proof  of 
such  assertion  is  offered;  and  while  the  converse  is  equally  difficult  of  proof,  the  porosity  of 
pinholed  concretes  under  test  and  the  presence  of  like  pinholes  throughout  any  and  every  sec- 
tion of  such  concretes  gives  warrant  for  belief  that  they  are,  by  their  multitude,  of  great  im- 
portance when  their  combined  water-conveying  abilities  are  considered. 

43.  Excess  Water  as  a  Cause  of  Porosity. — Aside  from  segregated  pockets  of  stone  (which 
also  are  caused  by  excess  water),  water  voids  are,  however,  quantitatively  more  important  than 

are  airholes  as  passageways  for  penetrant  or  percolating  water. 
Water  voids  are  relatively  massive,  approaching  segregations 
even  when  not  so  classified;  and  inasmuch  as  the  water  once 
lying  in  them  has  either  flowed  away,  or  been  evaporated,  con- 
tinuity of  passageways  for  subsequent  water  flow  is  strongly 
indicated,  if  not  proven  by  the  fact  of  this  loss.  An  example 
of  such  water  voids  and  flow  passages  in  a  commercial  concrete, 
intended  to  be  of  superior  grade,  is  shown  in  Fig.  13.  This  is 
typical  of  innumerable  passageways  of  like  character  found 
Fig.  13.— Water  voids  passage-  trenerally  in  overwet  concretes, 
way    in    concrete.    (Magnified  .  -    ^t.  •   i  i         au  •  i  i      •  ^  j: 

diams.)  44.  Shrinkage  Cracks. — fehrmkage  cracks  m  concrete  are  of 

a  general  type  and  so  universal  as  to  be  viewed  by  the  majority 
either  with  eyes  unseeing,  or  regarded  with  the  contempt  that  comes  from  familiarity.  Their 
importance  both  as  a  condition  and  as  an  indicator  of  internal  processes  is,  however,  of  the 
greatest  importance. 

Shrinkage  cracks  are  of  a  general  type,  irregular  in  line  and  radiating  from  a  common  center, 
usually  a  pore  of  greater  or  less  size.  This  is  to  be  expected,  inasmuch  as  such  a  pore  is  at  least 
a  possible  point  of  egress  for  water  from  the  mass  immediately  sur- 
rounding. Further,  flow  is  freest  from  such  an  open  center,  so  that 
under  evaporation  or  other  processes  it  soon  becomes  a  point  of 
dryness;  and  inasmuch  as  it  is  already  a  point  of  weakness,  relief 
planes  radiate  from  it-  gradually  as  drying  proceeds  inward,  until 
shrinkage  stresses  are  balanced  by  internal  resistance. 

44a.  Types  of  Shrinkage  Cracks. — Perhaps  the  com- 
monest type  of  shrinkage  crack  is  three-branched.  This  is  to  be 
seen,  on  every  hand  in  concretes  and  stuccos,  both  in  the  gross 
(Fig.  14)  and  in  microscopic  sizes  (Fig.  15).  Where  numerous 
pore  centers  exist,  complicated  systems  build  up  by  the  junction  of  a  multitude  of  like  radiat- 
ing cracks  from  "crazing",  with  oftentimes,  deeper  and  more  serious  disruptions,  as  in  Fig. 
16.    In  both  Fig.  14  and  Fig.  16  the  centers  have  been  outlined  in  circles.    Like  cracks  in 

1  See  chapter  on  "Proportioning  Concrete"  in  Sect.  2,  and  on  "Water"  in  Sect.  1. 

2  N.  C.  Johnson:  Eng.  Rec,  Jan.  23,  1915;  Dec.  30,  1916. 
»  N.  C.  Johnson:  Eng.  Rec,  Deo.  4,  1915. 


Sec.  2-446] 


GENERAL  METHODS  OF  CONSTRUCTION 


85 


drying  earth  are  everywhere  to  be  observed,  the  three-branched  crack  permitting  spherical 
contraction  and  rehef  with  minimum  disturbance. 

446.  Shrinkage  Cracks  and  Porosity.— Necessarily,  such  shrinkage  cracks  in 
concrete  are  open  passageways  for  water.  This  is  attested  on  every  hand  by  the  crystalline 
filling  of  dissolved  salts  left  behind  in  such  shrinkage  cracks.  Fig.  17  is  typical  of  such  condi- 
tions, which  exist  where  the  fluid  supply  is,  or  becomes,  somewhat  limited,  so  that  super- 
saturation  and  crystallization  may  be  brought  about.  Moreover,  as  is  evidenced  by  such 
crystalline  fillings,  these  cracks  once  conveyed  fluid  through  the  concrete.  Cracks  of  like 
formation  are  equally  potent  to  convey  other  fluid;  and,  if  the  supply  is  ample,  to  remove 
soluble  portions  of  the  concrete,  with  mechanical  dislodgment  and  removal  of  inert  particles 
released  by  such  solution.  The  original  passageway  is  thus  speedily  enlarged,  possibly  to  harm- 
ful proportions  and  certainly  to  increased  water-carrying  capacity.  Evidence  as  to  such  quanti- 
tative removal  of  material  is  given  on  sheltered  surfaces  of  concrete,  such  as  inspection  galleries 


'if 

nnil 

Fig.  15. — Microscopic  shrinkage  crack. 
(Magnified  150  diams.) 


Fiu.  16. 


P^a.  17. 


of  concrete  dams,  where  deposits  removed  from  the  concrete  and  aggregating  many  tons  are  not 
infrequently  piled  on  floors  and  cling  to  walls. 

44c.  Prevention  of  Shrinkage  Cracks. — Shrinkage  cracks  like  the  foregoing  arc 
difficult  of  prevention.  They  may  be  minimized  in  number  and  severity  by:  (1)  use  of 
graded  materials;  (2)  avoiding  the  use  of  excess  water;  (3)  adequate  mixing;  (4)  careful  placing 
to  avoid  segregation;  and  (5)  curing  (annealing)  under  proper  conditions  of  moisture,  so  that 
shrinkage  stresses  will  be  developed  only  at  a  rate  commensurate  with  the  slow  increase  of 
strength  in  concrete.  This,  in  connection  with  slow  drying  and  hardening  of  colloids,  largely 
explains  the  high  strength  of  concretes  cured  under  water,  and  conversely,  explains  the  easier 
disintegration  of  concretes  in  which  too  rapid  drying  occurs. 

But  though  the  foregoing  five  principles,  if  made  effective  in  practice  under  skilled  direc- 
tion, would  result  in  better  concretes  as  to  water-tightness,  with  correlative  strength  and  en- 
durance, their  field  observance  is  so  limited  as  to  be  negligible.  Adequate  mixing  will  not  be 
had,  so  long  as  engineers  countenance  and  tacitly,  if  not  openly,  approve  inadequate  mixing  in 
the  interest  of  quantity  output.  Graded  sand  and  stone  will  not  be  used  unless  cheaper  than 
other  available  materials,  so  long  as  the  same  price  per  yard  in  forms  is  paid  for  one  as  for  the 
other.  Excess  water  will  be  used  until  insistence  is  had  for  the  use  of  lesser  quantities.  Careful, 
uniform  placing  needs  standardization  and  enforcement  by  engineers  of  such  standards. 
Moist  curing,  or  annealing  of  large  sections  is  often  a  physical  impossibility,  but  often  it  can 
be  done  if  required.  The  practice  of  curing  commercial  concrete  is  now  extending;  a  fact 
which  offers  much  encouragement.  Though  many  problems  yet  remain  unsolved,  our  present 
knowledge  is  sufficient  for  great  improvement,  once  engineering  sentiment  for  right  practice  is 
brought  to  the  point  of  putting  them  into  effect.  The  cause  of  pervious  concretes  lies  not  so 
much  in  lack  of  knowledge  as  to  how  to  make  concretes  that  are  impervious,  as  in  neglect  to 
put  into  effect  the  knowledge  at  hand. 


86 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-45 


45.  Pervious  Concretes  and  Laitance. — Laitance — the  porous,  chalky  material  which  rises 
during  deposition  to  greater  or  less  extent  at  the  surface  of  concretes — is  a  chief  foe  of  water- 
tightness.  The  deposit  is  particularly  deep  with  excess  water,  or  too  fine  or  dusty  aggregates, 
or  both.  Concrete  subsequently  placed  on  this  laitance  fails  utterly  to  bond;  and  seepage 
readily  takes  place  along  this  construction  or  "day's  work"  joint,  often  followed  by  later  dis- 
integration. Laitance  an  inch  or  more  thick,  scrolled  with  a  lath,  on  top  of  a  newly  poured 
foundation  block  4  ft.  in  depth,  is  shown  in  Fig.  5,  page  74.  In  sections  of  greater  height,  as 
in  reservoir  walls,  especially  where  overwet  concretes  are  indulged,  the  deposit  will  be  of  greater 
depth,  usually  extending  through  the  body  of  the  wall  to  form  a  horizontal  joint,  open  to  per- 
colating water. 

Occasionally  such  laitance  deposits  are  localized,  forming  pockets;  and  inasmuch  as  such 
pockets  are  formed  from  the  finer  material  assumedly  lying  distributed  in  inter-particle  spaces 
throughout  the  concrete  mass,  their  isolation  implies  and  often  proves  the  existence  of  segre- 
gated and  open  pockets  of  ballast  at  other  points.  This  is  easily  to  be  understood  when  continu- 
ous deposition  in  one  part  of  overwet  concretes  is  observed  in  field  work  with  runoff  of  lighter 
materials  as  the  mound  grows. 

In  all  concrete  work  subject  to  water  action  in  any  degree,  laitance  planes  may  be  sub- 
stantially avoided  by  filling  forms  without  permitting  set  of  one  portion  before  the  portion  next 
above  is  deposited.  Running  off  ''soupy"  portions  from  the  top  of  forms  while  the  mass  is 
fluid  is  a  palliative  measure  that  may  be  used,  or  removal  of  laitance  after  setting  may  be  at- 
tempted. No  measures  yet  devised  are  wholly  adequate,  in  that  none  basically  remove  the 
cause  of  complaint. 

46.  Effect  of  Temperature  and  Atmospheric  Effects  on  Water-tightness. — Temperature 
effects  in  finished  structures,  and  those  due  to  atmospheric  changes,  may  result  in  opening 
passageways  capable  of  conveying  water.  The  coefficient  of  expansion  of  concrete  is  approxi- 
mately the  same  as  that  of  steel  (see  Art.  32,  Sect.  5).  Adopting  a  linear  unit,  the  movement 
at  any  point  may  be  found  by  multiplying  the  distance  expressed  in  terms  of  this  unit  of  this 
point  from  a  fixed  point  by  the  degrees  change  of  temperature  experienced  or  anticipated.  In 
massive  masonry,  the  interior  experiences  little  thermal  change.  Actual  dimensional  changes 
in  such  structures  are  probably  compensated  for  by  internal  flow.^ 

Variations  in  moisture  content,  even  after  prolonged  set,  affect  the  volume  of  concrete 
from  0.05  to  0.08%  in  the  usual  atmospheric  range.  This  may  be  outwardly  evidenced  by 
cracks,  but  is  more  generally  taken  up  in  internal  stresses  in  the  concrete  and  reinforcement. 
Such  changes  are  to  be  anticipated  from  our  knowledge  as  to  the  colloid  content  of  concretes 
and  the  absorptive  and  dessicative  properties  of  such  materials. 

If  consideration  of  anticipated  temperature  and  moisture  changes  indicates  that  a  given 
structure  will  be  liable  to  cracking  by  stresses  thus  induced,  expansion  joints  must  be  provided. 
Their  use  is  preferable  to  their  omission  in  most  cases,  but  they  must  be  most  carefully  formed. 
Copper  or  lead  flashing,  or  asphalt  or  elaterite  mastic  and  fabrics  have  been  found  efficacious 
when  properly  applied,  but  all  precautions  must  be  observed  as  to  obtaining  density  in  the  sur- 
rounding concrete.  With  mastic  compounds,  dryness  of  the  adjacent  concrete  must  be  secured 
in  order  to  obtain  proper  bond,  else  leakage  at  the  joint  will  occur. 

47.  Integral  Waterproofing  Compounds. — The  foregoing  paragraphs  have  given  an  in- 
sight into  the  causes  of  porous  or  leaking  concretes.  Where  penetration  and  flow  of  water  occur, 
it  has  been  pointed  out  that  an  actual,  physical  passage  or  passages  exist,  that  these  passage- 
ways may  be:  (1)  pinholes,  or  pores,  resulting  from  occluded  air;  (2)  water  voids,  or  spaces  left 
by  excess  water;  (3)  shrinkage  cracks  radiating  from  a  pore,  or  hole  of  greater  or  less  size,  with 
joining  of  a  myriad  of  like  cracks  into  complicated  systems  of  cracks  in  concretes  that  dry  too 
rapidly;  (4)  segregation  due  largely  to  excess  water,  with  open  pockets  of  stone;  (5)  laitance,  in 
pockets  or  strata,  due  largely  to  excess  water;  and  (6)  temperature  or  other  cracks,  due  to  at- 
mospheric changes. 

1  F.  R.  McMillan:  Bull.  University  of  Minnesota. 


Sec.  2-47a] 


GENERAL  METHODS  OF  CONSTRUCTION 


87 


It  is  to  be  expected  that  the  customary  violations  of  the  natural  laws  governing  concrete 
which  bring  such  passageways  into  existence  should  cause  wide  demand  for  something  purchas- 
able which  would  afford  rehef  from  consequences.  If  any  agent  exists  or  is  to  be  found,  which, 
when  added  to  concrete  made  with  lack  of  care,  is  capable  either  of  preventing  or  of  closing  the 
passageways  through  which  water  penetration  or  transmission  is  brought  about,  without  detri- 
ment to  the  strength  or  other  properties  of  the  concrete,  it  may  be  ranked  as  a  noteworthy  dis- 
covery. There  is  some  question,  however,  as  to  whether  any  substance,  particularly  in  econom- 
ical percentages,  will  accomplish  this  end  to  any  save  a  minor  degree.  Consideration  of  the 
open  void  volumes  and  segregated  areas  in  many  concrete  structures  reflect  the  magnitude  of 
the  task.  It  is  probable  that  proper  practices  and  materials  and  they  alone  are  adequate  as 
well  as  unsurpassed  in  securing  water-tight  and  enduring  concretes. 
:i  47a.  Integral  Waterproofing  Classification. — Integral  waterproofings  now  on 

I  the  market  may  be  grouped  under  four  heads: 

(a)  Special  materials  added  to  the  mixing  water. 

(&)  Special  materials  added  dry  to  the  cement  at  the  job. 

(c)  Cement  to  which  has  been  added  the  special  materials  during  manufacture. 

(d)  Special  materials  and  cement  applied  as  a  plaster,  this  being  intended  to  so  bond  with 
the  concrete  surface  as  to  become  integral  with  it. 

The  special  materials  employed  in  the  foregoing  are  substantially  as  follows : 

(a)  Various  forms  of  metallic  salts,  such  as  chloride  of  lime;  oil  emulsions;  lime  soaps,  sus- 
f:  pehded  in  water;  and  like  compounds.    The  actions  of  oil  emulsions  is  to  form  soaps  in  combi- 
nation with  the  lime  of  cement;  that  of  soap  solutions  as  lubricants  and  formers  of  insoluble  fillers 
by  reaction  with  cement.    Lime  chloride  has  a  catalytic  action  difficult  properly  to  define,  but 
tending  to  hasten  set  rather  than  either  to  lubricate,  or  to  form  pore-filling  compounds. 

(b)  Dry  powders  of  floury  consistency,  formed  of  metallic  stearates,  such  as  lime  soap, 
often  with  alum  and  hydrated  lime.  Their  properties  are  claimed  to  be  void-filling  and 
lubricating. 

(c)  Like  substances,  or  glycerides  of  limes,  mixed  with  cement  during  manufacture. 

(d)  The  same  as  (c),  used  as  a  surface  plaster. 

476.  Value  of  Integral  Waterproofing  Compounds. — There  is  no  general  authori- 
tative conclusion  yet  determined  as  to  the  value  of  integral  compounds.  Field  testimony  differs, 
probably  according  as  the  methods  and  materials  of  one  use  have,  through  inherent  excellence 
or  weakness,  proven  either  adequate  or  inadequate  to  produce  impervious  concrete.  The 
most  extensive  work  that  has  thus  far  been  done  is  published  in  Tech.  Paper  3,  by  R.  J.  Wig  and 
R.  H.  Bates  of  the  U.  S.  Bureau  of  Standards.  A  majority  of  present  commercial  waterproofers 
were  tested  in  the  course  of  the  work  therein  detailed,  but  a  subsequent  series  requested  by 
several  manufacturers  of  tested  compounds,  with  concretes  to  be  made  under  commercial 
conditions,  has  not  yet  matured. 

The  conclusion  of  the  foregoing  tests  is  that  no  additive,  proprietary,  or  open,  will  of  itself 
overcome  initial,  serious  deficiencies  of  material,  or  admit  of  defective  practices;  and  no  addi- 
tive so  far  known  is  superior  in  results  to  an  excess  of  cement  and  the  use  of  graded  sand  of 
proper  quality  with  a  little  water  as  circumstances  permit. 

47c.  Rendering  Defective  Structures  Impervious. — It  is  often  necessary  to  ren- 
der an  existing  structure  as  nearly  waterproof  as  possible.  The  end  to  be  attained  is,  of  course, 
the  closing  of  all  water  passageways.  The  proper  method  to  use  is  dependent  upon  the  size, 
character,  and  origin  of  the  pores  or  passageways  in  the  concrete.  If  the  pores  are  very  small, 
some  inert  filler  such  as  clay  or  silt  may  be  sufficient;  or  a  soap  and  alum  mixture,  such  as  that 
employed  in  the  Sylvester  process,  may  be  applied.  If  the  pores  are  of  slightly  larger  size,  paraf- 
fine  or  a  paraffine-carrying  oil,  or  bitumen,  or  an  asphaltic  oil  may  be  successfully  used.  Paraf- 
fine  may  be  applied  either  hot  or  cold.  If  applied  cold,  it  is  dissolved  in  a  volatile  carrier  in 
saturated  solution.  Applied  to  the  surface  of  the  concrete,  it  penetrates  to  a  greater  or  less 
depth  according  to  the  dryness  and  porosity  of  the  concrete.    Within  a  short  time  the  volatile 


88 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-48 


carrier  is  evaporated,  leaving  the  paraffine  in  the  holes.  Paraffine  may  also  be  applied  in  a 
molten  condition  and,  to  render  successful  its  use,  the  concrete  must  first  be  rendered  sufficiently 
warm  by  artificial  heat  so  that  the  melted  paraffine  may  be  thoroughly  rubbed  in.  Hot  paraffine 
treatment  is  one  of  the  most  durable  of  waterproofing  methods  for  work  exposed  to  weather,  but 
it  requires  considerable  experience  to  secure  a  successful  result. 

Bitumens  of  one  grade  or  another  are  applied  either  in  solution  or  hot,  as  in  the  paraffine 
surface  treatment.    They  also  may  be  incorporated  in  paints  which  are  applied  to  the  surface. 

Any  bitumens  employed  must  possess  a  high  degree  of  elasticity  and  durability  and  must 
have  considerable  bonding  ability  with  the  concrete.  To  this  end  all  concrete  surfaces  to  which 
bitumens  are  applied  should  be  thoroughly  dried  and  preferably  should  be  warm  at  the  time  of 
applications.  Material  should  be  well  rubbed  into  corners  and  recesses;  and  the  waterproofing 
film  should  be  continuous  throughout. 

In  applying  bituminous  paints  and  solutions  it  is  a  prerequisite  to  success  that  the  coating 
shall  be  applied  on  that  side  of  the  concrete  against  which  the  water  pressure  is  exerted.  If  this 
is  done,  the  materials  will  be  carried  into  the  water  passageways,  but  if  this  is  neglected  the 
materials  will  be  forced  out  so  that  their  application  is  waste. 

48.  Waterproofing  by  Cement  Grouting. — Neat  cement  grout  has  often  been  tried  as  a 
waterproofing  coating,  applied  either  as  a  surface  plaster  or  as  a  surface  wash.  It  has  also  been 
used  as  a  crack  filler,  but  inasmuch  as  it  is  virtually  impossible  to  make  a  coating  or  filling  of  this 
kind  adhere  to  set  concrete,  its  use  is  rarely,  if  ever,  attended  with  success.  In  difficult  situa- 
tions attempts  have  been  made  to  use  cement  grout  under  pressure  as  a  waterproofer,  but  the 
instances  on  record  where  this  has  been  successfully  done  do  not  indicate  generally  satisfactory 
results.  It  seems  to  be  requisite  that  any  waterproofing  mixture  shall  be  more  or  less  plastic 
and  viscous  and  that  it  shall  be  so  applied  as  to  deform  and  closely  fill  passageways  in  the  con- 
crete under  pressure  of  the  water. 

49.  Membranous  Waterproofings. — Membranous  waterproofing  is  an  elastic,  continuous 
sheet  or  membrane  completely  covering  or  surrounding  a  structure  to  be  waterproofed  (see  Fig. 


Tte  cover  I  , 

-s'-o-'-A 


Fig.  1 


•.  o 

'■-■■LBuH-  laps 
Nofe-'-  Thickness  of  waterproofing  exagger- 
ated to  distinguish  the  phes 

Fig.  19. 


18).  This  membrane  is  laid  in  several  overlapping  layers  (Fig.  19),  impregnated  and  fastened 
down  with  some  bituminous  compound.  The  membranous  system  of  waterproofing  is  adapted 
principally  to  the  waterproofing  of  structures  in  course  of  erection,  such  as  subways,  tunnels, 
building  foundations,  retaining  walls,  arches,  reservoirs,  etc. 

The  bituminous  materials  employed  as  sealing  compounds  in  the  membrane  method  of 
waterproofing  are:  (a)  coal-tar  pitch  applied  hot;  (6)  asphalts  applied  hot;  (c)  asphalt  mastic 
applied  hot;  {d)  especially  prepared  asphaltic  compounds  sold  under  various  trade  names. 

The  membranes  to  be  used  with  the  above  sealing  compounds  are:  (a)  tarred  felt;  (6) 
asphalted  felt;  (c)  burlap;  id)  burlap  saturated  with  asphalt  or  tar;  (e)  combinations  of  canvas 
and  felt,  or  canvas  and  burlap,  or  felt  and  burlap. 

49a.  Application  of  Membranous  Waterproofing. — Success  of  membranous 
waterproofing  depends  largely  upon  the  care  with  which  the  materials  are  applied.  It  is  neces- 
sary first  to  prepare  the  concrete  surface.  It  must  neither  be  too  rough,  nor  too  wet,  nor  cov- 
ered with  dirt  or  foreign  substance;  and  it  must  not  possess  a  glaze  due  to  richness  of  cement 
surface.    It  is,  therefore,  necessary:  (1)  that  all  dirt  and  foreign  matter  shall  be  removed  before 


Sec.  2-496] 


GENERAL  METHODS  OF  CONSTRUCTION 


SO 


waterproofing  is  applied;  (2)  that  when  it  is  appHed  the  concrete  shall  be  rendered  dry,  either  by 
drainage  and  evaporation  or  by  the  application  of  artificial  heat;  (3)  that  the  concrete  shall  he 
thoroughly  set  (as  is  indicated  in  the  requirement  for  dryness) ;  (4)  that  any  glazed  surfaces  shall 
be  picked  or  rubbed  down  in  order  that  the  materials  may  adhere;  (5)  that  form  ties  or  other  pro- 
jections that  might  puncture  the  waterproofing  shall  be  removed;  and  (6)  that  any  metal  sur- 
faces encountered  shall  be  dry,  clean,  and  free  from  rust  or  dirt. 

496.  Continuity  of  Membrane. — Lack  of  continuity  may  be  fatal  to  the  success 
of  any  waterproofing  membrane.  The  waterproofing  sheet  must,  therefore,  be  applied  con- 
\  tinuously  over  the  whole  surface  to  be  treated,  footings  and  foundations  included.  All  joints 
■  in  the  membrane  must  be  broken  at  least  4  in.  on  cross  joints  and  12  in.  on  longitudinal;  and 
at  least  12  in.  of  lap  must  be  left  at  corners  to  form  good  junctions  with  adjoining  sections. 
Where  it  is  necessary  to  stop  work,  a  lap  of  at  least  12  in.  shall  be  provided  for  joining  on  new 
work.  Each  layer  of  bituminous  or  other  material  must  com- 
pletely cover  the  surface  on  which  it  is  spread,  without  cracks  or 
blow-holes;  and  the  fabric  must  be  rolled  out  smoothly  and  pressed 
over  the  cementing  material  so  as  to  insure  its  sticking 
thoroughly  and  evenly  over  the  entire  surface. 

49c.  Protection  of  Waterproofing.^ — After  the 
waterproofing  has  been  put  in  place  it  must  be  properly  pro- 
tected from  injury.  Such  injury  may  occur  when  backfilling 
with  earth;  when  depositing  concrete  against  the  waterproofing 
(see  Fig.  20);  when  laying  brick  or  rubble,  or  from  careless  piling 
of  materials  on  the  completed  waterproofing  work.  Injury  from 
workmen's  shoes  is  not  infrequent.  It  should  be  remembered 
that  a  completed  membranous  waterproofing  is  usually  soft  and 
liable  to  injury  and  the  chances  of  so  doing  should  be  reduced  to  a 

minimum.  A  single  point  of  entry  for  water,  particularly  if  inaccessible  when  the  work  is 
completed,  may  render  ineffective  all  precautions  against  leakage. 

The  following  table  gives  the  numbers  of  ply  of  waterproofing  required  with  various  heads 
of  water: 

50.  Rules  for  Making  Concrete  Imper- 
vious.— (a)  To  make  concrete  that  shall  be 
impervious,  the  rules  basically  governing  the 
making  of  dense  concrete  apply  with  special 
force.    These  are: 

1.  Use  proper  materials,  i.e.,  clean  and 
preferably  graded  sand;  hard,  durable  stone; 
cement  that  conforms  to  standard;  and  clean 
water. 

2.  Use  proper  proportions  of  proper  ma- 
terials, i.e.,  avoid  arbitrary  proportions;  use 
careful  measurement  for  each  batch;  test 
each  shipment  of  sand  for  uniformity  of 
grading;  if  variation  is  found,  properly  com- 
pensate by  variation  of  proportions. 

3.  Properly  and  adequately  mix  the  ma- 
terials, i.e.,  not  only  stir  together  the  several 
ingredients,  but  prolong  the  operation  suffi- 
ciently to  secure  the  needful  consistency  and 
distribution,  particularly  of  the  cement. 


Number  of  Ply  of  Waterproofing  Required 
FOR  Varying  Heads  of  Waters 


Material 

Head  of 
water 

Coal  tar 
and 
felt 

Commer- 
cial 
asphalt 
and  felt 

Special 
felts  and 

com- 
pounds 

Asphalt 
mastic, 
thickness 
in  inches 

0 

2 

2 

1 

h' 

1 

3 

3 

2 

% 

2 

4 

4 

3 

H 

6 

5 

5 

4 

H 

8 

6 

6 

5 

H 

10 

7 

7 

6 

15 

8 

8 

7 

% 

20 

9 

9 

8 

1  From 
M.  H.  Lewis. 


Modern    Method     of  Waterproofing, 


90 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-51 


4.  Use  a  minimum  of  water  that  will  permit  adequate  filling  of  forms  and  contact  with 
reinforcement. 

5.  Place  carefully  informs  to  avoid  segregation  or  unequal  distribution. 

6.  Expel  as  much  as  possible  of  occluded  air  by  puddling,  or  vibrating,  or  jarring  of  forms  as 
filling  proceeds. 

7.  Fill  forms  continuously  to  top,  preferably  overflowing,  to  avoid  stoppage,  or  laitance  planes. 

8.  Properly  protect  concrete  against  rapid  evaporation  and  against  unusual  heat  or  cold  during 
the  setting,  hardening,  and  curing  periods  to  avoid  shrinkage,  frost,  or  other  crackings  and 
disruptions. 

9.  Remove  visible  segregations  as  soon  as  discovered,  replacing  with  good  concrete,  well 
rammed  into  place.  Do  not  rely  on  surface  plastering  of  defects.  Such  attempts  are  unwork- 
man-like  and  ineffective. 

10.  Construct  expansion  or  contraction  joints  with  extreme  care.  Do  not  rely  for  water- 
tightness  on  any  supposed  bond  between  abutting  concrete  sections. 

(b)  Integral  waterproofings  cannot  be  relied  upon  to  avert  the  consequences  of  improper 
manufacture. 

(c)  Membranous  waterproofings  are  of  service  in  closing  water  passageways  in  existing  de- 
fective structures  when,  and  only  when,  carefully  apphed. 

FINISHING  CONCRETE  SURFACES 

51.  Character  of  Surface  Finish  Desired. — The  character  of  finish  desirable  to  produce  on 
concrete  surfaces  is  determined  by  the  ends  to  be  served.  The  majority  of  requirements  for 
special  finishes  are  architectural,  varying  according  to  the  character  of  the  structure  and  with 
the  location  of  the  surface. 

52.  Removing  Form  Marks. — For  all  concrete  work  exposed  to  view,  forms  should  be 
exceedingly  well  constructed,  producing  plane  surfaces  and  straight,  sharp  lines  and  true  angles 

in  the  finished  concrete.  In  work  of  this 
character,  extra  care  is  usually  taken  to  ob- 
tain even-textured,  dense  surfaces  by  using 
a  mixture  of  proper  consistency  and  by 
careful  spading  and  puddling.  Such  sur- 
faces necessarily  reproduce  all  defects  of  the 
mold,  so  that  after-treatment  is  necessary  to 
remove  the  form  marks,  as  well  as  to  relieve 
the  "dead"  color  due  to  excess  of  cement  at 
the  surface,  with  oftentimes  efflorescence, 
or  other  whitish  deposits,  indirectly  occa- 
sioned thereby. 

It  is  elementary  optics  that  blemishes 
are  least  visible  on  a  non-uniform  light- 
diffracting  "matt"  or  stippled  surface. 
Form  marks,  therefore,  are  concealed  by 
producing  such  a  surface.  This  may  be 
done  by  tooling,  by  rubbing,  by  brushing. 
Fig.  21.-Rotary  concrete  surfacer  being  used.    Note      «^   ^y  sand-blasting,   and  SUch  treatments 

contrast  between  finished  and  unfinished  surface.        have  a  further  advantage  of  modifying  the 

dead  color  above  referred  to  by  exposing  a 
multitude  of  sand  grains  to  fight,  so  that  by  reflection  from  their  facets,  the  gray-green  of 
cement  is  relieved  and  brightened. 

52a.  Tooling. — Tooling  concrete  surfaces  is  more  or  less  costly,  depending  upon 
the  length  of  time  the  concrete  has  set  and  upon  its  hardness.  Bush-hammering,  crandalling, 
or  axing  may  be  done  by  hand,  or  a  pneumatic  or  electric  tool  may  be  employed  at  considerable 


Sec.  2-526] 


GENERAL  METHODS  OF  CONSTRUCTION 


91 


advantage.  One  type  of  surfacing  tool  permitting  of  tooling  or  of  grinding  and  the  method  of  its 
use  is  shown  in  Fig.  21. ^  Its  capacity  is  rated  at  60  to  70  sq.  ft.  of  surface  per  hour  on  concrete 
from  1  to  21  days  old.  Fig.  22  shows  a  hand  bush-hammered  surface  of  colored  aggregates,  and 
Fig.  23  a  picked  surface. 

Only  small-sized  aggregate  should  be  used  in  facing  material  to  be  tooled,  as  it  is  hard  to 
dress  and  to  obtain  uniform  results  on  surfaces  where  large  angular  stones  are  encountered. 
The  concrete  should  be  thoroughly  hardened  before  work  is  commenced,  especially  if  sharp 
clean  surfaces  are  desired.  The  concrete  should  preferably  be  about  2  months  old,  although  if 
it  is  allowed  to  stand  too  long  the  labor  involved  will  be  unnecessarily  great. 

A  variety  of  surface  effects  may  be  obtained  by  tooling,  as  the  effect  produced  in  any  given 
■  case  depends  upon  the  kind  of  tool  used.  Some  variation  in  the  appearance  of  the  finished  sur- 
face may  also  be  obtained  by  the  manner  in  which  the  tool  is  handled.  By  striking  a  perpen- 
dicular blow  no  lines  or  marks  are  left  in  the  surface,  whereas  with  a  glancing  blow,  tooth  marks 
are  left  which  can  be  made  parallel  to  each  other  or  at  various  angles.    Tooling  cannot  ordinarily 


Fig.  22.  Fig.  23. 

Fig.  22. — Surface  finish  obtained  by  hand  bush-hammering.    The  contrast  of  shades  is  produced  by  using  dif- 
ferent colored  aggregates.    The  concrete  in  the  dark  portion  was  made  with  red  sandstone,  while  the  light  por- 
tion was  made  with  trap  rock. 
Fig.  23. — Picked  surface. 

be  performed  satisfactorily  on  gravel  concrete,  as  the  pebbles  will  be  dislodged  before  being 
chipped. 

526.  Rubbing. — If  a  rubbed  surface  finish  is  desired,  the  coarse  aggregate  should 
be  well  spaded  back  from  the  face  of  the  work  and  the  forms  should  be  removed  before  the 
concrete  has  set  hard,  preferably  in  a  day  or  two  after  the  concrete  is  poured.  It  is  necessary 
with  green  concrete  to  use  care  in  removing  forms  to  avoid  spalling,  as  it  is  very  difficult,  if  not 
impossible,  to  adequately  repair  such  spalls  by  patching  with  mortar.  It  is  necessary,  also, 
to  remove  form  wires  or  other  projections  before  rubbing  and  to  point  with  mortar  any  pockets 
or  open  places  in  the  surface.  The  process  of  rubbing  consists  in  grinding  down  the  surface 
of  the  concrete  sufficiently  to  remove  all  impressions  of  the  timber  or  other  irregularities,  using 
a  brick  of  carborundum,  emery,  concrete,  or  soft  natural  stone.  In  connection  with  the  rubbing 
(which  is  accomplished  with  a  circular  motion),  a  thin  grout  composed  of  cement  and  sand 
should  be  applied  to  the  surface,  well  rubbed  in,  and  the  work  afterward  washed  down  with 
clean  water.  The  grout  is  used  simply  to  fill  surface  imperfections  and  care  must  be  taken  not 
to  allow  it  to  remain  as  a  film  on  the  surface. 

This  method  of  treatment  produces  a  comparatively  smooth  surface  of  uniform  color  much 
superior  to  that  obtained  by  the  all  too  prevalent  method  of  painting  with  a  grout,  which  almost 
invariably  crazes,  cracks,  and  peels  off.  Rubbing  is  a  very  acceptable,  cheap  way  of  finishing 
concrete  surfaces. 

1  The  Berg  Electric  Rotary  Surfacer,  Elevator  Supplies  Co.,  N.  Y. 


92 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  ^-52c 


Fig.  24. — Wire-brushed  surface 
treated  with  acid. 


52c.  Brushing. — A  brushed  finish  is  obtained  by  removing  with  a  brush  the 
surface  film  of  mortar  which  forms  over  the  aggregate.  This  should  be  done  while  the  concrete 
surface  is  still  green.  The  brushing  should  be  started  just  as  soon  as  it  is  possible  to  do  so  with- 
out removing  particles  of  aggregate.  The  time  required  for  sufficient  hardening  can  only  be 
determined  by  experimenting  with  the  particular  surface.  The  forms  should  be  constructed  so 
they  may  be  taken  down  in  sections  and  give  access  to  the  face  of  the  concrete  without  taking 
away  the  standards  which  provide  strength  for  the  forms  as  a  whole. 

The  process  consists  of  scrubbing  or  brushing  the  concrete  surfaces  with  ordinary  fiber 
(or  wire)  brushes  and  water  until  all  the  surface  cement  has  been  washed  off,  leaving  the  coarse 

aggregate  exposed.  The  ordinary  fiber  brush  will  not  answer 
if  the  surface  is  permitted  to  get  too  hard.  A  brush  about  4  in. 
wide,  made  by  clamping  together  a  sufficient  number  of  sheets 
of  wire  cloth,  has  been  found  to  be  very  effective. 

The  appearance  of  a  brushed  finish  can  be  improved  by 
washing  with  hydrochloric  (muriatic)  acid  applied  with  a  brush. 
The  acid  (which  should  be  diluted  with  6  parts  water) 
thoroughly  cleans  the  surface  of  the  aggregate,  thereby  inten- 
sifying the  color  and  texture  of  same.  The  treated  surface 
can  be  made  of  any  desired  color  by  the  proper  selection  of 
colored  aggregates,  but  care  should  be  taken  to  make  sure 
that  the  materials  used  are  not  affected  by  the  acid.  The 
surface  should  be  thoroughly  washed  after  the  acid  treatment 
as  otherwise  it  will  have  a  mottled,  streaky  appearance. 

A  wire-brushed  surface  treated  with  acid  is  shown  in 
Fig.  24. 

52d.  Sand-blasting. — A  sand-blast  finish  is  very  much  the  same  in  appearance 
as  that  obtained  by  brushing  the  concrete  surface  while  it  is  green.  Sand-blasting  produces  a 
granulated  finish  somewhat  similar  to  sandstone  but  not  so  uniform,  because  the  aggregates  are 
likely  to  be  brought  out  irregularly. 

The  concrete  should  be  thoroughly  hardened  before  sand-blasting,  especially  if  sharp 
edges  and  surfaces  of  a  fine,  uniform  texture  are  desired.  All  pronounced  ridges  should  be 
removed  by  tooling  previous  to  sand-blasting  since,  in  attempting  to  remove  these  ridges  with 
the  sand-blast,  the  surface  on  either  side  is  apt  to  be  cut  too  deep  and  depressions  in  the  surface 
intensified  or  made  more  prominent  instead  of  being  erased.  All  strips  nailed  to  the  forms  to 
make  moldings,  joints,  and  courses  should  be  left  in  place  while  the  surface  is  being  sand-blasted, 
as  otherwise  the  sharp  angles  and  edges  will  be  rounded  off. 

53.  Use  of  Colored  Aggregates. — The  most  satisfactory  concrete  surface  of  a  given  color 
and  texture  can  be  obtained  by  properly  finishing  a  surface  faced  with  a  mixture  composed  of 
cement  and  an  aggregate  of  the  proper  size  and  color.  The  color  is  obtained  from  the  exposed 
aggregate,  and  not  by  adding  coloring  matter  to  the  mixture.  The  successful  production  of 
the  desired  surface  is  also  dependent  upon  the  proper  grading,  proportioning,  mixing,  and  plac- 
ing of  the  materials  and  upon  the  method  of  finishing  the  surface. 

Where  special  or  expensive  materials  must  be  employed  to  obtain  the  desired  finish,  they 
may  be  used  only  in  the  mixture  applied  as  a  facing  to  the  exposed  surface.  Such  a  facing  is 
usually  1  to  1)^  in.  thick.  The  best  method  of  placing  the  facing  material  on  vertical  surfaces 
is  by  the  use  of  a  metal  facing  form  or  mold,  consisting  of  short  lengths  of  iron  plates  8  to  10  in. 
wide  and  about  6  ft.  long  with  three  angle  irons  riveted  to  each  plate.  The  upper  end  of  the 
long  plate  should  be  provided  with  handles  and  slightly  flared  to  assist  in  depositing  the  material. 
The  metal  form  is  placed  against  the  wall  form  with  the  handles  up  and  the  outstanding  legs  of 
the  angles  tight  against  the  wooden  form.  The  space  between  it  and  the  back  of  the  wall  is 
filled  with  ordinary  concrete  backing  and  the  1-in.  or  l}4-m.  space  between  the  metal  form  and 
the  face  form  is  filled  with  facing  material.    The  metal  form  should  not  be  permitted  to  remain 


|3ec.  2-54] 


GENERAL  METHODS  OF  CONSTRUCTION 


93 


intil  initial  set  takes  place,  but  should  be  frequently  raised  to  prevent  the  formation  of  seams 
between  the  facing  and  the  concrete  backing. 

:  64.  Addition  of  Colors  to  Concrete. ^ — Pigments  may  be  added  to  concrete  to  give  colors 
!)£  one  shade  or  another.    All  such  pigments  should  be  chemically  inert  and  of  mineral  origin. 

lit  is  to  be  borne  in  mind  that  Portland  cement  is  of  itself  a  pigment,  gray-green  when  unhy- 

•Irated,  white  when  hydrated;  and  that  the  brilliance  of  any  pigment  will  be  modified  and  its 
•olor  made  somewhat  uncertain  due  to  varying  percentages  of  hydrated  or  unhydrated  cement 
)resent  at  any  portion  of  the  surface.  Cement  stains  of  varying  shades  may  be  obtained  in  the 
)pen  market  and,  when  used  on  dry  concrete,  give  excellent  results.  ^  Inasmuch  as  in  using 
;uch  stains,  the  pigment  is  confined  to  the  surface,  they  are  more  economical  than  are  body 

•;olors  and  there  is  less  risk  of  detriment  to  the  concrete  through  chemically  active  pigments. 

I      65.  Use  of  White  Cement. — The  uses  of  white  Portland  cement  in  decorative  concretes 

ire  manifold.  White  Portland  cement  is  necessarily  a  white  pigment;  and  its  use  in  connection 
vith  other  pigments,  or  with  colored  aggregates,  or  stippled  or  mottled  surfaces,  should  be 

j'arefully  tried  out  before  the  final  mixture  is  determined  and  employed. 

!'  66.  Plaster  Finishes. — Plasters  of  one  kind  or  another  rarely  if  ever  bond  effectively  to 
;oncrete  surfaces,  without  an  intermediate  agent.  This  phase  of  the  art  is  in  a  transition  stage 
it  present,  but  it  is  much  to  be  desired  that  permanent  bond  may  be  produced  between  concrete 
md  plaster  either  applied  directly,  or  on  some  intermediate  agent  of  definite  and  proven  value. 

67.  Surfacing  Concrete  Floors.  ^ — Concrete  floors  are  advantageously  surfaced  to  prevent 
I'lossible  dusting  as  well  as  to  produce  a  smooth  finish.  Decorative  effects  may  be  produced 
is  desired  by  the  use  of  selected  colored  aggregates,  with  or  without  pigments  or  stains  to  color 
:he  mortar.    The  grinding  operations  for  such  floors  are  similar  to  the  grinding  of  terazzo  floors. 

68.  Specification  for  the  Production  of  a  Rubbed  Surface. — -The  following  specification 
is  suggested : 

Immediately  upon  stripping  the  forms  from  the  concrete  and  while  the  material  is  green,  patch  all  broken 
lorners  and  such  parts  of  the  surface  where  the  face  has  been  removed  with  the  removal  of  forms  to  bring 
lame  to  the  general  level  of  the  surrounding  surface,  using  for  this  purpose  a  1  :  1  mixture  of  cement  and  sand. 
Ul  wires,  naills,  etc.,  that  may  be  projecting  beyond  the  surface  of  the  concrete  shall  be  cut  off  at  least  H  in. 
Jack  from  the  surface  and  the  holes  patched  with  a  like  mortar. 

When  all  patches  have  well  hardened  and,  in  no  case  less  than  48  hr.  after  patching,  cut  down  with  suitable 
.ools  all  board  makings,  projections,  swellings  or  lumps,  so  as  to  bring  the  ceiling  or  wall  to  a  reasonably 
straight  surface.  A  reasonably  straight  surface  shall  be  construed  to  be  one  which  will  show  fair  and 
true  when  tested  with  a  straight  edge. 

The  rubbing  may  be  done  at  any  time  convenient  after  the  rough  grinding  has  been  completed.  The 
method  of  rubbing  shall  be  as  follows: 

The  entire  surface  is  to  be  thoroughly  wet  down  and  kept  moist.  With  carborundum  or  like  abrasive 
block,  grind  in  a  mix  of  1:2  cement  and  white  sand  swabbed  on  the  surface  in  small  patches,  the  grinding-in 
being  done  when  the  material  is  wet,  water  being  added,  if  necessary,  to  keep  the  material  sufficiently  plastic 
until  the  grinding  operation  has  been  completed.  This  material  shall  be  ground  into  the  surface  until  all  voids, 
lines,  and  wood  markings  have  disappeared  and  until  all  surplus  material  not  used  for  filling  in  the  above- 
mentioned  voids,  etc.,  has  been  removed  from  the  surface.  Should  markings  appear  in  spots  where  the  plastic 
material  has  been  ground  in  in  larger  quantities,  they  shall  be  removed  by  rubbing  lightly  with  a  cork  float. 

No  brush  work  or  mixture  of  cement  shall  be  applied  on  this  surface  after  the  grinding  has  been  completed, 
and  where  larger  voids  appear,  same  will  be  carefully  pointed  up  with  the  ground-in  material  and  with  a  cork 
float. 

The  inside  corners  of  all  fillets,  belt  courses,  and  the  intersecting  planes  of  the  ceiHng  panels  and  beams, 
shall  be  ground  sharp.  All  outside  edges  shall  be  ground  off  either  side  and  carefully  smoothed  off  and  straight- 
ened with  the  cork  float. 

FORMS 

59.  General  Requirements.— In  order  to  obtain  satisfactory  concrete  work  the  forms  should 
6e  durable  and  rigid,  and  should  be  so  well  braced  that  bulging  or  twisting  cannot  occur.  The 

1  See  Art.  4&,  Sect.  4. 
-  See  Art.  6d,  Sect.  4. 

*  See  chapter  on  "Concrete  Floors  and  Floor  Surfaces"  in  Sect.  4. 


94 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-60 


joints,  also,  should  be  made  tight  enough  to  prevent  any  material  leakage  of  the  liquid  mass,  as 
such  leakage  will  mar  the  appearance  of  the  finished  work. 

Forms  should  have  sufficient  strength  to  properly  support  the  loads  which  they  are  called 
upon  to  carry.  Horizontal  members,  such  as  floor  sheathing  and  supporting  joists,  should  be 
able  to  support  the  weight  of  the  concrete  and  the  construction  load.  Vertical  members,  such 
as  wall  sheathing  and  supporting  studs,  should  be  designed  to  resist  the  hydrostatic  pressure 
of  wet  concrete  which  is  about  145  lb.  per  sq.  ft.  for  each  vertical  foot  of  height. 

60.  Economical  Considerations. — The  cost  of  forms  constitutes  a  large  item  of  expense  in 
the  building  of  reinforced-concrete  structures  and  this  cost  varies  to  a  considerable  extent  with 
the  kind  of  form  construction  adopted.  Form  work,  of  course,  should  in  every  case  leave  the 
finished  concrete  true  to  line  and  surface,  but  even  with  this  accomplished  a  great  deal  can  be 
done  in  so  designing  forms  and  in  so  planning  the  detailed  methods  of  their  construction  that 
erection  and  removal  will  be  greatly  facilitated  without  undue  waste  of  lumber.  As  a  general 
rule,  the  most  important  consideration  is  that  of  ease  in  form  removal  as  great  economy  may  be 
effected  by  using  form  units  over  and  over  again  with  a  minimum  of  repairs. 

Simplicity  and  symmetry  in  form  work  should  always  be  given  consideration.  In  buildings, 
uniform  story  heights  should  be  selected  whenever  possible  in  order  to  prevent  continual  re- 
making of  column  forms,  and  frequent  changes  in  column  sizes  should  be  avoided  (at  least  in 
the  case  of  light-floor  construction),  not  only  on  account  of  the  column  forms  themselves,  but 
on  account  of  the  beam  and  girder  forms  or  slab  forms  which  frame  into  them.  Also,  where  it 
is  feasible,  beam  sizes  should  be  so  chosen  that  local  standard  widths  of  lumber  may  be  employed 
without  splitting;  and,  at  the  same  time,  the  sizes  and  spacing  of  the  beams  should  be  made  so 
uniform  that  the  contractor  may  use  his  forms  repeatedly,  thus  greatly  reducing  the  expense  for 
lumber  and  eliminating  the  cost  of  making  new  forms.  In  many  cases  it  will  be  found  that  a 
slight  excess  of  concrete  will  save  many  times  its  cost  in  carpenter  work  and  lumber. 

61.  Lumber  for  Forms. — The  kind  of  lumber  to  use  for  forms  depends  upon  the  character 
of  the  work  and  the  available  supply  in  the  local  yards.  Spruce  seems  to  be  the  best  all-round 
material.  It  can  readily  be  obtained  in  almost  any  locality  and  is  undoubtedly  an  excellent 
lumber  to  use  for  joists,  studs,  and  posts.  For  sheathing,  however,  white  pine  is  better  than 
spruce  by  reason  of  its  smoothness  and  its  resistance  to  warping,  but  this  wood  is  generally  too 
expensive  (except  for  cornice  and  ornamental  work),  and  spruce  makes  a  good  substitute. 
If  white  pine  is  to  be  used  for  sheathing,  the  fact  should  not  be  overlooked  that  this  kind  of 
lumber  has  little  durability  on  account  of  its  extreme  softness  and  would  not  give  good  results 
if  the  forms  were  to  be  used  many  times. 

Aside  from  spruce  or  white  pine,  Norway  pine  and  southern  pine  are  generally  the  most 
available  and  give  satisfaction.  Hemlock  is  not  usually  desirable,  especially  for  that  part  of 
form,  work  which  comes  into  contact  with  the  concrete',  but  it  is  sometimes  used  for  ledgers, 
studs,  and  posts.  This  wood  is  too  coarse-grained  to  be  suitable  for  sheathing  and  is  liable  to 
curl  when  exposed  to  the  weather  or  to  wet  concrete. 

It  is  safe  to  say  that  lumber  which  is  only  partially  seasoned  should  be  the  kind  employed 
in  form  construction.  Kiln-dried  has  a  tendency  to  swell  when  soaked  by  the  concrete,  and 
this  swelling  causes  bulging  and  distortion  of  the  forms.  Green  lumber,  on  the  other  hand, 
dries  out  and  shrinks  if  allowed  to  stand  too  long  before  the  concrete  is  placed;  fortunately, 
though,  this  tendency  of  the  green  lumber  to  check  and  warp  may  be  prevented  to  some  extent 
by  keeping  the  boards  thoroughly  saturated  with  water.  When  using  natural,  well-seasoned 
lumber  care  should  be  taken  not  to  drive  the  work  up  too  close,  since  forms  should  always  be 
left  in  a  position  to  experience  some  slight  swelling  without  any  undesirable  results. 

Sheathing  lumber  should  be  dressed  at  least  on  one  side  and  both  edges,  even  for  non-ex- 
posed surfaces,  as  the  removal  and  cleaning  of  the  forms  are  greatly  facilitated  thereby.  In  face 
work,  where  a  smooth  and  true  surface  is  quite  important,  the  lumber  employed  should  be 
dressed  on  all  four  sides.  Lumber  which  is  dressed  in  this  manner  is  easy  to  work  up  and  place, 
and  this  fact  alone  usually  more  than  offsets  the  cost  of  dressing. 


Sec.  2-62] 


GENERAL  METHODS  OF  CONSTRUCTION 


95 


In  floor  and  wall  panels,  tight  joints  between  boards  may  be  obtained  by  using  either  tongue- 
and-grooved  stock  or  stock  cut  with  one  edge  beveled  and  the  other  square.  Beveled-edge 
stuff  is  especially  good  where  very  dry  lumber  is  used,  for  the  reason  that  buckling  is  prevented 
by  the  edges  crushing  as  the  boards  swell.  Tongue-and-grooved  stuff,  however,  gives  the  best 
results  under  ordinary  conditions.  This  stock  suffers  to  some  extent  from  breakage  and  costs 
more  than  beveled-edge,  but  it  gives  smoother  surfaces  after  repeated  use.  Joints  in  forms 
for  columns,  beams,  and  girders  are  sometimes  made  tight  simply  by  dressing  the  lumber  true 
to  edge,  forming  what  are  called  square  joints  or  butt  joints. 

The  thickness  of  lumber  to  use  in  form  work  depends  to  some  extent  upon  the  number  of 
times  the  forms  are  to  be  used  and,  in  the  case  of  floor  and  wall  sheathing,  upon  whether  the 
boards  are  to  be  built  into  panels  or  nailed  each  time  to  the  supporting  joists  or  studs.  Gener- 
ally speaking,  1-in.  stock  dressed  both  sides  to  '^^{q  in.  (called  J^-in.  boards)  is  employed  for 
floor  sheathing;  1,  13^,  or  l^^-m.  stock  (approximately  l^^e-in.,  dressed)  for  column  and  wall 
sheathing  and  for  the  sides  of  beams  and  girders;  and  13^  or  2-in.  stock  (l^-in.  dressed)  for 
beam  and  girder  bottoms.  The  size  and  spacing  of  joists,  studs,  girts  and  posts  depend  upon 
the  strength  and  rigidity  required  (see  Art.  65). 

62.  Removal  of  Forms. — The  length  of  time  that  forms  should  remain  in  place  depends 
upon  a  number  of  factors,  chief  among  which  are:  (1)  the  temperature  and  humidity  of  the  air; 
(2)  the  nature  of  stress  to  which  the  member  is  to  be  subjected;  (3)  the  normal  setting  and  hard- 
ening properties  of  the  concrete;  and  (4)  the  relation  of  the  dead  to  the  live  load. 

As  is  well  known,  weather  has  a  great  deal  to  do  with  the  setting  and  hardening  of  concrete. 
The  warmer  and  drier  the  weather,  the  more  rapid  the  hardening.  Cold  or  wet  weather,  on 
the  other  hand,  retards  hardening  and  the  forms  under  such  conditions  must  remain  in  place 
a  much  greater  length  of  time.  If  concrete  freezes,  it  will  not  continue  to  harden  until  it  has 
thawed,  and  then  it  will  acquire  strength  very  slowly.  ^ 

The  forms  for  members  subjected  to  bending  should  remain  in  place  longer  than  forms  for 
columns  or  walls.  In  other  words,  slabs,  beams,  and  girders  which  depend  upon  the  bonding 
action  between  the  steel  and  concrete  for  their  ability  to  carry  any  material  load  should  not  be 
left  unsupported  as  early  as  vertical  compression  members  which  will  bear  their  own  weight 
when  the  concrete  is  quite  green. 

The  normal  setting  and  hardening  properties  of  the  concrete  vary  with  the  quality  of  the 
cement,  the  consistency  and  richness  of  the  mixture,  and  the  freedom  of  the  small  aggregate 
from  impurities.  Some  cements  harden  more  rapidly  than  others  and  permit  an  earlier  removal 
of  forms.  Forms  may  also  be  removed  sooner  for  rich  mixtures  than  for  lean.  Then  again,  if 
impurities  are  present  in  the  sand,  the  concrete  may  set  abnormally  and  failure  will  result  if  the 
concrete  is  not  given  a  sufficient  time  to  harden. 

The  greater  the  proportion  of  dead  to  live  load,  the  longer  forms  should  remain.  For 
example,  forms  for  an  overhanging  cornice  should  remain  in  place  longer  than  forms  for  almost 
any  other  member,  since  the  dead  weight  is  a  very  large  percentage  of  the  total  weight  which  it 
is  designed  to  carry.  By  a  similar  reasoning,  long-span  beams  or  slabs  should  be  supported  a 
longer  time  than  short  ones;  roofs  longer  than  floors;  columns  in  the  upper  stories  longer  than 
columns  in  the  lower  stories;  and  columns  in  general  longer  than  footings. 

It  is  becoming  the  practice  on  the  best  work  to  mold  cubes  of  concrete  from  each  day's 
work  and  allow  them  to  set  on  the  job  under  the  same  conditions  as  the  concrete  in  the  struc- 
ture. 2  When  it  is  thought  desirable  to  remove  the  forms,  these  cubes  are  tested  for  compression 
in  order  to  determine  whether  the  concrete  has  sufficient  strength  to  carry  its  load.  Good  judg- 
ment should  be  exercised  even  under  such  conditions  since  the  plan  does  not  provide  for  the 
possibility  of  an  occasional  poor  batch  of  concrete. 

Many  builders  have  rules  for  the  removal  of  forms  under  ordinary  conditions.  Such  rules, 
or  course,  can  only  be  roughly  approximate,  and  experience  and  judgment  are  necessary  in 

1  See  Art.  29  and  Art.  16,  Sect.  5. 

^  See  chapter  on  "Field  Tests  of  Concrete." 


96  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  2-63 


using  them.  The  following  rules  are  recommended  by  the  Illinois  Department  of  Factory 
Investigation  :^ 

Time  Required  Before  Removing  Forms 


Above  GO°F. 

50°  to 
60°F. 

40°  to  50°F. 

Less  than  40°F. 

Columns  

Side  forms  for  girders 
and  beams. 

Bottom  forms  of  slabs  (6 

ft.  or  less  span). 
Bottom  forms  of  beams 
and  girders  (less  than 

14-ft.  span). 


Form  work  in  buildings  should  be  so  designed  that  the  column  forms  may  be  removed 
without  in  any  way  disturbing  the  supports  of  the  beams  and  girders.  This  practice  bares  the 
concrete  of  the  column  to  the  hardening  action  of  the  air  and  permits  a  defect  to  be  detected 
and  remedied  before  any  load  is  brought  to  bear  upon  the  column.  The  beam  and  girder  sides 
are  next  taken  down,  but  this  is  not  done  until  the  slabs  are  strong  enough  to  stand  up  without 
support.  Sometimes,  however,  as  a  matter  of  safety,  the  slab  supports  (namely,  the  sheathing 
and  joists)  are  replaced  with  temporarj^  uprights  bearing  against  a  plank  on  the  underside  of  the 
slab.  The  beam  and  girder  bottoms  and  the  posts  supporting  them  are  left  in  place  longer 
than  any  of  the  other  formwork,  and  should  not  be  taken  down  until  there  is  absolutely  no 
doubt  as  to  the  strength  of  the  members  supported.  Walls  are  usually  built  separately  from 
the  other  parts  of  the  building,  and  a  wall  form  may  be  removed  whenever  the  concrete  in  the 
wall  is  hard  enough  to  bear  its  own  weight. 

63.  Number  of  Sets  of  Forms  in  Building  Work. — The  number  of  sets  of  forms  which  are 
necessary  in  building  work  depends  upon  the  weather,  the  variation  in  the  shape  of  the  members 
from  floor  to  floor,  and  the  floor  area.  Under  reasonably  good  summer  conditions  13^^  sets  of 
forms  (forms  for  1)-^  stories)  will  serve  the  purpose  and  allow  the  work  to  progress  at  the  usual 
rate  of  a  story  in  a  week  or  10  days.  If  the  floor  framing,  however,  is  particularly  complicated, 
one  set  of  forms  may  be  the  more  economical  if  the  speed  of  construction  is  not  the  leading  con- 
sideration. In  such  a  case,  of  course,  extra  lumber  must  be  used  for  beam  and  girder  bottoms 
and  for  supports  which  must  be  left  in  place.  Where  the  floor  area  is  large  and  the  construc- 
tion is  fairly  uniform  throughout,  even  less  than  one  set  of  forms  with  additional  beam  bottoms 
and  posts  may  be  sufficient. 

64.  Examples  of  Form  Design. 

64a.  Column  Forms. — Fig.  25  shows  a  typical  form  for  a  rectangular  column. 
Two  sides  of  the  column  are  held  together,  as  shown,  by  bolts,  and  the  two  opposite  sides  by 
hardwood  wedges  between  the  bolt  and  the  form.  The  sheathing  or  lagging  boards  run  the 
entire  length  of  the  column  and  are  made  up  into  panel  units  by  means  of  the  cleats,  which  serve 
also  as  clamps.    A  somewhat  similar  column  form  is  shown  in  Fig.  38,  page  102. 

A  common  type  of  rectangular  column  form  where  wooden  wedges  are  used  to  do  all  the 
clamping  is  illustrated  in  Fig.  26.  The  tightening  is  made  possible  by  the  use  of  stop  blocks  on 
each  clamping  piece.  When  a  reduction  is  made  in  the  size  of  column,  these  blocks  must  either 
be  ripped  off  or  additional  blocks  nailed  on.  The  boards  comprising  each  side  of  the  column 
form  are  usually  battened  or  cleated  together  so  as  to  form  a  panel  unit.  This  practice  allows 
the  clamps  to  be  put  on  separately  and  thus  permits  stop  blocks  on  the  clamps  to  be  easily 

1  See  also  rules  given  in  "Concrete,  Plain  and  Reinforced,"  by  Taylor  and  Thompson  (1916  edition). 

2  Add  1  day  for  each  additional  foot  of  span. 


Within  3  days 

5 

days 

Within  4  days 

6 

days 

Within  4  days^ 

8 

days 

Within  14  days^ 

18 

days 

Not  less  than  10  days 
Not  less  than  10  days 

Not  less  than  14  days 

Not  less  than  14  days 


Not  until  tests 
have  been 
made  indicat- 
ing that  the 
concrete  is  set. 


i  Sec.  2-64a] 


GENERAL  METHODS  OF  CONSTRUCTION 


97 


changed  when  the  column  form  is  remade.  It  is  a  common  practice  to  make  up  the  sides  of 
,  column  forms  with  narrow  strips  of  sheathing  in  order  to  facilitate  the  reduction  in  size  of  columns 
If  from  floor  to  floor.    A  method  of  reduction  sometimes  employed  by  the  Aberthaw  Construction 


Fig.  25. 


Co.  is  shown  in  Fig.  27.  The  column  form  represented  here  is  also  illustrated  in  Plate  III, 
page  114.  The  use  of  narrow  sheathing  strips  applies  especially  to  interior  column  forms  since 
exterior  or  wall  columns  are  usually  of  the  same  width  from  basement  to  roof  and  change  but 
little  in  thickness. 

fa  J  Blocks  nailed  Hardwood 


Fig.  26. 


Fig.  28  and  Plate  II,  page  113,  show  a  method  of  bracing  column  forms  by  means  of  4 
by  4-in.  "whalers"  or  posts.    The  use  of  Henderson  clips  should  be  noted.    Sometimes  the 
bolting  is  done  directly  to  the  whalers. 
7 


98 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-64a 


la^gr/nj  planed  four  5/ 


■Clip 
Ordinal 


First.  Reduction 

\Pieces  ' b''  removed, 
side  x"  moved  in,  s'xA" 
deal-  cut  doyvn  and  I'lcS" 
set  in  as  shown  behind 
boarding. 

Fig.  27. 


Second  Reduction 
Pieces  "a" and  b" removed, 
side  "x" moved  in,  3x4''cuf 
down  and  I x  s" nailed^ 
'behind  cleats 


n 

n             n  - 

1 

.  n 

jj-          11           II  • 

1 

Plan 


Fie.  28.- 


Detail  Cff  Column  Section  B-B 

-Wall  column  forms  employed  in  Morrill  building,  Portland.  Me. 


Sec.  2-ma] 


GENERAL  METHODS  OF  CONSTRUCTION 


99 


Other  types  of  rectangular  column  forms  in  common  use  are  shown  in  Figs.  29,  30,  and  31. 
:  The  cleats  which  form  part  of  the  clamps  are  nailed  to  the  sides  when  making.    The  clamp 
[  shown  in  Fig.  31  is  patented  and  known  as  the  "New  England  Column  Clamp,"  controlled 
by  the  N.  E.  Column  Clamp  Co.,  Boston,  Mass.    It  consists  of  angle  irons  punched  at  frequent 
intervals  with  bolts  for  holding  the  form  together  wherever  needed.    Angles  and  bolts  may  be 
I  bought  in  the  open  market.    The  New  England  Column  Clamp  Co.  sells  only  the  rights  to  use. 
Fig.  32  illustrates  still  another  type  of  rectangular  column  form.    The  use  of  horizontal 
sheathing  should  be  noted.    The  sheathing  is  nailed  to  the  vertical  pieces  before  erection. 

A  patented  steel  clamp,  known  as  the  "Gemco  Column  Clamp"  and  manufactured  by  the 
Gemco  Mfg.  Co.,  Milwaukee,  Wis.,  is  shown  in  Fig.  33.  These  clamps  are  described  by  the 
manufacturers  as  follows: 


Fig.  29.  Fig.  30.  Fig.  31.— New  England  column 

clamp. 


A  Gemco  Square-column  Clamp  is  composed  of  four,  straight,  interchangeable,  steel  bars,  each  2  in.  wide 
by  YiQ  in.  thick.  One  end  of  each  bar  is  provided  with  a  hardened  toothed  locking  dog  pivoted  between  two  plates 
which  are  firmly  riveted  to  the  opposite  sides  of  the  bar.  These  plates  fully  protect  the  locking  dog  from  damage, 
but  sufficient  space  is  allowed  to  permit  the  bars  to  slide  freely  when  the  locking  dog  is  not  engaged. 

The  clamp  is  set  by  pressure  on  the  tightening  lever  which  slides  over  the  free  end  of  the  bars,  as  shown  in 
Fig.  33.  When  the  bars  are  drawn  to  position,  the  locking  dog  is  set  by  pressure  of  the  fingers  or  light  tap  of  a 
hammer  and  it  positively  locks  the  clamp.  Tightening  lever  is  detachable  and  can  be  used  on  any  Gemco  Square- 
column  Clamp. 

A  Gemco  Clamp  can  be  assembled,  tightened  and  set  in  1  min.  It  automatically  squares  a  column  and 
can  be  tightened  from  all  sides  so  as  to  positively  close  all  cracks,  thus  retaining  all  the  valuable  part  of  the  mixture 
which  would  otherwise  flow  out  with  the  water.  Gemco  Clamps  will  square  a  rectangular  pier  or  column  in  the 
same  manner. 

These  clamps  can  be  removed  in  the  same  time  which  it  takes  to  adjust  them.  The  tightening  lever  is 
used  to  partially  relieve  the  strain  when  the  locking  dog  can  be  disengaged  by  the  use  of  a  claw  hammer  and  a 
nail  or  punch  inserted  in  the  hole  at  the  corner  of  the  dog.  After  two  diagonally  opposite  corners  are  loosened  the 
entire  clamp  is  free.  By  working  two  men  on  opposite  sides  of  the  column  and  at  diagonal  corners  of  the  clamps, 
the  work  of  setting  or  wrecking  can  be  completed  in  a  very  short  time. 

When  knocked  down  these  straight,  interchangeable  bars  of  steel  are  easily  transferred  from  floor  to  floor 
Or  building  to  building. 

To  avoid  unnecessary  expense  by  using  large  clamps  on  small  columns  the  Gemco  Square-column  Clamps 
are  manufactured  in  three  stock  sizes.    Special  sizes  made  only  on  specific  order. 


100 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-64a 


Stock  No. 

Column  size, 
inches 

Weight, 
pounds 

24 

291^ 

C-11  

30 

35 

C-12  

36 

C-13,  Tightening  lever 

4-K 

Another  patented  type  of  all-steel  column  clamp  which  requires  no  wood  framing  is  shown 
in  Fig.  34 — manufactured  by  the  K.  &  W.  Clamp  Co.,  Minneapolis,  Minn. 

All  square  or  rectangular-column  forms  should  have  bevel  strips  in  the  corners.  Sharp 
corners  in  concrete  work  should  always  be  avoided,  not  only  because  it  is  difficult  to  tamp 
concrete  so  as  to  obtain  perfect  corners,  but  because  the  edges  are  likely  to  be  chipped  off  when 
the  forms  are  removed  or  while  the  concrete  is  still  green.  The  bevel  strips  are  usually  nailed 
to  two  opposite  panel  units  when  the  forms  are  being  made  up. 


Fig.  32. 


Octagonal  and  round-column  forms  with  wooden  clamps  are  not  susceptible  of  ready 
arrangement  into  units,  and  are  clumsy  and  quite  expensive  to  make.  The  problem  seems  to  be 
solved  in  present-day  practice  by  the  use  of  either  iron  bands  or  chains.  Fig.  35  shows  a 
form  clamp  manufactured  by  the  Sterling  Wheelbarrow  Co.,  Milwaukee,  Wis.,  which  can  be 
used  on  any  type  of  column  form.  The  band-iron  placed  around  the  form  (view  a)  is  passed 
through  the  clamping  head,  and  drawn  tight.  The  manufacturers  describe  the  operation  as 
follows: 

The  operator  grasps  the  band  with  one  hand  and  ratchets  the  lever  several  times.  This  ratcheting  grips 
and  releases  the  band,  drawing  it  perfectly  tight  no  matter  how  kinked  the  band  was  before  being  put  around  the 
form.  When  he  sees  that  the  band  is  tight  enough,  the  operator  presses  the  lever  down  close  to  the  form,  thus 
crimping  the  band  in  such  a  way  that  slippage  is  impossible  (view  b),  and  locks  the  clamp  by  inserting  the  lever  into 


Sec.  2-64a] 


GENERAL  METHODS  OF  CONSTRUCTION 


101 


one  of  the  openings  in  the  locking  device  (view  c).  When  knocking  down  the  form,  it  is  necessary  simply  to  release 
the  lever  from  the  locking  device,  return  the  clamping  head  to  position,  and  pull  the  band  out. 


C 

Fig.  35. — Sterling  form  clamp. 


A  Gemco  Clamp  for  round  columns  (Fig.  36)  is  described  by  the  manufacturers  in  the 
following  manner: 


102 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-64a 


A  Gemco  Round-column  Clamp  is  made  of  a  strip  of  m-in.,  16-gage  band  iron,  one  end  of  which  carries  a 
malleable-iron  casting  which  holds  the  hardened  tooth  locking  dog.  When  in  use  the  free  end  of  the  band  iron  is 
slipped  under  the  locking  dog  and  the  clamp  can  be  quickly  and  easily  drawn  to  and  set  at  any  desired  degree  of 
tension  with  a  tightening  lever.  The  lever  is  detachable  and  can  be  used  on  any  size  of  Gemco  Round-column 
Clamp. 

A  clamp  may  be  struck  or  wrecked  in  less  time  than  required  for  setting,  and  in  this  operation  the  detachable 
lever  is  used  to  relieve  the  strain. 

Gemco  Round  Clamps  are  made  in  two  stock  sizes — for  24-in.  and  36-in.  columns.  Special  sizes  made 
to  order. 


Stock  No. 

Column  size,  inches 

Weight,  pounds 

C-20  

24 

3 

C-21  

36 

2K 

Fig.  36. — Gemco  round-column  clamp.  Fig.  37. — Universal  round-column  clamp. 

Another  patented  clamp  for  circular  columns  is  shown  in  Fig.  37,  manufactured  by  the 
Universal  Form  Clamp  Co.,  Chicago,  111.    These  clamps  are  made  in  one  size  only,  i.e.,  size 


c   C  c  < 


Fig.  38. 


C-1  for  i^-in.  rods,  5  in,  long  overall.  A  tightening  wrench  shown  in  Fig.  60,  page  117,  is 
used  with  this  clamp. 


Sec.  2-646] 


GENERAL  METHODS  OF  CONSTRUCTION 


103 


Wire  and  rod  clamps  described  under  the  heading  "Wall  and  Pier  Forms"  (page  111)  are 
used  to  some  extent  on  forms  for  columns. 


646.  Beam  and  Girder  Forms. — Fig.  38  is  an  isometric  view  of  a  typical  floor. 
Joists  support  the  slab  sheathing  and  are  carried  in  turn  by  ledgers  or  joist  bearers  (see  also 


•  Beam  opening 


Fig.  40. 


Plates  I  and  IV,  pages  112  and  115  respectively).    The  method  of  clamping  the  beam  and 
girder  forms  is  shown  more  in  detail  in  Figs.  39  and  40.    Separate  blocks  are  sometimes  used 
instead  of  a  joist  bearer.    Plate  II,  page  113,  shows  a  method  of 
supporting  slab  forms  by  notching  out  the  beam  cleats  to  receive 
the  joists. 

A  number  of  different  methods  are  employed  to  clamp  beam 
and  girder  forms  and  prevent  them  from  spreading  due  to  the 
pressure  of  wet  concrete.  The  method  referred  to  above  is  per- 
haps the  most  common,  but  bolts  either  above  or  below  the  beam  ^^-3'' 
bottom  are  sometimes  employed.  Clamping  by  means  of  ribbands 
is  well  illustrated  in  Plates  I  to  III  inclusive,  pages  112  to  114. 

Typical  girder-form  construction  is  shown  in  Fig.  40.    Some-  Fig.  41. 

times  the  girder  sides  are  not  erected  complete,  the  portion  between 

the  beams  being  erected  in  separate  sections,  as  shown  in  Plate  I,  page  112.    The  lower  part  of 
the  girder  sides  are  made  of  thick  plank  in  order  to  provide  a  suitable  support  for  the  beams. 
A  common  method  of  bracing  the  outer  side  of  a  wall  beam  is  shown  in  Plate  I.  Another 


104 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-64c 


method  is  by  means  of  a  cantilever  brace.  Methods  shown  in  Fig.  28  and  Plate  II,  page  113, 
should  also  be  noted.  Fig.  41  shows  a  form  of  ordinary  post  or  shore  in  common  use.  Haunch 
design  may  be  seen  in  Plates  I  and  IV,  pages  112  and  115  respectively. 

64c.  Slab  Forms. — Two  types  of  slab  forms  need  to  be  considered  for  ordinary 
construction  where  beams  and  girders  are  employed:  (1)  the  panel  type  (the  only  type  of  form 
construction  so  far  treated) ;  and  (2)  slab  forms  made  up  into  box  shape,  comprising  the  joists 
and  the  sides  of  the  beams  and  girders. 

In  the  usual  type  of  construction,  designated  above  as  type  1,  the  beam  and  girder  forms 
are  either  erected  complete  and  the  posts  set  in  place  after  the  erection,  or  the  beam  and  girder 
bottoms  are  spiked  in  place  to  the  post  caps,  and  the  sides  are  erected  as  separate  units.  After 
this  much  is  accomplished  by  either  method,  the  joists  are  then  put  in  position  and  the  panel 


Fig.  42. 


units  are  placed  on  top  of  them  without  nailing.  Notching  out  of  the  slab  panels  is  usually 
necessary  at  the  columns.  When  the  forms  are  to  be  used  but  once,  the  slab  sheathing  is  not 
made  up  in  advance  into  panels,  but  is  lightly  nailed  to  the  joists  after  they  are  in  place. 

Fig.  42  shows  one  method  of  making  up  slab  forms  into  box  shape — the  form  construction 
being  that  used  at  the  University  of  Wisconsin.  Planks  extend  in  two  directions  supporting 
the  cells.    The  steel  and  continuous  stirrups  are  set  for  demonstration  only. 

A  collapsible  core  box  is  used  by  at  least  one  prominent  builder  (Fig.  43).  A  plank  resting 
on  cleats  on  the  sides  of  the  cores  forms  the  bottom  of  the  beam  mold.  The  main  girders  are 
molded  in  similar  spaces  between  the  ends  of  the  cores  in  one  panel  and  those  in  the  next  panel. 
The  molds  are  made  in  two  equal  parts  with  a  hinged  joint  through  the  longitudinal  center  line 
of  the  upper  surface,  and  are  held  open  by  transverse  struts  between  the  lower  edges.  When 
the  forms  are  to  be  removed,  the  transverse  struts  are  knocked  out  and  the  boxes  are  collapsed. 
The  use  of  these  molds  presupposes  a  standardized  layout. 


Fig.  43. 


Forms  for  flat-slab  floors  are  much  simpler  than  for  the  ordinary  beam-and-girder  construc- 
tion— with  the  exception,  of  course,  of  the  forms  for  the  flaring  column  heads.  Typical  de- 
signs of  forms  for  flat-slab  floors  are  shown  in  Fig.  44  and  Plate  V,  page  116.  Corrugated 
iron  has  been  used  to  a  considerable  extent  for  sheathing  where  the  ceiling  surface  does  not 
need  to  be  absolutely  smooth. 

A  new  and  novel  system  of  form  work  (Fig.  45)  has  been  devised  by  Jesse  E.  Hodges,  of 
Cincinnati,  which  is  applicable  to  both  beam-and-girder  and  to  fiat-slab  constructions. 
Edward  O.  Keator  &  Co.  of  Cincinnati,  Ohio,  are  sole  agents  for  this  system. 

The  slab  forms  consist  of  very  light  metal  sheathing  held  on  a  matting  (usually  wooden 
strips  2  in.  by  2}4  in.  by  4  ft.  6  in.)  which  is  supported  by  stringers  placed  about  4  ft.  on  centers. 


I 

Sec.  2-64c] 


GENERAL  METHODS  OF  CONSTRUCTION 


105 


The  matting  is  formed  by  connecting  the  small  wooden  strips  by  a  light  metal  chain  near  each 
end  so  as  to  allow  an  opening  of  about  2\i  in.  between  the  strips.  The  mats  are  made  of  short 
lengths  so  that  they  can  be  rolled  into  bundles  and  not  be  too  heavy  for  one  or  two  men  to  carry. 
Usually  one  stringer  is  used  halfway  between  beams,  and  ledgers  on  the  beam  sides  hold  the 
ends  of  the  mat.  The  stringers  do  not  have  to  be  changed  in  length  for  different  jobs  as  they 
can  be  used  in  long  lengths  and  lapped. 


Fig.  44. 


The  adjustable  shores  (Fig.  46)  are  made  from  8-ft.  lumber,  with  a  4  by  4-in.  post  and  two 
2  by  4-in.  side  pieces,  and  are  adjustable  from  8  to  14  ft.  This  range  is  sufficient  for  ordinary 
work  but  longer  shores  can,  of  course,  be  built  for  special  work.  In  erecting  one  of  these  shores, 
the  clamps  are  loosened  and  the  4  by  4  drawn  out  to  length  designated  by  a  measured  pole 
in  the  usual  manner.    Clamps  are  then  tightened  and  the  shores  raised.    The  feature  of  this 


Fig.  4o. — Hodges  system  of  foriiiwork. 


type  of  shore  is  a  positive  clamp  which  sets  itself  when  the  cam  is  in  driving  position  and  the 
shore  is  under  load.  This  shore  also  has  a  detachable  head  which  may  be  left  on,  in  setting 
shores  under  a  beam,  or  removed  in  using  the  shores  for  flat-slab  floors.  With  the  head  removed 
the  form  stringers  rest  in  a  fork  made  by  the  two  upper  pieces  of  the  shore,  which  makes  it  un- 
necessary for  a  man  to  climb  up  and  nail  cleats  on  each  side  of  the  joist  after  the  shore  is  in  place 


106 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-64c 


Wedges  are  unnecessary  with  the  Hodges  shore  as  leveHng  the  centering  for  the  floor  may  be 
accompHshed  with  a  kind  of  racket-jack  arrangement  shown  in  Fig.  47.  To  adjust  the  length 
of  shore  a  steel  bar  which  is  notched  to  form  a  rack  is  attached  to  one  face  of  the  4  by  4.    A  fork- 


preferably  S'-O" 


Top  of  4"X4" beveled  to  pass 
through  battens 


Section  "A  A" 
Fig.  46. — Hodges  adjustable  shore. 


ended  lifting  lever  is  then  fitted  over  the  timber,  with  its  fulcrum  bolt  resting  in  one  of  the  slots 
of  the  bar  and  the  ends  of  the  fork  engaging  the  lower  ends  of  the  2  by  4-in.  sticks.    With  the 


Cam 


Section  X-Y 
(Enlarged  } 


Fig.  47. 


cams  loosened,  the  upper  portion  of  the  shore  is  raised  by  bearing  down  on  the  lever  handle, 
and  when  in  proper  position  is  locked  by  the  cams. 

Another  type  of  adjustable  shore  is  shown  in  Fig.  48,  manufactured  by  the  H.  W.  Rocs 


jj  Sec.2-64c]  GENERAL  METHODS  OF  CONSTRUCTION  107 

Co.,  Cincinnati,  Ohio,  and  known  as  the  *'Roos  Self-lock  Adjustable  Shore."  It  is  made  up 
for  average  use  with  a  6-f  t.  piece  of  standard  pipe  and  two  pieces  of  2  by  4's  dressed  side  and  edge, 
8  ft.  long.  Only  the  necessary  castings  are  sold  by  the  company  above  mentioned.  The  opera- 
tion of  the  shore  consists  in  taking  the  extension  member  by  the  two  legs  and  lifting  it  to  the 


Fig.  48. — Roos  self-lock  adjustable  shore.  Fig.  49. — Gemco  adjustable  steel  shoring. 


desired  height.  The  slightest  pressure  on  the  two  legs  of  the  extension  member  toward  the  pipe 
causes  the  yokes  to  grip  and  the  shore  is  ready  for  the  load.  The  greater  the  load  the  greater 
the  grip.  For  finer  adjustment  the  shore  can  be  raised  or  lowered  with  the  jacking  device 
which  can  be  attached  to  any  point  under  the  two  legs  of  the  shore  by  turning  the  handled  screw 


Fig.  50. 


and  the  upper  membar  can  be  set  at  its  final  height  with  the  adjusting  lever.  A  turn  of  the 
thumb-screw  lock  sets  the  yokes  and  prevents  any  possible  release  through  outside  jarring. 
The  jacking  device  is  then  removed  for  adjusting  the  next  shore. 

"Gemco  Adjustable  Steel  Shoring"  is  shown  in  Fig.  49.    The  shores  are  adjustable  in 


108 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-64d 


height  from  9  ft.  to  12  ft.  6  in.  For  adjusting  the  height  or  raising  the  load,  a  detachable  lever 
is  used.    These  shores  are  manufactured  by  the  Gemco  Mfg.  Co.,  Milwaukee,  Wis. 

There  are  many  other  types  of  wooden  floor  forms  but  those  described  above  illustrate  the 
main  features  in  floor-form  design.    For  steel  floor  forms  see  page  135. 


Section  A-B 

Fig.  51. 


64ci!.  Column  Heads. — The  tops  of  column  forms  are  sometimes  made  separate 
from  the  column  forms  proper.  Generally  this  is  done  either  to  avoid  remaking  the  column 
tops  to  fit  varying  sizes  of  beams  and  girders,  or  to  facilitate  the  construction  of  special  form 


centering 


Post" 


/r'emoyable 
\2'i<4'[  blocks 

K 

-'Framed  to  true 
oct:7^on  foJbe  2d'^p/us 
c//ameter  of  co/umn 


y/ood  plank-  centering 


■Jo/st 


^■Purlin 


Fig.  52. 


heads.  Fig.  50  shows  an  assembly  of  column  heads  for  regular  interior  columns  of  the 
Larkin  Go's,  building,  Buffalo,  N.  Y.,  designed  by  the  Aberthaw  Construction  Co.,  the  contrac- 
tors.   These  heads  are  also  shown,  but  not  in  detail,  in  Plate  IV,  page  115. 

The  problem  of  the  column  head  in  flat-slab  construction  has  been  met  practically  from 


Sec.  2-64dJ 


GENERAL  METHODS  OF  CONSTRUCTION 


109 


Fig.  54. — Steel  column  head  to  fit  octagonal  column. 


110 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-64(i 


the  first  by  the  use  of  metal  in  some  form.  The  metal  mold  used  by  the  Aberthaw  Construc- 
tion Co.  in  the  Massachusetts  Cotton  Mills  at  Lowell,  Mass.,  is  shown  in  Fig.  51.  Note  that 
the  head  is  very  simple,  a  square  where  it  leaves  the  column,  with  flaring  beveled  corners,  which 
finally  form  an  octagon  at  the  ceiling  level. 

Fig.  52  shows  a  type  of  column-head  form  used  in  constructing  the  Larkin  warehouse  at 
Chicago,  111.    It  is  one  of  the  standard  types  of  flaring  column  caps  manufactured  by  the  Des- 


^y- Apron  Strip 


!  <-Dia.Coh> 


ijnih. 


■I2"R. 


Top  Diameter  —X-Head 

''^  \^*30peninQ-Y  extension 
Column 


rClamp 


extension 


Plan  of  Forming  of 
24-inch  Column 


Upper  unit-'--'' 

Plan  of  Joint  Where 
Units  Telescope 


Section  of  Complete 
Column  Form 


Standard  iS'Head 


Wedffe--- 

Fia.  55. — Adjustable  steel  column  heads.  Hydraulic  Pressed  Steel  Co. 


lauriers  Column  Mold  Co.,  St.  Paul,  Minn.  The  columns  themselves  were  molded  by  steel 
forms  and  these  forms  were  placed  after  the  erection  of  the  upper  floor  falsework.  The  column- 
cap  section  was  suspended  from  the  floor  forms  and  the  remaining  column  sections  bolted  to  it. 

Figs.  53  and  54  show  adjustable  column  heads  as  manufactured  by  the  Blaw  Steel  Construc- 
tion Co.;  conical  and  octagonal  heads  only  are  illustrated  here,  but  this  company  also  makes 
rectangular  head  molds  and  molds  which  spread  from  a  rectangular  section  at  the  column  to  an 


Sec.  2-646] 


GENERAL  METHODS  OF  CONSTRUCTION 


111 


octagonal  shape  at  the  floor  slab.  The  conical  head  is  in  two  parts;  the  top  portion  remains  the 
same  for  all  columns  while  the  bottom  is  fitted  to  columns  of  various  diameters.  The  octagonal 
mold  is  also  adjustable  at  the  lower  end  and  may  be  used  in  connection  with  either  octagonal 
and  circular  steel  column  forms  or  with  wooden  octagonal  forms.  The  Hydraulic  Pressed  Steel 
Co.,  Cleveland,  Ohio,  manufacture  round  steel  column  forms  with  both  standard  and  adjust- 
able column  heads  (see  Figs.  55  and  56). 


Sheef"  mefal  decking  for  depressed  pane! 


Cover  opening  with-' 
quari-er  strip 

^'Fa/se  yyork  block  nailed 
fo  framing  for  support 
of  head  form. 

Frame  fo gi/e  from  lj'fo2" 
clearance  for  actual  diameter 
of  head 


•Bo/t  together 


Fig.  56. — Method  of  forming  depressed  panels. 


64e.  Wall  and  Pier  Forms. — Forms  for  bridge  piers  and  for  walls  of  appreciable 
height  are  usually  constructed  of  either  1-in.  or  2-in.  plank  nailed  to  studs  and  held  by  horizontal 
waling  pieces,  with  tie  bolts  extending  across  the  pier  or  wall  between  opposite  wales.  The 
wales,  which  often  consist  of  two  planks  fastened  together  but  separated  by  spacing  blocks, 
are  set  edgewise  against  the  form  studs  and  the  tie  bolts  are  carried  through  the  openings  which 
occur  in  the  waling  pieces.  Wire  is  sometimes  used  for  bracing  and  is  tightened  either  by  wedges 
or  by  twisting.  The  wire  pulls  against  spreaders  which  are  inserted  between  forms  and  which 
are  removed  as-  the  concrete  level  rises. 

Where  bolts  are  employed  in  pier  and  wall  construction,  a  number  of  different  methods  are 
used  for  withdrawing  the  bolts.  One  method  is  to  cover  each  bolt  with  old  pipe  cut  somewhat 
shorter  than  the  inside  dimensions  of  the  forms,  and  to  place  a  wood  washer  at  each  end  of  the 
pipe.  When  the  forms  are  taken  down,  the  bolts  are  easily  drawn  out  of  the  pipes,  the  wood 
washers  are  then  cut  out  of  the  face  of  the  concrete,  and  the  holes  pointed  up.  Another  method 
is. to  make  the  bolts  in  three  pieces,  with  the  middle  piece  occupying  the  same  position  between 
the  forms  as  the  pipe  above  described.  This  middle  section  is  connected  with  the  end  pieces  by 
means  of  ordinary  unions.  When  the  concrete  has  set  sufficiently,  one  turn  releases  the  end 
sections  and  the  holes  left  in  the  work  are  plugged  with  mortar.  Still  another  method  is  to  use 
a  patented  casting  with  set  screw,  also  a  tightening  wrench  and  rod  puller.  The  tightening 
wrench  is  a  device  for  the  purpose  of  exerting  a  pressure  against  the  form  to  draw  it  in  line  or  to 
desired  dimensions.  The  rod  puller  is  for  removing  or  pulling  the  tie  rods  from  the  concrete 
after  the  concrete  has  set  sufficiently  to  stand  alone. 

The  second  method  described  is  shown  in  Figs.  57,  58  and  59.  (In  Fig.  59  wire  is  used  in- 
stead of  the  middle  piece  of  bolt.)  The  bar  couplings  shown  in  Fig.  57  are  manufactured  by  the 
Marion  Malleable  Iron  Works,  Marion,  Ind.,  and  are  stocked  in  seven  sizes  threaded  to  take 
bolts  H,  H,  1,  IH,  and  l}i  in.    "Universal  Cone  Nuts,"  shown  in  Fig.  58,  are  manu- 


8 


114 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-64e 


;ec.2-64el  GENERAL  METHODS  OF  CONSTRUCTION  115 


Plate  IV. 


Section  B-S 

Assembly  of  forms,  Larkin  Co.'s  building,  Buffalo,  N.  Y. 


116 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-64c 


Sec.  2-64e] 


GENERAL  METHODS  OF  CONSTRUCTION 


117 


t/se  of  ty/re  form  tightener 


One  face  of  all  to  be  finished  Both  faces  of  wall  to  be  finished 

Fig.  61. 


Fig.  64. — Typical  pier  forms  used  in  bridges  of  Luten  design. 


Sec.  2-64e] 


GENERAL  METHODS  OF  CONSTRUCTION 


119 


factured  by  the  Universal  Form  Clamp  Co.,  Chicago,  111.  Cut  shows  washers  used  with  cones 
and  countersunk  into  forms,  but  this  is  not  necessary.  Universal  rod  clamps  (Fig.  60)  can  be 
used  on  the  outside  of  forms  in  place  of  nuts  and  washers.  The  device  shown  in  Fig.  59,  known 
as  "Tyscru,"  is  being  marketed  by  the  Unit- Wall  Construction  Co.,  New  York  City. 

A  patented  casting,  rod  tightener,  and  rod  puller  such  as  used  in  the  third  method  above 
described  are  shown  in  Fig.  60.  These  devices  are  manufactured  by  the  Universal  Form  Clamp 
Co.,  Chicago,  111.  The  rod  clamps  are  made  in  six  sizes,  namely:  No.  1  for  3'^-in.  and  ^ie-in. 
rods;  No.  2  for  ^^-in.  rods;  No.  3  for  }^-in.  rods;  No.  4  and  No.  4  extra  heavy  for  ^^-in.  rods;  and 

;  No.  5  for  ^^-in.  rods.    The  No.  4  is  recommended  for  column  clamping  and  No.  4  extra  heavy 

ijifor  large  retaining  walls. 

Patented  wire  form  clamps  are  illustrated  in  Figs.  61,  62  and  63.  The  wire  form  tightener, 
shown  in  Fig.  61,  is  manufactured  by  the  Marion  Malleable  Iron  Works,  Marion,  Ind.,  and  is 
made  in  three  sizes,  threaded  to  take  ^i,  and  1-in.  bolts.  The  tightener  is  simply  attached 
to  a  wire  slipped  through  from  one  side  of  the  forms  and  a  bolt  is  screwed  into  it  from  the  face 

d4'^-l8'^  Jon^ivfaslen 


Fig.  05. 


side.  By  turning  this  bolt  any  degree  of  tension  may  be  obtained  in  the  wire.  The  "  Universal 
Wire  Clamp"  is  illustrated  in  Fig.  62.  The  clamp  is  placed  against  wales  or  studding  and  wires 
bent  as  shown  in  (a).  The  clamp  should  be  placed  in  a  position  so  as  to  allow  the  wires  to  enter 
the  slots  at  nearly  right  angles.  For  locking  all  that  is  necessary  is  to  pull  handle  down  so  that 
it  takes  a  position  as  shown  in  (6)  and  (c).  The  ''American  Wire  Clamp"  is  shown  in  Fig.  63 
and  is  similar  in  operation  to  the  clamp  just  mentioned.. 

Where  especially  good  work  is  desired,  forms  are  lined  with  galvanized  iron.  For  high 
piers  or  walls,  the  forms  are  constructed  in  large  panels.  After  the  concrete  has  been 
constructed  to  a  proper  height  and  the  last  course  has  set  several  days,  the  panels  are  discon- 
nected and  hoisted  to  a  higher  position  and  then  reassembled  for  concreting,  and  so  on. 

When  the  ends  of  bridge  piers  are  rounding,  special  forms  are  necessary.  In  the  construc- 
tion of  the  Atherton  Ave.  bridge  over  the  Pennsylvania  R.  R.  tracks  in  Pittsburg,  the  forms 
for  the  curved  ends  of  the  piers  were  built  of  1-in.  by  2-in.  strips  nailed  to  horizontal  segmental 
wales.  These  wales  were  nailed  to  the  wales  of  the  side  forms.  The  rounding  forms  were  kept 
in  place  by  wiring  to  dowels  set  in  the  foundation  concrete.  Before  starting  the  erection  of  the 
form  work,  a  flexible  panel  was  made  by  nailing  galvanized-iron  sheets  to  the  1-in.  by  2-in.  strips. 
This  panel  was  bent  against  the  wales,  which  acted  like  hoops.  Curved  pier  forms  used  in 
bridges  of  Luten  design  is  shown  in  Fig.  64. 


120 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-65 


Fig.  65  illustrates  a  simple  method  employed  by  the  Aberthaw  Construction  Co.  for  build- 
ing a  wall  of  considerable  height  by  means  of  movable  forms.  A  simple  method  is  also  shown 
in  Fig.  66. 

Wall  forms  of  small  height  may  be  braced  by  battered  posts  outside.  Fig.  67  shows  forms 
for  a  concrete  foundation  wall  for  small  buildings  where  no  cellar  is  necessary.    Such  forms  may 


Fig.  66.  Fig.  67. 


either  be  constructed  in  sections  or  built  in  place.  It  should  be  noted  that  the  forms  are  sus- 
pended over  the  trench  and  are  not  allowed  to  rest  upon  the  new  concrete.  Figs.  68  and  69 
show  other  methods  of  form  construction  for  low  walls.  No  outside  form  is  needed  in  the 
lower  part  of  such  walls  as  shown  in  Fig.  68  when  the  earth  is  extremely  hard  and  firm. 

Fig.  70  shows  a  common  type  of  form  design  for  curtain  walls  below  windows.  Curtain 
walls  for  complete  wall  panels  are  of  similar  construction. 


Fig.  68.  Fig.  69. 


66.  Design  of  Forms. — Although  form  design  in  most  cases  has  been  left  entirely  to  the 
discretion  of  the  superintendent  or  foreman  on  the  job,  it  has  been  found  by  a  number  of  en- 
gineering contractors  that  it  pays  on  large  or  important  work  to  have  the  forms  designed  in  the 
drafting  room,  provided  such  designing  work  is  done  under  the  direction  of  a  man  of  practical 
ability.  This  plan  is  not  only  more  economical,  but  also  eliminates  the  possibility  of  an  error 
being  made  in  the  proper  size  and  spacing  of  form  members. 


Sec.  2-65o] 


GENERAL  METHODS  OF  CONSTRUCTION 


121 


Many  details  of  form  design  depend  almost  entirely  upon  judgment  and  experience;  but 
the  size  and  spacing  of  supports  for  sheathing  in  slab,  column,  and  wall  forms  and  the  spacing 
of  posts  for  slabs,  beams,  and  girders  are  capable  of  being  determined  by  scientific  calculation 
and  such  practice  results  in  the  use  of  a  minimum  quantity  of  lumber  consistent  with  the  deflec- 


Forms  -for  Sill 
fldte  cast  after  Curfcrfn  Wall ) 


Elevation 


tion  allowed.  In  no  case  should  the  spacing  of  the  supports  be  greater  than  a  safe  span  for 
the  sheathing.  Deflection  should  always  be  considered  in  order  to  give  sufficient  stiffness  and 
thus  prevent  partial  rupture  of  the  concrete. 

65a.  Values  to  Use  in  Design. — In  calculating  floor  forms,  we  must  add  to  the 
weight  of  the  concrete  itself,  a  live  load  which 
may  be  assumed  as  liable  to  come  upon  the 
concrete  while  it  is  setting.  This  live  load  is 
usually  taken  at  75  lb.  per  sq.  ft.  except  in 
cases  where  the  floor  is  made  a  storage  for 
cement  or  sand. 

The  pressure  of  concrete  against  forms 
depends  principally  upon  the  rate  of  filling 
and  the  temperature.  The  accompanying 
table^  is  from  tests  made  by  Major  Francis 
R.  Shunk,  Corps  of  Engineers,  U.  S.  A. 

Tests  on  the  pressure  of  wet  concrete 

iFrom  Eng.  Rec,  Jan.  15,  1910. 


Rate  of  filling 
(vertical 
feet  per 
hour) 

Temperature 

80° 

70° 

60° 

50° 

40° 

2 

530 

560 

600 

680 

790 

3 

690 

720 

810 

920 

1,080 

4 

820 

870 

980 

1,130 

1,340 

5 

930 

990 

1,120 

1,310 

1,570 

6 

1,020 

1,090 

1,250 

1,480 

1,780 

7 

1,090 

1,170 

1,350 

1,620 

1,970 

8 

1,130 

1,240 

1,440 

1,740| 

122 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-65a 


poured  rapidly  have  been  made  under  average  conditions  by  the  Aberthaw  Construction  Co., 
Boston,  Mass.  The  following  table^  gives  the  results  observed  in  the  pouring  of  two  columns 
of  small  cross-sectional  area.  It  should  be  noticed  that  the  wet  concrete  exerted  a  hydrostatic 
pressure  equivalent  to  that  of  a  liquid  weighing  from  140  to  150  lb.  per  cu.  ft.  or  very  nearly 
that  of  a  liquid  having  the  same  weight  as  the  concrete. 


Description  of  concrete 

Head 
(ft.) 

Pressure 
(lb.  per 
sq.  ft.) 

Hydraulic 
equivalent 
(lb,  per  cu. 

ft.) 

Time  of  pouring,  9  min  

3.08 

460 

149 

Mixture,  1: 1^:3  

6.08 

yuu 

148 

Stone,  1-in.  run-of-crusher  

No.  1 

column 

9.08 

1,330 

146 

12.08 

1,710 

142 

Wt.  of  mixture,  152  lb.  per  cu.  ft  j 

15.08 

2,110 

140 

Time  of  pouring,  14  min  

2.75 

407 

148 

5.75 

840 

146 

Mixture,  1:1:1  

No.  2 

8.75 

1,280 

146 

column 

■ 

11.75 

1,700 

145 

14.75 

2,080 

141 

17.75 

2,450 

138 

From  the  results  of  the  tests  just  mentioned  it  would  seem  that  145  lb.  per  sq.  ft.  per  foot 
of  height  is  a  rational  value  to  use  for  the  lateral  pressure  of  concrete  in  the  design  of  forms. 
This  same  value  was  also  arrived  at  from  laboratory  and  field  tests  made  under  the  supervision 
of  Prof.  A.  B.  McDaniel  and  N.  B.  Garver  at  the  University  of  Illinois  in  1913,  1914,  and  1915. 

Opinions  differ  as  to  the  proper  coefficient  to  use  in  the  moment  formula  when  making  com- 
putations for  the  strength  of  floor  sheathing  and  joists.    It  is  probable  that  the  formula 

M  =      may  safely  be  used  in  all  cases  except  for  single-span  joists  where  the  concrete  is  conveyed 

to  place  by  small  dump  cars  on  a  portable  track.  With  dump  cars  the  concentrations  on  a  sin- 
gle-span joist  may  be  so  heavy  that  the  negative  bending  moments  of  the  dead  load  will  be 

relatively  very  small  as  compared  to  the  positive  moments  and  the  formula  M  =  -g-  should 

undoubtedly  be  employed.    When  the  bending  moment  is  figured  as  ikf  =        the  deflection 

3  w"{l")'^ 

should  be  determined  by  the  deflection  formula  D  =        — —  (see  "Notation,"  page  124). 

o84  iLl 

This  formula  is  the  ordinary  one  for  calculating  deflection  except  that  the  coefficient  is  taken  as 
a  mean  between  for  a  beam  with  fixed  ends  and  ^^§4  for  a  beam  with  ends  simply  supported. 
For  lumber  commonly  used  in  form  construction  E  may  be  assumed  at  1,200,000  lb.  per  sq.  in. 

The  fiber  stresses  allowed  in  form  design  may  well  be  higher  than  those  it  would  be  desir- 
able to  use  in  more  permanent  construction.    The  following  values  are  usually  employed: 

Maximum  fiber  stress  in  spruce  or  equal : 

for  timbers   1,200  lb.  per  sq.  in. 

for  column  yokes  ;   1,800  lb.  per  sq.  in. 

Horizontal  shear  for  spruce  or  equal  •    200  lb.  per  sq.  in. 

Crushing  perpendicular  to  grain  in  spruce  or  equal   400  lb.  per  sq.  in. 


1  From  Concrete-Cement  Age,  Oct.,  1913. 


Sec.  2-656] 


GENERAL  METHODS  OF  CONSTRUCTION 


123 


The  crushing  of  form  lumber  perpendicular  to  the  grain  should  not  be  overlooked.  Although 
a  3  by  4-in.  or  4  by  4-in.  post  may  be  braced  at  least  every  6  ft.  in  height  and  have  apparently  an 
allowable  compressive  strength  of  about  800  lb.  per  sq.  in.,  such  a  post  should  not  be  permitted 
to  carry  more  than  one-half  such  a  load  due  to  crushing  of  the  lumber  perpendicular  to  the  grain 
in  the  crosspiece  or  girt  over  the  post.  Especially  is  this  true  where  a  granolithic  finish  is  to  be 
cast  with  the  slab,  as  settlement  would  ruin  the  slab  surface.  Large  hardwood  wedges  should 
be  used  to  prevent  any  settlement  due  to  crushing  under  the  post. 

The  maximum  deflection  which  may  be  allowed  a  form  timber  is  not  definitely  known. 
Some  designers  allow  very  small  deflections  for  joists  and  use  full  live  and  dead  load  in  design- 
ing. Others  reason  that  any  serious  deflection  will  be  caused  only  by  the  dead  weight  of  the 
wet  concrete  and  for  that  reason  allow  comparatively  large  deflections.  Deflections  allowed 
in  practice  vary  from  an  arbitrary  maximum  of  }^  in.  for  all  timbers  to  maximum  deflections 
of  3^6  0  of  the  span. 

656.  Drafting-room  Methods. — The  following  article  is  taken  by  permission 
from  a  paper  presented  at  the  Twelfth  Annual  Convention  of  the  American  Concrete 
Institute  by  E,.  A.  Sherwin,  Resident  Engineer,  Aberthaw  Construction  Co.: 

The  first  study  and  drawings  to  be  made  form  a  general  assembly.    Usually  several  different  combinations  of 
timbers  and  methods  of  assembling  the  panels  are  sketched  up  and  compared  as  to  cost.    Other  things  being 
equal,  of  course,  the  cheapest  design  is  adopted.    A  record  of  costs  of  the  various  units  which  go  to  make  up  the 
complete  centering  scheme  is  therefore  necessary. 
Points  to  be  remembered  in  this  study  are: 

1.  Joists  and  girts  should  be  in  as  few  lengths  as  possible  to  save  time  in  sorting  on  the  job. 

2.  Use  stock  sizes  and  lengths  of  lumber. 

3.  Keep  number  of  panels  and  pieces  to  a  minimum. 

4.  Provide  easy  stripping. 

5.  Allow  clearance  enough  for  slight  inaccuracies  in  making  up  and  erecting,  swelling  of  panels,  etc. 

6.  Panels  should  be  a  whole  number  of  boards  in  width,  if  possible,  for  ease  in  making  up. 

7.  Units  to  be  as  big  as  can  be  handled  and  joists  used  as  panel  cleats  where  possible. 

8.  Provide  for  re-use  of  panels. 

9.  Beams  to  be  handled  as  trough  units  when  the  job  is  regular  and  units  can  be  re-used. 

10.  Consider  use  of  floor  domes  or  inverted  boxes  when  beams  are  close  together.  In  this  way  beam  sides 
and  slab  are  erected,  stripp^ed  and  moved  as  a  unit.  When  either  of  the  last  two  systems  is  used  the  beam  sides 
should  be  given  a  slope  to  prevent  hard  stripping. 

11.  Provide  for  reshoring  if  necessary. 

12.  Have  bracing  above  the  men's  heads. 

13.  When  four  beam  haunches  occur  at  a  column  consider  making  haunches  as  a  unit  similar  to  a  column 
head  in  flat -slab  construction. 

14.  Consideration  of  steel  forms. 

A  general  assembly  shows  how  the  various  parts  are  to  be  put  together,  supported,  tied,  and  braced  to  resist 
the  concrete  pressure  and  the  weights  coming  upon  the  members.  This  drawing  in  its  final  shape  can  be  made  on 
tracing  cloth  with  soft  pencil.  The  dimension  arrows,  lettering  and  figures  should  be  inked  so  that  clear  prints 
can  be  made  to  avoid  errors  in  the  field.    These  assemblies  should  be  filed  permanently  for  reference  on  future  work. 

When  it  is  necessary  to  strip  the  floor  centering  for  re-use  before  the  concrete  has  been  in  place  long  enough 
to  gain  its  full  strength,  provisions  for  proper  support  of  the  green  slab  must  be  made  in  the  design  of  the  floor  forms. 
The  safest  and  cheapest  method  of  doing  this,  in  the  writer's  opinion,  is  to  place  boards  between  the  floor  panels 
and  wedge  posts  up  to  a  bearing  under  these  boards  before  the  centering  posts  are  knocked  out.  In  this  way  the 
slab  is  never  left  unsupported,  as  is  the  case  when  posts  are  replaced  after  all  the  centering  is  down.  These  boards 
should  be  placed  according  to  a  plan  and  shall  be  located  so  as  to  shorten  the  spans  of  the  main  reinforcing  bands. 

After  the  general  scheme  for  the  forms  has  been  decided  upon  the  detail  panel  drawings  are  prepared.  By 
panel,  in  this  paper,  is  meant  several  boards  cleated  together  into  a  unit  to  be  used  as  a  form  for  some  part  of  a 
concrete  member.  Every  different-sized  panel  is  first  sketched  roughly  on  standard  6  by  9-in.  sketching  pads. 
These  pads  have  holes  punched  at  the  top,  so  that  as  sketches  of  the  different  kinds  of  panels  are  made  they  can  be 
bunched  together  and  brass  rivets  put  through  the  holes.  These  sketches  are  transferred  in  more  detail  onto  thin 
tracing  paper.  The  standard  sheet  is  25  by  33  in.,  divided  by  a  1-in.  space  into  two  halves  of  five  spaces  each. 
These  details  are  used  at  the  job  mill  for  making  up  the  panels.  The  blue-prints  sent  to  the  mill  man  are  cut  up 
into  5  by  6-in.  units,  with  one  detail  on  each,  and  are  given  to  the  carpenters  at  the  making-up  benches.  On  these 
detail  sheets  for  each  panel  there  is  given  the  panel  mark  (which  is  stenciled  onto  the  finished  panel),  the  number 
wanted,  and  the  floor  on  which  they  are  to  be  used.  The  sizes  of  the  stock,  dimensions  and  alterations,  when  panels 
are  to  be  re-used,  should  be  clearly  marked. 


I 


124 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-66 


A  system  of  symbols  as  follows  is  easily  learned  by  the  workmen  and  should  be  kept  standard: 
B,  beam  side;  BB,  beam  bottoms;  F,  floor  slab  panels;  P,  plinth  forms;  H,  haunch  forms;  C,  column  sides; 
W,  wall  panels. 

Thus  518  means  beam  side  number  18,  and  its  location  is  shown  on  the  key  plan. 

These  detail  sheets  can  be  drawn  up  entirely  with  soft  pencil  on  paper,  as  they  are  not  valuable  after  the  forms 
are  once  made.    Rubber  stamps  for  a  great  deal  of  the  lettering  will  save  time. 

Where  time  allows  and  plans  are  complete  it  is  advantageous  to  get  out  one  kind  of  panel  at  a  time.  In  any 
case  the  first  panels  to  be  sent  to  the  making-up  mill  should  be  the  typical  floor  panels.  These  can  be  used  economic- 
ally in  building  foundation  walls,  etc.,  and  in  this  way  the  job  can  get  an  extra  use  out  of  them. 

It  is  impossible  to  get  a  satisfactory  cost  unit  for  doing  this  form  drawing.  A  price  per  square  foot  or  per 
detail  varies  widely  according  to  the  number  of  details  required  and  the  number  of  square  feet  that  can  be  made 
from  one  detail  in  different  buildings.  A  big  building  where  a  large  duplication  of  the  different  kinds  of  units  is 
possible  will  cost  much  less  per  square  foot  for  this  work  than  a  small  building  which  is  badly  cut  up.  The  average 
cost  per  sheet  has  been  found  to  be  about  $4.50  complete.  This  includes  time  spent  on  studies,  assemblies,  key 
plans,  scheduling,  and  checking.  The  number  of  sheets  required  on  buildings  of  different  sizes  of  the  same  type 
is  fairly  uniform  according  to  the  size.  The  number  varies  from  30  sheets  on  a  small  building  up  to  100  or  more  on 
a  large  building  with  irregularities.  By  reducing  the  cost  of  the  sheets  to  drafting-room  hours,  by  dividing  the 
probable  total  cost  by  the  average  rate  per  hour,  a  fairly  close  estimate  of  the  number  of  men  required  to  turn  out  a 
job  in  a  specified  time  can  be  made.    This  is  useful  on  rush  work. 

The  key  plan  mentioned  above  is  really  a  diagram  of  the  floor  plan  upon  which  are  shown  the  locations  of 
the  various  form  panels.  This  plan  is  the  only  one  which  the  workmen  consult  in  erecting  the  formwork.  It 
must,  therefore,  be  complete  and  clear. 

This  plan  can  best  be  made  by  tracing  the  floor  plan  on  cloth  from  a  blue-print,  indicating  the  beams  and  holes 
in  the  floor  and  the  columns  and  walls  in  the  story  below.  The  lines  should  be  heavily  inked  and  the  figures  large 
enough  and  spaced  so  that  the  tracing  can  be  reduced  and  the  photo  reduced  to  convenient  size  for  the  foremen  to 
handle  on  the  job.  A  big  blue-print  is  inconvenient  and  fades  in  the  strong  sunlight.  As  a  rule,  to  avoid  mis- 
understandings, a  key  plan  should  be  prepared  for  each  floor  in  the  building. 

The  key  plan  may  be  supplemented  by  a  letter  to  the  job  in  which  should  be  noted  the  assumptions  made  in 
preparing  the  details.  These  notes  might  include  such  information  as  clearances  allowed,  grades  at  which  forms  are 
to  start,  scheme  for  re-use,  etc. 


66.  Tables  and  Diagrams  for  Designing  Forms. 

66a.  Notation. — The  following  notation  is  used  in  the  tables  and  diagrams: 
b  =  breadth  of  member  in  inches. 
d  =  depth  of  member  in  inches. 

I  =  span  of  member  in  feet.  " 


I" 

=  span  of  member  in  inches. 

w 

=  uniform  load  per  linear  foot. 

w" 

=  uniform  load  per  linear  inch. 

w' 

=  total  load  on  floor  in  pounds  per  square  foot  =  dead  weight  of  slab  per  square  foot 

plus  75  lb.  per  sq.  ft.  live  load. 

h 

=  head  in  feet. 

D 

=  deflection  in  inches. 

E 

=  modulus  of  elasticity  in  pounds  per  square  inch. 

I 

=  moment  of  inertia  in  inches*. 

f 

=  maximum  fiber  stress  in  pounds  per  square  inch 

M 

=  bending  moment  in  foot-pounds. 

Mr 

s 

=  resisting  moment  in  inch-pounds. 
=  spacing  in  inches. 

n 

=  number  of  spaces. 

n' 

=  number  of  spaces  between  column  yokes. 

k 

=  largest  dimension  of  column  in  inches. 

P 

=  concentrated  load  in  pounds. 

V 

=  total  maximum  vertical  shear  in  pounds. 

2\bdl 

V 

=  maximum  unit  horizontal  shear  (pounds  per  square  inch) 

666.  Fiber  Stresses  Allowed. — The  fiber  stresses  allowed  are  those  given  in 

Art.  65a. 


Sec.  2-66c]  GENERAL  METHODS  OF  CONSTRUCTION  125 

66c.  Formulas  Used. — The  spacing  of  joists  was  determined  in  Table  I  by  the 


formulas : 

For  flexure 


For  deflection 


For  horizontal  shear 


2000^2 


D  =  0.0225 

a 

When  D  =  l-g  in. 

When  D  =  3^4  in. 

1" 


When  D  = 


360 


VsOOd 
12 

VlWOd 
12 


40 
27' 


(Depths  for  joists  are  taken  li  in.  less  than  nominal  sizes.) 


In  Table  II,  Part  A: 
For  flexure 


2000 


In  Table  II,  Part  B : 
For  flexure 

»  =  1600^, 


For  D  =  }yi  in. 

s  =  11,100^, 

For  horizontal  shear 
bd 


For  D  = 


r 

360 


s  =  1780 


bd^ 


3200 


For  horizontal  shear 
bd 


3200 


w'l 


Table  III: 

Deflection  of      in.  governs. 


590,000(145)d^ 


In  Table  IV  the  concentrated  loads  from  the  joists  were  considered  on  a  simple  span  in 
calculating  the  bending  moment.  The  worst  case  was  assumed — that  is,  when  one  joist  comes 
it  mid-span.  Since  a  girt  is  usually  continuous  for  at  least  two  spans  and  the  full  live  load  never 
^caches  it,  the  moment  of  resistance  of  the  timbers  was  multiplied  by  1.2.  Nominal  sizes  of  the 
jirts  were  used  in  the  computations. 

For  flexure 

2406^2  +  |-P(n2  +  2n) 


3P(n  +  1) 





Horizontal  shear  is  to  be  considered  separately.  From  the  above  considerations  it  would  seem 
that  an  allowable  horizontal  shear  of  (200) (1.2)  =  240  lb.  per  sq.  in.  may  safely  be  u.sed. 


126 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-66C 


Diagram  I: 
For  flexure 


For  deflection 


Diagram  II: 
For  flexure 


336,000d2 


145/1 


l,590,000d= 


2380, 


For  deflection  {D  = 


I" 


'h{i"y 


95,400d 


•238 

When  d  =  2  in.  When     =  4  in.  When     =  6  in. 

I"  =  28.3  in.  I"  =  40.0  in.  V  =  49.0  in. 

These  results  are  based  on  a  value  of  /c  =      and  the  values  given  may  at  least 
be  increased  to  30,  42,  and  50  respectively. 
For  shear  (y  =  200  lb.  per  sq.  in.) 

I"  =9d  -  {I"  -  k) 


Table  V: 


19,060 


h  =  Y'  A/l9,060n' 


Formulas  to  use  with  table: 


^.  ,  ,„.095?)d2 

Diameter  of  bolt 


\2l" 


Net  area  of  washer 


21"  -  k 


Illustrative  Problems. — 1.  Required  the  proper  spacing  of  2  by  8-in.  joists  having  a  span  of  7.5  ft.  to 
support  forms  for  a  5-in.  slab  in  beam-and-girder  construction,  assuming  1-in.  sheathing. 

Table  I  shows  that  2  by  8-in.  joists  spaced  31  in.  on  centers  will  give  sufficient  strength  if  the  bending  moment 

is  assumed  equal  to  j^-    For  this  spacing  the  table  indicates  that  the  deflection  is  somewhat  over  }^in.  but  less 

(7.5)2 

than  M  in.  and  much  less  than  Heo  span.    Accurately,  D  =  0.0225 -i^-y^  =  0.16  in.    From  Table  III  we  find  that 

the  spacing  cannot  be  greater  than  30  in.  without  the  deflection  of  the  sheathing  exceeding  H  in.,  which  is  not 
advisable. 

wZ2  (7  5)  2 

For  M  =  -g-,  the  spacing  would  be  (0.8)  (31)  =  25  in.  from  Table  I  and  the  deflection  D  =  0.030  -fJJ  ^ 

0.22  in.    From  Table  II,  the  spacing  would  be  22  +  H(8)  =  24.7  in. 

For  M  =  —  and  the  deflection  limited  to  H  in.,  Table  II  shows  the  proper  spacing  to  be  21  +  H(8)  =  23.7  m. 

2.  Assume  joists  in  the  preceding  problem  to  be  supported  midway  between  beams.    Determine  their 

economical  size  and  proper  spacing,  assuming  M  =  Jq"  and  deflection  limited  to  H  in. 

It  will  be  sufficiently  accurate  to  assume  the  span  as  4  ft.  From  either' Table  I  or  II,  we  find  that  2  by  4-in. 
joists  may  be  employed  spaced  25  in.  on  centers. 

3.  Determine  size  and  span  length  of  girt  in  the  preceding  problem  to  support  the  joists  midway  between 
beams. 

Load  coming  from  each  joist  is  (3.75)  {^^12)  (137.5)  =  1075,  or  say  1000  lb.,  accurately  enough.  From  Table 
IV  we  find  that  a  3  by  4-in.  girt  with  posts  spaced  3.8  ft.  c.  to  c.  could  be  used,  or  a  3  by  6-in.  girt  with  posts  5.6 
ft.  c.  to  c,  or  a  4  by  6-in.  girt  with  posts  6.6  ft.  c.  to  c. 

Horizontal  shear  must  be  considered  separately  considering  a  joist  to  occur  close  to  one  support.  Assuming 

2260  '  ' '  ' 

a  4  by  ^-in.  girt  with  posts  6.6  ft.  on  centers,  V=  2260  lb.  and  v  =  ^*^4y(gy  ="  142  lb.  per  sq.  in.,  which  is  less  than 
the  allowable  value. 


GENERAL  METHODS  OF  CONSTRUCTION 


127 


128 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-66c 


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Sec.  2-66c] 


GENERAL  METHODS  OF  CONSTRUCTION 


129 


A  3  by  4-in.  post  could  sustain  (3)  (4)  (400)  =  4800  lb.  without  injuring  the  fibers  of  the  girt.  It  would  only 
be  required  to  support  3450  lb.,  consequently  this  size  of  post  is  suitable. 

4.  Assuming  the  cross-section  of  beam  below  slab  as  14  by  18  in.  (23  in.  total  depth)  determine  the  safe  span 
for  the  beam  bottom  to  be  made  of  2-in.  plank. 

Live  plus  dead  load  on  beam  bottom  is  75  +  2)'i2(150)  =  3625  lb.  per  sq.  ft.  Diagram  I  shows  the  maximum 
span  to  be  43  in. 

5.  Find  the  proper  spacing  of  3  by  4-in.  posts  to  support  the  forms  for  8  by  16-in.  beams  (cross-section  given 
below  slab)  spaced  6  ft.  on  centers  with  a  4-in.  floor  slab.    Assume  that  no  girt  is  placed  at  midspan  of  joists. 

Total  load  on  beam  per  linear  foot  is  (125)  (G)  +  =  883  lb.  not  considering  the  weight  of 

the  forms,  which  may  be  neglected. 
4800 

of  posts  =  -ggg-  =  5.4  ft. 

6.  Determine  the  size  and  spacing  of  joists,  girts,  and  posts  to  support  an  11-in.  flat  slab  floor. 
Assuming  1-in.  sheathing  we  find  from  Table  III  that  the  joists  cannot  be  placed  more  than  27  in.  on  centers. 

Table  I  shows  that  for  2  by  8-in.  joists  the  spacing  of  girts  may  be  made  6.5  ft.  The  load  coming  from  each  joist 
is  (6.5)  (2JI2)  (212.5)  =  3110  lb.,  or  accurately  enough  3000  lb.    From  Table  IV  we  find  that  for  4  by  6-in.  girts  the 

posts  may  be  placed  3.8  ft.  on  centers.    Horizontal  shear  on  girts  must  be  considered  separately,    v  =  ^2.  't^tt^n  =  273 


144 

Safe  bearing  of  post  on  fibers  of  cap  =  (3)  (4)  (400)  =  4800  lb.    Safe  spacing 


lb.  which  is  somewhat  greater  than  the  allowable  value  and  a  6-ft.  spacing  of  the  girts  is  necessary. 

Table  III. — Safe  Span  for  Floor  Sheathing 

(inches) 

Based  on  M  =  —  with  deflection  limited  to  H  in. 
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(4)  (6) 


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7.  What  spacing  of  vertical  studs  is  required  for  a  wall  form  with  l^-in.  sheathing  and  a  height  of  12  ft. 
Diagram  I  shows  the  spacing  to  be  18  in. 

8.  Assuming  a  24  by  24-in.  column  with  I"  =  37  in.,  determine  the  spacing  of  the  column  yokes. 
For  2  by  4-in.  yokes  placed  on  edge,  the  value  of  I"  to  be  used  in  Table  V  should  be 


(37)  (1.23^ 


(2)  (37)  (24)  -  (24)2 


372 


42.5  in.,  say  42  in. 


For  4  by  4-in.  yokes,  the  value  of  1"  to  be  used  should  be  (37)  (0.87)  (0.935)  =  30  in. 

For  shear  the  actual  value  of  I"  must  not  be  taken  less  than  9c?  -  (Z"  -  k)  =  (9)  (4)  -  (37  -  24)  =  23  in. 
for  either  the  2  by  4-in.  or  the  4  by  4-in.  yokes.    Evidently  the  shear  in  the  yokes  will  be  less  than  the  allowable. 

Other  things  being  equal.  Diagram  II  shows  that  1-in.  sheathing  would  be  more  economical  than  VA-in. 
when  2  by  4-in.  yokes  are  used.    The  table  shows  that  the  same  number  of  yokes  would  be  used  in  the  two  cases. 

The  spacing  center  to  center  for  the  2  by  4-in.  yokes  for  a  10-ft.  column  with  1-in.  sheathing  would  be  as  follows 
in  inches  starting  at  the  top:  30-20-14-11-10-9-8-7. 


.095M2 


vail 


Where  the  strength  of  yokes  governs  their  spacing,  the  bolts  must  have  a  diameter  of 

.^(0.095)  (2)  (16) 


ues  of  k  and  I' 


The  net  area  of  washer  should  be 


Thus  for  the  2  by  4-in.  yokes,  diameter  of  the  bolts  must  be  at  least 
3bd^         (3)  (2)  (16) 


50 


using  actual 


0.25  in. 


21"  -  k 

9.  Assuming  a  12  by  12-in.  column  with  I' 


50 


1.92  sq.  in. 


22  in.,  determine  the  spacing  of  2  by  4-in.  yokes  placed  on 


edge. 


The  limiting  value  of  I"  for  shear  on  yoke  is  (9)  (4)  -  (10)  =  26  in.    Thus  actual  values  oil"  and  k  must 
be  considered  as  26  in.  and  (26  -  10)  =  16  in.  respectively,  which  gives  a  value  of  I"  to  be  used  xn  Table  V  of 
1(2)  (26)  (16)  -  (16)2^/12 
(26)2  \l6 


(26)  (1.23) 


25.6  in.,  say  26  in. 


130 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-6Gc 


1             Load  coming  from  each  Joisf  In  pounds  j 

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Sec.  2-G7] 


GENERAL  METHODS  OF  CONSTRUCTION 


67.  Systematizing  Formwork  on  Buildings.^ 

67a.  Sawmill  and  Yard. — The  sawmill  should  be  located  after  a  study  of  the  job  site  in  a  position 
where  there  is  plenty  of  space  for  piling  the  stock  and  finished  panels.  The  sawmill  shed  and  equipment  should  be 
standard  so  that  it  can  be  erected  and  put  in  operation  as  soon  as  possible  in  order  to  reduce  hand-sawing  to  the 
minimum.  A  sawmill  at  its  best  is  dangerous.  For  this  reason  every  precaution  should  be  taken  to  protect  the 
workmen  by  efficient  saw,  machine,  and  belt  guards.  The  mill  should  be  near  the  builcling  so  as  to  reduce  the  cost 
of  moving  panels.    This  moving  cost  is  an  important  item  in  obtaining  low  erection  costs  and  will  amount  to  a 

Diagram  I 

Spacing  of  Vertical  and  Horizontal  Studs  (or  Column  Yokes)  at  Any  Given  Depth 

Below  Surface  of  Concrete 

(Based  on  strength  and  deflection  of  sheathing) 

If  - 

—  2Q  Deflection  limited  to  in. 


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10          15          20          25         30         35         40         45  50 

3  "  Spac/ngr  In  inches 


considerable  item  when  the  mill  is  poorly  located,  either  from  lack  of  planning  or  from  lack  of  space  for  the  plant 
around  the  building. 

The  mill  yard  should  be  so  arranged  that  the  stock  will  go  in  one  direction  from  the  lumber  piles  to  the  saws, 
to  the  making-up  benches  and  to  the  finished  panel  piles,  which  should  be  nearest  the  building. 

The  lumber  when  received  is  checked  as  to  quality  and  quantity.  The  stock  is  then  sorted  and  piled  accord- 
ing to  size  and  length,  each  pile  having  its  size  plainly  marked. 

It  is  then  an  easy  matter  for  the  millman  to  make  a  lumber  ledger  of  all  the  stock  in  his  yard.  Thus  at  all 
times  it  is  possible  to  know  the  stock  available,  for  as  the  lumber  is  used  deductions  can  be  made  and  the  running 
total  kept  up  to  date. 

676.  Shop  Procedure. — The  millman  divides  the  panel  details  into  boards  to  make  the  required 
width  of  the  panel.    The  number  of  b6ards  of  each  kind  needed  to  make  the  .number  of  panels  wanted  are  ordered 
moved  to  the  saw  to  be  cut  to  proper  length  and  thence  to  the  make-up  bench,  where  cleats  of  the  proper  size  and 
^  By  R.  A.  Sherwin,  Resident  Engineer,  Aberthaw  Construction  Co.    IVom  paper  presented  at  the  Twelfth 
Annual  Convention,  American  Concrete  Institute. 


132 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-676 


Diagram  II 

Spacing  of  Column  Yokes  or  Horizontal  Studs  at  Any  Given  Depth  Below  Surface 

OF  Concrete 

(Based  on  strength  and  deflection  of  the  yokes  or  studs) 


Based  on  M  = 


Deflection  less  than  3^  in. 


/O         15         ^0         25        30        35        40  45 
s  =  3pac/n^  of  column  yokes  or  horizontal  studs  in  inclnes 

Directions  for  Using  Diagram  II  and  Table  V 
For  2X4-in.  yokes  or  studs  (flat)  multiply  actual  I"  by  1 .73  before  using  diagram  or  table. 
For  2X4-in.  yokes  or  studs  (on  edge)  multiply  actual  I"  by  1 .23  before  using  diagram  or  table.  • 
For  3X4-in.  yokes  or  studs  (on  edge)  multiply  actual  I"  by  1 .00  before  using  diagram  or  table. 
For  4X4-in.  yokes  or  studs  (on  edge)  multiply  actual  I"  by  0.87  before  using  diagram  or  table. 
For  3X6-in.  yokes  or  studs  (on  edge)  multiply  actual  I"  by  0.67  before  using  diagram  or  table. 
For  4X6-in.  yokes  or  studs  (on  edge)  multiply  actual  I"  by  0.58  before  using  diagram  or  table. 
For  6X6-in.  yokes  or  studs  (on  edge)  multiply  actual  I"  by  0.47  before  using  diagram  or  table. 


50 


For  6X<i-in  yokes  or  studs  (on  edge)  multiply  actual  I"  by 


before  using  diagram  or  table. 


For  columns  the  value  of  I"  to  be  used  in  diagram  or  table  should  be  the  value  of  I"  as  found  above  multiplied 


'h  -  ^2 


,  in  which  expression  the  actual  values  of  I"  and  h  are  to  be  substituted. 


3  X  4-in.  aiid  4  X  4-in.  yokes,  actual 

3  X  6-in.,  4  X  6-m.,  and  6X6-m.  j  ^ 


In  determining  spacings  from  the  diagram  or  table  for 

values  of  I"  greater  than  |5o'o}  ^"^^         ^^^^  ^  deflection  of  yokes  greater  than  >8  in.,  and  actual  values  of  I" 

greater  than  |  72  0  }       ^  ^"^^  S^^®  ^  deflection  greater  than  3^4  in. 

In  determining  spacings  from  the  diagram  or  table,  actual  values  of  I"  must  not  be  considered  as  less  than  deter- 
mined by  the  formula 

1"  =  9d-{l"  -  k) 

otherwise  horizontal  shear  will  be  greater  than  200  lb.  per  sq.  in.  The  corresponding  actual  value  of  k  (which  will 
be  called  k')  should  be  determined  by  subtracting  the  value  of  a  (see  sketch""  from  the  value  of  I"  found  by  the  above 
formula.    The  value  of     to  use  in  diagram  or  table  should  then  be  found  as  explained  above  and  finally  multiplied 


Sec.  2-676] 


GENERAL  METHODS  OF  CONSTRUCTION 


133 


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134 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-67c 


length  are  already  waiting,  having  been  previously  ordered  through  the  mill.  Another  order  to  the  bench  car- 
penters, which  is  clipped  to  the  blue-print  sketch  of  the  panel,  enables  them  to  cleat  together  the  boards  into  the 
finished  panel.  The  panel  is  then  taken  away  by  a  laborer,  stenciled  with  its  location  mark,  oiled  and  piled  until 
ready  for  use  in  the  building. 

All  this  is  done  by  orders  written  on  standard  order  forms  of  three  kinds,  one  for  moving  the  stock,  another 
for  sawing,  and  the  last  for  making  up.  Duplicates  of  the  orders  are  placed  on  the  millman's  progress  board  so 
that  he  knows  at  all  times  how  the  work  is  progressing,  for  when  an  order  is  completed  and  returned  to  him  its 
duplicate  is  taken  down.    Each  kind  of  order  is  of  different  color  so  as  to  be  easily  identified. 

There  are  several  points  in  connection  with  making  up  panels  which  may  be  considered  here. 
As  much  assembling  as  possible  should  be  done  at  the  bench.  Rangers  for  wall  beams  can  be  attached  and 
ledgers  to  support  joists  can  be  nailed  to  the  interior  beam  side  cleats  at  the  proper  depth.  When  inserts  need  to 
be  placed  in  the  sides  of  beams,  the  holes  for  the  bolts  which  hold  them  can  be  located  on  the  details  and  the  holes 
bored  at  the  mill.  The  groove  strip  for  steel  sash  and  also  the  corner  fillet  can  be  put  on  the  column  sides  and  beam 
bottoms.    Bevel  key  strips  for  walls  should  also  be  nailed  lightly  to  the  panels  when  necessary. 

Heavy  cleats  for  big  wall  columns  should  be  cut  and  bored,  but  not  attached  to  the  panels.  The  panel  can  be 
cleated  with  IH-in.  boards,  and  is  thus  made  much  lighter  and  easier  to  handle  in  erecting.  Cleanouts  at  the 
bottom,  on  two  opposite  sides  of  all  columns,  should  be  made  at  the  mill.  Reduction  strips  should  be  nailed  at  the 
edge  of  all  panels  which  reduce  in  size  when  reused. 

All  small  pieces  liabl  •  to  get  lost  or  used  for  other  purposes  can  be  dipped  in  red  paint  so  that  their  small  size 
will  be  respected  by  the  carpenters  when  looking  for  loose  boards. 

Much  waste  in  making  up  li-m.  panels  can  be  prevented  if  the  floor  is  laid  out  to  make  the  majority  of  the 
panels  a  whole  number  of  boards  wide.  Roofers  come  5?^  to  bYz  in.  wide,  and  it  is  an  easy  matter  to  plan  the 
panels  to  come,  say,  seven  or  eight  boards  wide,  which  means  no  waste  in  ripping  one  board  to  make  the  width. 
The  lengths  should  be  planned  as  near  stock  lengths  as  possible  Panels  made  of  spliced  boards  are  expensive  to 
make  and  are  easily  broken. 

New  or  Used  Material? — It  is  not  economical  in  labor  to  make  up  panels  from  lumber  which  has  already  been 
in  contact  with  concrete  several  times.  If,  however,  panels  are  in  good  condition,  they  can  be  cleaned  and  repaired 
at  a  considerable  saving,  both  in  labor  and  material. 

67c.  Cleat  Spacing. — The  cleat  spacing  for  the  various  kinds  of  panels  should  be  kept  uniform  so  that 
the  strips  on  the  benches,  for  spacing  the  cleats,  will  not  need  to  be  moved  for  every  set  of  panels. 

For  beam  sides  2  by  3-in.  cleats,  flat,  can  be  used  on  panels  up  to  30  in.  deep;  2  by  4-in.,  flat,  up  to  42  in.;  and 
3  by  4-in.,  on  edge,  above  42  in.  deep.    Nails  should  be  specified  as  follows: 

Wire  nails  should  be  used  for  formwork  because 
No.  Size  Width  of  board,  inches        ^ase  in  driving  and  drawing.    The  holding  power  is 

,    _  ,  also  sufficient.    Double-headed  nails  should  be  used 

3   IQd  6H  and   7¥i  ■  .        n  u      j      u-  u  u       x    u   i  j  u 

in  securing  all  boards  which  have  to  be  loosened  be- 

2   lOd  2?4    to    5^4  f  ... 

t  inj  T      *u     o-!/  fore  stripping. 

1   10a  Less  than  2'?4  t»i      •       *  t^-  u  ttt    t       a  • 

J    3      4   1    t  Planmng  of  Field  Work. — An  im- 

,  ,      ,  ,.    ,      ^  ^  f^^^         portant  feature  of  the  field  work  is  a  planning  depart- 

8d  coated  and  clinch  ends  in  %-in.  boards.  +      u       u    •  •         i  i  •  j 

'  ment,  whose  business  it  is  to  plan  the  work  in  advance 

so  that  at  all  times  the  several  gangs  will  have  definite 

tasks  to  do  and  be  supplied  with  suflBcient  material  with  which  to  do  the  work. 

The  moving  boss  has  an  important  position  in  this  field  work.  He  is  responsible  for  getting  the  proper  panels 
to  their  correct  location  in  the  building  and  for  having  all  other  stock  called  for  on  the  assembly  plan  on  the  job 
ahead  of  the  erection  carpenters.  When  the  forms  are  stripped  he  must  move  the  panels,  which  are  to  be  remade 
before  their  next  use,  to  the  remaking  benches,  and  thence  to  their  next  location.  It  is  expensive  to  have  high- 
priced  carpenters  waiting  for  stock  or  using  stuff  not  suited  for  the  job  they  have  to  do. 

The  erection  of  the  centering  and  the  assembling  of  the  panels,  after  the  latter  have  been  moved  to  their 
proper  location  in  the  building,  are  done  by  carpenters.  It  is  economical  to  employ  good  carpenters  and  to  keep 
them  employed  constantly.  A  gang  of  men  that  understand  formwork  on  concrete  buildings,  the  methods  used, 
and  the  grade  of  work  desired,  is  a  valuable  asset  for  any  firm  specializing  in  reinforced-concrete  work. 

A  competent  foreman  should  be  in  charge  of  all  carpenter  labor.  He  should  be  consulted  by  the  planning 
department  so  that  "team  work"  will  prevail. 

Quality  in  concrete  building  work  is  usually  more  desirable  than  low  costs.  Good  lines  and  surfaces  will  be 
remembered  after  the  cost  is  forgotten.  These  results  can  be  obtained  only  by  the  careful  supervision  of  the  erec- 
tion of  forms. 

67e.  Stripping  of  Forms. — When  forms  are  to  be  reused,  as  is  usually  the  case,  stripping  should  be  done 
as  carefully  as  possible.  An  intelligent  foreman  in  charge  of  a  stripping  gang  is  a  good  investment.  Any  man  can 
wreck  forms  cheaply,  but  a  man  who  can  strip  the  forms  and  leave  them  in  good  condition  for  reuse  is  in  the 
end  the  cheapest  stripper.    He  saves  the  time  of  the  high-priced  carpenters  in  remaking  and  fitting  broken  panels. 

The  question  of  when  to  strip  is  one  for  the  building  designer  to  decide,  and  his  instructions  should  be  care- 
fully followed.  It  is  cheap  insurance  to  make  enough  forms  so  that  no  chances  need  be  taken  of  weakening  the 
structure  by  stripping  while  the  concrete  is  still  green. 

The  panels  which  need  to  be  altered  before  reuse  should  be  remade  from  the  blue-prints  showing  the  neces- 
sary changes.    A  bench  for  this  purpose  can  be  set  up  in  the  story  where  the  forms  are  stripped.    It  is  sometimes 


Sec.  2-68 J 


GENERAL  METHODS  OF  CONSTRUCTION 


135 


advisable  in  a  high  building  to  set  up  power  saws  in  one  of  the  upper  stories  for  cutting  off  panels  and  getting  out 
stock  for  remaking  and  repairing. 

A  large  gang  of  carpenters  working  overtime  is  sometimes  necessary  in  order  to  deliver  a  building  on  time. 
This  is  expensive,  however.  The  workmen  cannot  give  back  in  efficient  labor  the  value  of  their  high  wages.  Ten 
hours  is  about  all  the  average  man  can  work  without  falling  off  greatly  in  efficiency.  Night  work  on  forms  should 
be  avoided  if  possible. 

When  speed  is  not  the  essence  of  the  contract,  there  is  time  to  plan  the  erection  work  more  carefully.  Smaller 
gangs  can  be  used  and  their  tasks  and  the  material  for  them  routed  by  slips  similar  to  those  used  in  making  up  panels. 

An  important  item  in  the  field  work  is  the  erection  of  economical  safe  stages.  The  stages  should  be  carefully 
designed  as  to  the  worst  possible  load  to  come  upon  them,  and  the  design  should  be  strictly  followed  in  the  field. 
A  man  thoroughly  familiar  with  lumber  should  be  made  inspector  as  to  the  quality  of  the  stock  used  for  stages. 
A  good  stage  makes  the  workmen  more  efficient  and  is  a  good  insurance  investment. 

68.  Steel  Forms. — Steel  forms  have  always  been  used  more  or  less  for  sewers,  curbs,  and 
sidewalks,  but  now  the  application  of  steel  forms  to  floor  and  column  construction  is  advancing 


Fig.  71.— Blaw  light  wall  forms  on  foundation  wall  for  plant  of  Hubbard  &  Co.,  Pittsburgh,  Pa. 

at  an  exceedingly  rapid  rate.  Steel  forms  are  almost  universally  employed  for  circular  columns 
and  for  flaring  column  heads.  Wall  forms  are"  also  much  used  and  have  given  satisfaction, 
especially  in  residences  and  other  structures  of  the  foundation-wall  type. 

Several  types  of  floor  forms  are  on  the  market  and  are  used  to  some  extent.  The  same  is 
true  of  forms  for  rectangular  and  octagonal  columns. 


136 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-68 


The  adjustment  in  height  of  steel  forms  for  circular  columns  is  obtained  by  telescoping 
the  ends.  Such  forms  are  usually  made  up  of  a  series  of  panels  of  thin  galvanized  steel  held 
rigidly  in  place,  like  staves  in  a  barrel,  by  means  of  stiff  steel  bands.  The  panels  are  somewhat 
flexible  and  are  sprung  in  or  out  depending  upon  the  size  of  the  column. 


Fig.  72.— Steel  floretyles. 


Fig.  53,  page  109,  and  Plate  V,  page  116,  show  steel  forms  for  circular  columns,  in  place, 
and  ready  for  the  pouring  of  the  concrete.  The  construction  around  the  column  heads  should 
be  noted.  The  form  illustrated  in  Fig.  53  is  manufactured  by  the  Blaw  Steel  Construction  Co. 
and  is  so  designed  that  all  variations  are  taken  care  of  with  a  single  set  of  forms.    Vertical  ad- 


FiG.  73. — iSteel  floretyles  with  end  caps. 


justment  is  obtained  by  telescoping  one  form  section  inside  of  the  section  below  it,  an  adjust- 
ment of  18  in.  being  permitted  between  each  two  sections.  Diameter  adjustment  is  provided 
for  by  the  use  of  form  panels  of  various  standard  widths.  The  edges  of  the  panel  sheets  are 
bent  back  to  form  flanges,  and  these  flanges  are  slotted.    The  panels  are  kept  to  any  desired 


Fig.  74. — Steel  floredomes. 


curvature  by  segmental  steel  bands  which  slip  through  the  slots  in  the  panel  flanges,  and  are 
drawn  tight  by  means  of  keys  or  wedges.  The  bands  are  not  adjustable,  and  a  complete  set 
must  be  provided  for  each  diameter  of  column  to  be  built.  The  form  panels  are  made  in  three 
standard  lengths,  6  ft.,  43^  ft.,  and  3  ft.  The  steel  column  forms  are  not  used  to  support  any 
part  of  the  floor,  as  is  usually  the  case  in  wood-form  construction,  so  that  the  floor  forms  may 
be  erected  complete  before  the  column  molds  are  set  up. 


Sec.  2-68] 


GENERAL  METHODS  OF  CONSTRUCTION 


137 


The  ''Hydraulic  "  column  forms  shown  in  Fig.  55,  page  110  (manufactured  by  the  Hydrau- 
lic Pressed  Steel  Co.,  Cleveland,  Ohio)  consist  of  galvanized-iron  units  held  together  at  the 


Fig.  75.— G.  F.  steel-tile. 


Fig.  76. — Meyer  steelforms. 


joints  with  quick-acting  clamps  and  shaped  with  steel  ring.  Any  height  of  column  or  size  of 
head  may  be  obtained. 

Fig.  71  shows  Blaw  light  wall  forms  for  foundation-wall 
work  where  wire  ties  are  used.  The  standard  wall-form  panel 
is  2  ft.  square  and  provided  with  holes  in  the  four  flanging 
angles  for  the  passage  of  fasteners.  Slots  are  also  provided  in 
the  plate  to  permit  of  the  insertion  of  the  wire  ties.  The  hori- 
zontal and  vertical  liners  are  used  to  keep  the  form  straight  and 
to  connect  panels  together  so  that  they  may  be  shifted  in  larger 
units  than  single  panels.  This  type  of  form  is  not  limited  to 
two-course  working,  but  may  be  used  in  pouring  any  desired 
height  of  wall  at  one  operation. 

Wall  and  foundation  forms  manufactured  by  the  Hydraulic  Pressed  Steel  Co.  consist  of 
uprights  which  are  aligned  and  accurately  spaced  3  ft.  3  in.  c.  to  c.  of  pressed  steel  liners. 

Between  these  uprights  steel-faced  plates  are 
clamped. 

A  type  of  permanent  (non-removable) 
steel  form  for  floor  construction  which  has  a 
similar  function  to  hollow  tile  in  terra-cotta 
hollow  tile  floors,  manufactured  by  the  Trussed 
Concrete  Steel  Co.,  is  shown  in  Figs.  72  and 
73.  This  type  of  floor  form  is  also  shown  in 
Fig.  35,  page  59.  "  Steel  Floredomes  "  shown 
in  Fig.  74  are  manufactured  by  the  same  com- 
pany for  two-way  construction  in  which  the 
loads  are  carried  in  two  directions  to  the  supports.  The  metal  domes  are  deeply  corrugated 
to  secure  stiffness  and  are  only  open  on  the  underside  so  that  the  joists  extend  on  all  sides  of 
the  dome.    The  standard  heights  of  ''Steel  Floretyles:"  6,  8,  10,  12,  and  14  in.  Approxi- 


FiG.  77. — Wiscoforms. 


138 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-69 


mate  width  at  base:  203^  in.,  exclusive  of  1-in.  flanges  along  bottom  edges,  which  add  2  in. 
to  this  dimension.  Standard  lengths  (nominal)  of  all  sizes:  4  ft.  and  3  ft. — actual  lengths  are 
4  ft.  1  in.  and  3  ft.  1  in.  to  provide  for  end  lap.  ''Steel  Floredomes"  may  be  obtained  in 
depths  of  6,  8,  10,  and  12  in.  and  21  by  21  in.  base.  Permanent  steel  floor  forms  similar  to 
"Steel  Floredomes"  are  furnished  by  the  General  Fireproofing  Co.,  Youngstown,  Ohio  (known 
as  G.F.  Steel-Tile,  Fig.  75).  .  Steel  floor  forms  which  are  removable  and  may  be  re-used  in  succes- 
sive floors  of  a  building  are  furnished  by  the  Concrete  Engineering  Co.,  Omaha,  Neb.  (known 
as  Meyer  Steelforms,  Fig.  76);  and  by  the  Witherow  Steel  Co.,  Pittsburg,  Pa.  (known  as  Wisco- 
forms,  Fig.  77). 

69.  Construction  Notes. — Nails  should  be  used  sparingly  in  the  construction  of  forms  ex- 
cept in  those  sections  which  are  to  be  used  over  and  over  again  without  change.  Unnecessary 
nailing  not  only  adds  to  the  labor  of  wrecking  but  is  liable  to  render  the  lumber  unfit  for  con- 
tinued use.  Where  nails  must  be  used  in  the  connection  of  form  sections,  the  heads  should  be 
left  protruding  so  that  they  may  be  drawn  without  injury  to  the  lumber.  A  special  form  of 
double-headed  nail  is  now  on  the  market  and  gives  satisfaction. 

The  location  of  column  forms  from  floor  to  floor  of  a  building  should  be  determined  by 
means  of  the  transit,  and  special  care  should  be  given  to  the  erection  of  these  forms  in  order  to 
make  sure  that  they  are  set  true  to  line  and  level.  Column  forms  should  be  held  in  position  by 
diagonal  braces  in  two  directions  nailed  to  adjustable  or  slotted  blocks  which  are  bolted  to  the 
concrete  slab — the  bolts  being  placed  when  the  floor  is  poured.  Sometimes  small  pieces  of 
plank  are  employed  instead  of  blocks,  and  these  are  nailed  directly  to  the  floor  slab  within  2  or 
3  days  after  pouring  and  while  the  concrete  is  still  green. 

Trouble  in  the  erection  of  floor  forms  may  usually  be  traced  to  inaccuracies  in  form  measure- 
ments. If  the  column  forms  are  of  the  proper  widths  and  if  the  beam  and  girder  forms  are 
cut  to  exact  lengths,  no  trouble  of  great  consequence  can  arise.  A  variation  of  more  than  }i 
in.  from  the  sizes  shown  on  the  drawings  should  not  be  permitted. 

One  method  of  erecting  forms  for  rectangular  columns  is  to  nail  three  of  the  sides  together 
lightly  before  raising  them  to  place,  and  then  to  set  the  remaining  side  afterward.  This 
enables  the  column  reinforcement  to  be  put  in  place  before  the  form  is  set.  Another  method  in 
common  use  is  to  assemble  the  column  form  complete  before  raising,  in  which  case  the  form 
must  be  raised  above  the  projecting  reinforcement  (belonging  to  the  footing  or  column  below) 
and  then  lowered. 

All  forms  for  concrete  require  a  coating  of  some  lubricant  to  prevent  the  concrete  from 
adhering  to  the  wood  and  making  a  rough,  unpleasing  appearance.  Crude  oil  or  petroline  is 
used  to  a  considerable  extent  and  preserves  the  forms  against  damage  by  alternate  wetting  and 
drying.    The  forms  should  preferably  be  oiled  before  they  are  set  in  place. 

Oil  should  not  be  used  on  forms  against  surfaces  which  are  to  be  plastered,  as  oil  prevents 
the  adhesion  of  the  plaster.    Wetting  with  water  in  such  cases  will  be  sufficient. 

Beam  and  girder  forms  should  be  raised  slightly  higher  at  the  center  than  at  the  ends  in 
order  to  prevent  sagging.  If  this  is  done,  deflection  and  compression  of  the  supports  will 
finally  leave  the  beams  and  girders  in  a  level  position.  A  deflection  equal  to  %  in.  in  every  10 
ft.  of  length  is  usually  provided  for. 

The  sides  of  beam  and  girder  forms  should  project  over  the  edges  of  the  bottom  plank. 
By  so  doing  it  becomes  possible  to  leave  the  beam  and  girder  bottoms  in  place  after  the  sides 
have  been  dropped. 

Slab  forms  of  the  ordinary  panel  type  should  be  made  in  sections  (usually  four  to  a  floor 
panel)  in  order  to  prevent  binding  and  permit  easy  removal.  A  splice  of  in.  is  usually 
allowed  between  adjacent  sections,  and  this  space  is  covered  with  a  strip  of  sheet  metal,  thus 
giving  some  leeway  in  fitting  the  sheathing  panels  into  place  without  unnecessary  cutting. 
Sometimes  it  is  a  good  plan  to  provide  for  a  loose  board  between  two  panels  near  the  center  of 
the  span  so  that  temporary  uprights  may  be  used  to  support  the  floor  slab  when  the  forms  are 
stripped. 


Sec.  2-70] 


GENERAL  METHODS  OF  CONSTRUCTION 


139 


All  posts  or  shores  should  rest  on  large  hardwood  wedges,  driven  in  pairs  to  an  even  bear- 
ing. Hard  driving  of  wedges  should  not  be  permitted  as  it  is  sure  to  injure  the  concrete  which 
is  setting  under  them.  In  some  instances  wedges  have  been  placed  at  the  top  of  the  posts 
instead  of  at  the  bottom,  as  is  the  usual  custom.  The  disadvantage  of  this  method  lies  in  the 
difficulty  of  driving  wedges  while  standing  on  a  temporary  support  but,  on  the  other  hand, 
by  top-wedging,  the  shores  or  posts  may  be  permanently  braced  before  the  form  work  is  leveled. 

Concrete,  when  poured  under  horizontal  or  inclined  forms  (such  as  in  footings),  will  exert 
an  upward  pressure,  and  such  forms  should  be  securely  anchored. 

When  posts  are  placed  on  plank  sills,  great  care  should  be  exercised  to  avoid  settlement  be- 
cause of  the  likelihood  of  hollows  coming  under  the  sills  due  to  unevenness  of  concrete  floors  or 
to  thawing  out  of  frozen  ground. 

Deflection  should  be  carefully  guarded  against  at  a  window  head  as  a  slight  deflection  at 
this  point  will  cause  considerable  trouble  and  expense  in  setting  the  window  sash. 

Forms  which  are  to  be  used  again  should  be  cleaned  as  soon  as  they  are  taken  down. 

In  removing  forms  the  green  concrete  must  not  be  disturbed  by  prying  against  it. 


BENDING  AND  PLACING  REINFORCEMENT 


70.  Checking,  Assorting,  and  Storing  Steel. — Steel  should  be  checked,  assorted,  and  stored 
as  soon  as  it  is  delivered  at  the  site.  It  should  be  blocked  up  several  inches  from  the  ground 
and  should  be  stored  in  such  a  manner  that  those  rods  needed  first  may  be  easily  reached. 

71.  Bending  of  Reinforcement. — Such  a  simple  matter  as  bending  of  rods  for  concrete 
reinforcement  might  seem  to  be  almost  too  unimportant  a  subject  to  be  worthy  of  very  much 
attention.  However,  when  it  comes  to  the  proposition  of  making  thousands  of  bends  per  day, 
factors  of  time  and  expense  in  this  work  are  most  important.  Of  course,  the  structural  design 
should  be  such  as  to  require  the  steel  bends  to  be  as  few  in  number  and  kind  as  possible,  but  much 
can  be  done  to  lessen  expense  by  the  manner  of  making  these  bends.  In  addition  to  economical 
considerations,  care  should  be  taken  to  see  that  the  bends  are  made  true  to  line  and  plane,  and 
that  the  steel  is  not  injured  during  the  operation. 

71a.  Types  of  Bends. — In  general,  there  are  five  different  types  of  bends  to  be 
made  with  reinforcing  rods  which  may  be  indicated  as  follows:  (1)  bending  of  heavy  beam  and 
girder  rods;  (2)  bending  of  the  vertical  reinforcing  rods  of  columns  at  or  near  floor  level  where 
columns  change  size;  (3)  bending  of  stirrups  and  column  hoops;  (4)  bending  of  slab  reinforce- 
ment, and  (5)  the  coiling  of  rods  or  wire  to  form  spiral  column  reinforcement.  In  making  each 
type  of  bend,  the  work  should  always  be  so  arranged  that  all  rods  of  the  same  size  and  shape 
are  bent  at  the  same  time.    This  avoids  remeasuring  and  resetting  of  templets. 

716.  Hand  Devices. — A  simple  method  of  bending  heavy  rods  is  shown  in  Fig. 
78.  Either  steel  bars  or  steel  plugs  5  or  6  in.  long  are  placed  in  holes  in  the  bending  table,  these 
holes  being  bored  at  the  points  where  the 


C/eafs  on  uncfers/de 


 ff 


1  F     1          i          . ,  1  j 

4  — 

— l-i  -y^^  h  ^n: — '4"" 

1  1                1  1   

Fig.  78. 


bends  are  to  be  made.  A  piece  of  plank 
is  nailed  to  the  table,  as  shown,  in  order 
to  hold  the  rod  in  place  while  being  bent. 
The  rod  is  then  placed  in  the  position  GH 
and  bent  around  the  plugs  C  and  Z>,  and 
then  around  the  plugs  B  and  E  until  the 
ends  AB  and  EF  are  parallel  to  GH. 

The  manner  in  which  rods  are  to  be  bent  is  generally  left  to  the  discretion  of  the  steel 
foreman.  The  general  practice  is  to  bend  beam  and  girder  reinforcement  by  using  a  heavy  pipe 
slipped  on  the  rod  and  then  making  the  bends  as  described,  using  either  steel  plugs  or  angles 
bolted  to  the  table. 

In  building  two  large  reinforced-concrete  buildings  for  the  General  Electric  Co.  at  Schenec- 
tady, N.  Y.,  the  Stone  &  Webster  Engineering  Corporation,  of  Boston,  accomplished  the  bending 


140 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-716 


of  the  heavy  rods  by  means  of  two  ^^-in.  steel  plates  mounted  one  on  top  of  the  other  on  a  bend- 
ing table,  and,  in  these,  holes  were  drilled  3-in.  on  centers  in  both  directions.  Steel  pegs  were 
dropped  in  the  holes  the  proper  distance  and  angle  apart,  and  the  rods  were  then  bent  by  hand 
using  a  2-in.  steam  pipe. 

R.  C.  Hardman,  in  Engineering  Record,  describes  as  follows  a  small  home-made  bar  bender 
for  bending  cold  bars  up  to  1  ^-in.  diameter,  where  not  greater  than  90-degree  bends  are  required : 

The  apparatus  consists  essentially  of  a  cast-iron  plate  containing  two  lugs  between  which  the  bar  is  placed,  a 
steel  lever  fastened  to  the  plate  by  means  of  a  steel  pin  about  which  it  acts,  and  a  set  of  fillers,  as  shown  in  Fig.  79. 

The  cast-iron  plate  can  be  cast  of  coarse  metal  in  any  foundry,  the  top  of  the  plate  with  which  the  lever  comes 
into  contact  being  machined.    The  bolt  holes,  certain  ones  of  which  must  be  countersunk  to  allow  free  action  of  the 

lever,  may  be  either  cored  or  drilled.  The  space  between  the  two 
lugs  should  be  slightly  larger  than  the  largest  size  bar  to  be  bent. 
The  filler  is  a  device  made  of  strap  iron  by  any  blacksmith,  which  fits 
around  the  lug  opposite  the  lever,  to  insure  a  tight  fit  for  bars 
smaller  than  the  maximum.  A  set  of  these  to  accommodate  the 
various  commercial  sizes  of  steel  bars  can  be  made  at  small  cost. 
To  insure  a  good  fit  the  edges  of  the  lug  around  which  the  "filler" 
is  placed  should  be  machined.  The  lever  is  made  of  1  by  2-in.  flat 
steel  forged  to  shape,  with  the  face  engaging  the  bar  slightly  upset 
on  the  upper  side.    Its  length  is  about  4  ft. 

The  operation  of  the  apparatus  can  be  readily  seen  in  Fig.  79, 
in  which  the  lever,  bar  to  be  bent  and  a  filler  are  shown  dotted. 
The  apparatus  is  fastened  to  a  bench  by  means  of  bolts,  and  counter- 
sunk so  that  the  top  of  the  plate  is  flush  with  the  top  of  the  bench. 

Two  men  can  make  cold  bends  under  1  in.  in  diameter.  On 
larger  sizes  three  men  are  required  unless  recourse  is  had  to  a  pipe 
extension  to  the  lever. 

The  cost  of  the  apparatus  should  not  exceed  $12  to  $15,  and  it  will  readily  pay  for  itself  on  a  small  job  which 
will  not  admit  of  a  more  versatile  bender. 

Several  hand  and  power  devices  are  on  the  market  for  the  bending  of  steel  reinforcement  and 
for  the  making  of  spiral  coils.    These  all  have  their  merits  and  have  given  satisfaction. 

Fig.  80  shows  the  Universal  bar  bender  which  may  be  fastened  to  any  bench  or  plank. 
It  is  a  light,  portable  device  weighing  about  60  lb.  and  capable  of  bending  all  ordinary  sizes  of 
reinforcing  bars  to  any  angle  desired,  without  any  adjustment  being  necessary.    The  top  half 


Fig.  79. — Small  home-made  bar  bender. 


Fig.  80. — Universal  bar  bender. 


Fig.  81. — Wallace  bar  bender. 


of  the  bender  can  be  removed  and  used  to  bend  bars  after  they  are  in  place.  The  bar  rolls 
around  the  pin  in  bending,  thus  distributing  the  strain  along  the  bar  and  reducing  the  chances 
of  fracture  at  the  bend. 

The  bender  is  equipped  with  a  5-ft.  crowbar  for  a  handle,  which  may  be  removed  and  used 
for  other  purposes.  To  bend  large  bars  easily,  the  handle  should  be  lengthened  by  using  an 
iron  pipe  over  the  crowbar. 

A  bar  bender  designed  for  heavy  work  and  manufactured  by  the  Wallace  Supplies  Mfg.  Co., 
Chicago,  111.,  is  shown  in  Fig.  81.  This  machine  has  an  auxiliary  ratchet  lever  which  operates 
a  pinion  against  a  series  of  teeth  in  the  frame  at  a  large  ratio,  thus  developing  great  power.  The 


Sec.  2-71c] 


GENERAL  METHODS  OF  CONSTRUCTION 


141 


ratchet  panel  may  be  thrown  out  of  engagement  and  machine  operated  with  the  reguhir  lever 
for  light  work. 

A  bender  manufactured  by  the  Waterloo  Construction  Co.,  Waterloo,  Iowa,  is  shown  in 
Fig.  82.  This  bender  bends  reinforcing  bars  up  to  and  including  13-^  in.  The  machine  is  fur- 
nished with  a  detachable  handle  7  ft.  long  for  convenience  in  handling. 

71c.  Power-operated  Benders. — Fig.  83  shows  a  power-operated  truck-mounted 
bar  bender  designed  to  bend  any  size  of  reinforcing  rod  that  is  likely  to  be  used  in  building  opera- 


FiG.  82. — Waterloo  bar  bender. 


tions.  Any  size  of  bar,  from  }4tol  }i  in.,  round,  square  or  deformed,  can  be  bent  to  any  angle 
desired;  or  spirals  formed  from  6-in.  diameter  to  any  required  size.  Weight,  complete,  ready 
for  shipment,  2700  lb.    The  machine  is  manufactured  by  Kardong  Bros.,  Minneapolis,  Minn. 

lid.  Care  to  be  Exercised  in  Bending. — Bending  reinforcement  should  be  done 
in  such  a  manner  that  the  bars  will  not  break  or  crack  at  the  bend;  that  is,  the  bends  should  not 
be  too  sharp  and  the  bending  force  should  be  applied  gradually  and  not  with  a  jerk.  Reinfor- 
cing bars  should  also  be  bent  cold  except  for  the  unusual  sizes  of  1  ^2  in.  and  upward,  when  heat 


Fig.  83. — Power-operated  bar  bender. 


may  be  required.  Warming  up  to  a  low  cherry  red  should  under  all  circumstances  be  the 
highest  heat  permitted.  Bars  to  be  bent  are  generally  not  larger  than  IK  in.  and  most  hand- 
bending  machines  on  the  market  do  not  claim  to  bend  bars  of  any  greater  diameter. 

Structural  grade  bars  will  bend  much  more  easily  and  with  less  danger  of  injury  than  either 
the  hard  grade,  rerolled  steel,  or  cold-twisted  bars.  In  fact,  the  three  last-mentioned  classes 
of  reinforcement  will  usually  require  heating  in  the  larger  sizes  before  bending  can  be  safely 


142 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-71e 


attempted.  Square  cold-twisted  bars  frequently  give  trouble  in  bending,  due  to  the  fact  that 
they  arei  apt  to  twist  out  of  their  proper  plane. 

lie.  Bending  of  Slab  Reinforcement. — Slab  reinforcement  is  usually  bent  after 
it  is  in  place  on  the  floor.    A  tool  for  this  purpose  is  shown  in  Fig.  84.    Sometimes,  however, 

slab  rods  are  bent  before  being  placed.     This  latter 

._  ^  method  seems  preferable  since  the  bends  can  be  more 

lliil:'  ■  accurately  made.    To  keep  the  cost  of  such  bending  as 

low  as  possible,  the  bending  machine  should  be  con- 
~>     structed  so  that  the  bends  may  be  made  with  great 

rapidity.    Such  a  machine  is  shoAvn  in  Fig.  85  and  was 

employed  on  the  General  Electric  Co. 's  buildings  referred 

to  above. 

This  machine  consists  of  two  units  which  can  be  placed  any  distance  apart  and  securely 
bolted  down  to  a  table.  Each  part  consists  of  a  steel  plate  on  which  is  mounted  two  smaller 
plates  having  angle  stops  attached.    Between  the  stops  is  located  a  casting,  which  is  pivoted  so 


Pos/t/on  of  rod  before  bend/ncf  


.  Stop  plafe 


/l^g^^e  Iron  fastened 
to  sf/d/nj  plate 

Fig.  85. 


that  it  can  readily  take  any  desired  position  between  the  angle  stops.  With  the  steel  rod  in 
position,  this  casting  can  be  turned  by  means  of  a  long  lever  attached  so  as  to  move  one  of  the 
mounted  plates.  On  the  upper  side  of  the  casting  are  four  lugs,  and  two  of  these  lugs  are  con- 
structed so  that  adjustable  collars  can  be  slipped  over  them,  thus  making  a  tight  fit  for  the  rods 
which  are  to  be  bent.  The  amount  and  the  angle  of  the  offset 
can  be  regulated  by  changing  the  distance  through  which  the 
lever  is  turned.  This  machine  offsets  a  rod  parallel  to  itself  and 
with  one  pull  of  the  lever  two  bends  can  be  made. 

72.  Placing  of  Reinforcement. — Steel  should  be  thoroughly 
cleaned  before  being  placed  in  the  forms  in  order  to  obtain  a  posi- 
tive adhesion  of  the  concrete  to  the  steel.  A  slight  film  of  red 
rust  is  not  objectionable,  but  no  rod  should  be  set  in  place  on 
which  rust  scales  have  formed  (see  Art.  54,  Sect.  1). 

All  reinforcing  metal  should  be  securely  fastened  in  correct 
positions  by  wiring  or  otherwise  before  the  placing  of  the  con- 
crete is  begun.  Particular  attention  should  be  given  to  loose-bar 
reinforcement — that  it  is  accurately  and  properly  supported  in 
position  and  that  it  is  not  disturbed  until  the  concrete  is  poured. 

The  advantages  to  be  derived  from  placing  beam-and-girder 
reinforcement  in  frames  has  been  considered  in  Art.  11,  Sect.  11. 
With  steel  in  frames  the  erector  has  simply  to  line  and  level 

them  in  the  forms,  place  braces  where  necessary,  and  make  end  connections  with  abutting  frames. 
Column  reinforcement  should  be  made  up  into  frames,  the  same  as  for  beams  and  girders. 

Slab  and  wall  rods  should  be  tied  with  wire  at  their  intersections  to  prevent  them  from  slip- 
ping or  getting  out  of  place.    The  usual  method  has  been  to  use  a  pair  of  pliers  and  to  cut  the 


Fig.  86. — Wiring  of  reinforce- 
ment using  Curry  Tyer. 


Sec.  2-73] 


GENERAL  METHODS  OF  CONSTRUCTION 


143 


wire  into  convenient  lengths,  A  device  known  as  the  Curry  Tyer  has  recently  been  placed  on 
the  market  for  wire  tying  which  has  made  a  great  record  for  itself  in  a  very  short  time.  Fig. 
86  shows  this  to  be  a  simple  and  practical  device.  The  ties  used  for  the  binding  are  uniform  in 
length  and  the  mechanical  action  of  the  tying  tool  gives  the  wire  a  uniform  number  of  twists. 
The  tie  is  looped  around  the  rods  and  the  ends  are  placed  on  the  hooks  of  the  tying  tool,  then  a 
quick  upward  jerk  of  the  wooden  handle  whirls  the  teeth  and  draws  the  wire  up  tightly. 

Another  method  of  tying  slab  and  wall  rods  together  at  their  intersections  is  shown  in  Fig. 
87.    These  Bar-iys  are  manufactured  by  the  Concrete  Steel  Co.,  in  the  three  types  illustrated. 


Fig.  87. — Bar-tyi 


The  tys  are  quickly  put  in  place  and  when  once  snapped  on  the  bar  will  resist  a  tremendous 
pressure. 

73.  Devices  for  Supporting  Reinforcing  Bars. — There  are  many  excellent  devices  on  the 
market  for  supporting  reinforcing  bars  at  the  proper  distance  from  the  forms.  Some  of  these 
devices  not  only  support  the  rods  but  give  them  the  proper  spacing  and  lock  them  in  position. 

Beam  spacers  sold  by  the  Universal  Form  Clamp  Co.,  of  Chicago,  111.,  are  shown  in  Fig.  88. 
They  are  made  in  three  sizes — namely:  4  in.,  5  in.,  and  6  in. — and  space  the  bars  accurately 

both  from  the  sides  of  form  and  center  to  center  of  bars. 
Easy  chairs  sold  by  the  same  company  are  adaptable  to 
either  a  one-way  or  a  two-way  system  of  slab  reinforce- 
ment. Fig.  89  shows  the  chair  before  being  placed  in 
position.  The  upright  tying  finger  enables  the  chair  to 
be  readily  seized  and  put  in  position.    Fig.  90  shows  the 


Fig.  88. — Beam  spacers. 


Fig.  89. — Easy  chair. 


Fig.  90. 


chair  applied  to  a  one-way  system  of  reinforcement.  After  the  chair  has  been  placed  in  posi- 
tion the  flexible  tying  fingers  are  bent  over  the  bar  from  opposite  sides  by  hand,  firmly 
securing  the  chair  to  the  bar.  This  chair  can  readily  be  applied  to  a  two-way  system  of  re- 
inforcement. Easy  chairs  are  made  in  three  sizes  so  as  to  provide  for  reinforcing  bars  varying 
in  diameter  from      to  1  in. 

A  device  for  supporting  slab  rods,  known  as  the  Securo  locking  spacer,  is  a  light  bar  passmg 
beneath  the  rods  and  having  depending  lugs  which  rest  on  the  bottom  of  the  form  and  so  keep 
the  rods  at  the  desired  height.    At  the  location  of  each  rod  the  bar  has  two  flexible  clips  which 


144 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-73 


Fig.  97. — Hy-chair. 


Sec.  2-73] 


GENERAL  METHODS  OF  CONSTRUCTION 


145 


are  bent  around  it,  and  these  serve  to  insure  the  use  of  the  proper  number  of  rods.  Three  strips 
of  Securo  slab  bar  spacers  are  used  per  panel  for  ordinary  spans.  Two  additional  upper  spacers 
are  used  where  slab  bars  run  in  two  directions.  Upper  spacers  are  also  used  in  flat-slab  con- 
struction. The  device  is  shown  in  Fig.  91  and  is  made  by  the  Metal  Building  Materials  Co. 
of  Chicago,  111. 

Securo  supporting  and  locking  spacer  for  beam  bars  is  shown  in  Fig.  92.  Three  spacers 
are  used  per  beam  for  ordinary  spans.    Upper  beam  spacers  are  employed  when  beam  rods 


Fig.  98. — Chair  spacer.  Fig.  99. — Continuous  slab  spacer. 


are  to  be  placed  in  two  or  more  layers  (Fig,  93).  Securo  beam  spacers  are  furnished  for  any 
widths  of  beams  and  for  any  number  of  bars  in  lower  and  upper  layers. 

Supporting  and  spacing  devices  manufactured  by  the  Concrete  Steel  Co.  are  shown  in 
Figs.  94  to  100  inclusive.  Ty-chairs,  shown  in  Fig.  94,  are  made  of  spring  steel  wire  for  tying 
any  combination  of  reinforcing  bars.    These  chairs  are  made  in  the  following  standard  sizes: 


No.  2 

No.  3 

No.  4 

Combinations  of  cross  bars. 

Combinations  of  cross  bars, 

Combinations  of  cross  bars. 

inches 

inches 

inches 

}yi  and  ^ 

Yi  and  Y2 

and 

\i  and 

Y2  and 

and  % 

M  and  % 

Yi  and  M 

Y/^  and  1 

%  and  % 

%  and  % 

and  11^ 

%  and  M 

H  and  % 

and  y^ 

J.'g  and  1 

The  Easel-chairs  shown  in  Fig.  95  are  designed  particularly  for  terra-cotta  or  steel  tile  and 
joist  construction.  Single  chairs  supporting  one  bar  are  made  2  in.  wide,  and  double  chairs 
supporting  two  bars  are  4  in.  wide  and  will  fit  any  size  bar.  The  standard  Easel-chairs  space 
the  underside  of  the  bar  1  in.  from  the  form. 

Bar-chairs  (Fig.  96)  are  used  for  supporting  single  bars.  They  are  easily  sprung  into  posi- 
tion, locking  on  the  bar  with  a  strong  tension  grip.  Bar-chairs  are  made  for  each  size  and  shape 
of  reinforcing  bars.    Standard  distance  from  underside  of  bar  to  forms  is  1  in. 

Hy-chairs  are  illustrated  in  Fig.  97.  They  are  made  from  2  by  )^-in.  flat  steel  with  any 
required  height,  and  are  used  for  supporting  single  reinforcing  bars  of  any  type  or  size.  They 
are  particularly  useful  on  fiat-slab  buildings  for  rigidly  holding  the  column  bars. 

Chair  spacers  and  continuous  slab  spacers  are  shown  in  Figs.  98  and  99  respectively. 
The  "chair  spacers"  are  made  of  spring  steel  wire.  The  "slab  spacers"  are  made  from  J-^-in. 
cold-rolled  angle  and  the  prongs  are  so  flexible  that  they  can  be  readily  bent  around  the  bars  by 
hand.    In  both  types  of  spacers  standard  distance  from  underside  of  bar  to  form  is  1  in. 

Adjustable  beam  saddles  (Fig.  100)  are  made  from  sheet  steel  and  used  in  beams  and  girders 
10 


146 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-74 


for  accurately  spacing  the  bars  and  holding  them  the  required  distance  from  the  forms.  Stand- 
ard distance  from  underside  of  bar  to  forms  is  13-^  in.  and  2  in. 

The  chair  lock  shown  in  Fig.  101  is  manufactured  by  the  Electric  Welding  Co.,  Pittsburg, 
Pa.    Stock  sizes  are  as  follows:  ^^-in.  round  cross  rod  by       3^^,  and  J-^-in.  round  main 

rods.  Any  size,  however,  can  be  furnished  to  fit  any  shape  of  rod.  Chair  pinchers  are  furnished 
in  two  sizes  for  fastening  the  locks  to  cross  rods. 

Staple  chairs  shown  in  Fig.  102  are  made  from  extra  stiff  sheet  steel,  cut  and  bent  to  develop 
two  pairs  of  pointed  prongs  projecting  in  opposite  chairs.  The  chairs  are  driven  into  the 
formwork  as  far  as  is  desired  and  in  the  exact  position  the  steel  is  to  occupy.  The  bars  are 
placed  and  the  upper  prongs  bent  down  over  the  bar  with  a  quick  blow  of  the  hammer.  The 
driven-in  points  do  not  seem  to  make  form  removal  difficult. 


Fig.    100. — Adjustable  bear 
saddle. 


Fio.  101.— Chair  lock 


Fig.  102. — Staple  chairs. 


THE  MANUFACTURE  AND  USE  OF  CONCRETE  STONE,  BLOCK  AND  BRICK 

By  Harvey  Whipple^ 

74.  Development  of  the  Industry. — Although  the  development  of  the  concrete  products 
industry,  embracing,  first  of  all,  the  manufacture  of  building  units,  began  earlier  than  reinforced 
concrete  building  construction,  it  has  lagged  behind  it.  This  has  been  due,  in  general,  to  a  lack 
of  trained  management.  And  the  trained  management  has  been  lacking,  perhaps,  because  of 
the  apparent  simplicity  of  operations  involved  in  the  manufacture  of  concrete  building  units.. 
In  the  early  days,  the  use  of  cheap  machines  of  questionable  value  was  common  and  many  of 
them  were  sold  on  such  a  basis  as  to  tempt  the  more  slovenly  artisans.  Men  who  had  made 
failures  of  other  work  sought  easy  money  by  making  block  beside  a  gravel  bank  and  following 
the  inadequate  directions  which  came  with  the  machine. 

Attracted  by  the  seeming  lack  of  any  complexity  in  the  essential  operations  of  block 
manufacture,  by  the  cheapness  of  the  machines  with  which  the  work  was  to  be  done,  and  by  the 
seeming  lack  of  any  necessity  for  any  auxiliary  equipment,  it  is  not  to  be  wondered  at  that  there 
were  many  enterprises  in  concrete  products  manufacture  of  woodshed  and  backyard  magnitude. 
The  result  was  that  many  cheap  buildings  put  up  with  this  new  product  soon  developed  the 
weaknesses  which  brought  down  upon  an  entire  industry  the  condemnation  which  was  earned 
by  its  incompetent  putterers. 

Many  of  these  early  products  were  not  even  sound  structurally.  Many  of  them  were 
extremely  porous.  The  appearance  of  a  concrete  block  wall  after  a  rain  and  the  slowness  with 
which  the  moisture  disappeared  in  subsequent  sunshine,  gave  rise  to  the  early  belief  that 
concrete  as  a  building  material  makes  for  dampness  and  is  unfit  for  dwellings.  The  fact  that 
the  early  block  had  hollow  spaces  giving  a  cored  wall  equal  to  25  to  50%  of  the  cross-sectional 


1  Managing  Editor  Concrete.    Author  "Concrete  Stone  Manufacture." 


Sec.  2-75] 


GENERAL  METHODS  OF  CONSTRUCTION 


147 


area,  led  to  the  extravagant  claims  not  only  that  no  moisture  could  get  through  the  wall  from  the 
outside,  but  that  such  a  wall  was  sufficiently  insulated  so  that  there  could  he  no  possible  danger 
of  condensation  on  the  interior  wall  surfaces.  The  blockmakers  had  the  architect  against 
them.  The  commonest  type  of  block  was  an  imitation  of  pitch  face  stone,  which  the  architect 
objected  to,  not  so  much  because  it  was  an  imitation,  as  because  it  was  a  very  poor  imitation 
of  the  real  thing.  Architects  also  objected  to  the  early  units  because  of  their  proportions  in 
height  and  length,  commonly  8  in.  high  by  16  in.  long. 

The  conditions  which  are  gradually  driving  the  incompetent  out  of  the  industry,  and  which 
are  closing  down  those  plants  which  are  inadequately  equipped,  poorly  managed,  and  under- 
capitalized, are  bringing  into  the  industry  men  who  were  first  unattracted  by  what  seemed  to 
be  a  "small  fry"  business.  The  possibilities  of  concrete  stone  manufacture  have  been  de- 
veloped very  remarkably  in  the  last  10  years,  and  much  more  rapidly  in  the  last  4  or  5  years,  so 
that  many  of  the  leading  architects  are  now  specifying  manufactured  stone  on  an  equal  basis 
with  natural  stone,  and  in  some  cases,  in  preference  to  natural  stone  in  important  building 
enterprises. 

i  There  are  very  few  who  doubt  the  value  of  well-made  concrete  building  units  and  it  remains 
only  for  intelligent  manufacturers  to  develop  their  business  along  lines  entirely  different  from 
those  which  characterized  the  industry's  early  efforts. 

A  most  important  thing  for  them  to  appreciate  at  the  outset  is  the  difference  between 
concrete  units  which  are  suitable  for  exposed  walls  and  for  the  trim  of  first-class  buildings,  and 
those  other  units  which  demand  no  architectural  consideration  and  which  are  used  to  replace 

!  common  brick  in  foundation  walls  and  such  walls  as  are  to  be  faced  with  some  other  material. 

I  75.  Two  Main  Lines  of  Work. — There  are  in  general  two  types  of  concrete  building  units. 
Their  manufacture  involves  two  distinct  lines  of  work.  One  is  in  the  production  of  standard 
units  in  quantity;  units  which  are  structurally  sound  but  have  no  special  claim  for  use  where 
any  architectural  purpose  is  to  be  served.  This  is  a  simple  bulk  proposition,  where  the  constant 
flow  of  materials  and  the  quantity  of  manufactured  output  are  largely  the  determining  factors 
in  the  success  of  the  enterprise.  The  other  line  of  work  is  in  the  manufacture  of  trim  stone  or 
standard  units  which  are  specially  faced  or  otherwise  surface  treated  to  make  them  suitable  for 
exposed  walls  or  trim  in  competition  with  natural  stone,  face  brick,  terra-cotta,  and  other 
well-known  building  materials  similarly  used. 

The  success  of  one  enterprise  or  the  other  depends  quite  as  much  upon  the  natural  supply 
of  other  building  materials  in  the  community  as  upon  the  enterprise  and  ability  of  the  particular 
manufacturer.  A  successful  enterprise  in  the  manufacture  of  trim  stone  and  ornamental  work 
necessitates  the  employment  of  modellers,  pattern  makers,  mold  makers,  workers  in  glue, 
plaster,  and  wood;  it  involves  the  use  of  selected  aggregates,  more  skilled  workmen  in  the 
molding  department,  and  frequently  the  employment  of  stone  cutters  in  the  finishing 
department. 

76.  Methods  of  Manufacture. — In  the  production  of  concrete  building  units  there  are  the 
wet  process  and  the  dry  process.  There  is  no  well-understood  definition  which  sharply  distin- 
guishes between  a  dry  mixture  and  a  wet  mixture  and  the  consistency  of  the  concrete  used  varies 
all  along  the  line  from  that  mixture  which  will  just  stick  together  when  squeezed  in  the  hand,  to 
the  other 'extreme,  a  mixture  which  is  of  a  soupy  consistency. 

There  are  three  general  classifications  in  manufacturing  methods,  each  calling  for  the  use  of 
different  equipment.  These  three  are  the  so-called  dry-tamp  method  of  manufacture;  the  so- 
called  pressure  method;  and  the  wet-cast  method. 

76a.  Dry-tamp  Method. — The  dry-tamp  method  is  the  one  most  commonly 
employed.  It  is  the  method  whose  products  have  in  the  main  given  concrete  block  its  early 
bad  reputation;  it  is  a  method  whose  uses  are  quite  satisfactory  when  in  intelligent  hands  and 
where  there  are  methods  of  curing  the  products  which  contain  so  low  a  percentage  of  gaging 
water;  and  it  is  the  method  whose  abuses  have  resulted  in  many  of  the  bad  products  that  have 
brought  unmerited  criticism  in  some  cases  of  the  entire  output  of  the  concrete  products  industry. 


148 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-766 


The  dry-tamp  product  may  be  made  in  an  ordinary  wooden  box,  but  as  commonly  known  it  is 
made  in  the  mold  boxes  of  simple  machines,  so  familiar  everywhere  (see  Fig.  103).  The  mix- 
ture should  have  just  as  much  water  in  it  as  will  permit  the  quick  removal  of  the  product  from 
the  mold  in  which  it  is  made.    The  abuse  of  the  method  is  in  using  too  Httle  water. 

766.  Pressure  Method. — Pressure  machines  are  not  so  common  in  the  field  as 
they  were  at  one  time  although  their  use  is  undoubtedly  increasing  at  present.    There  are  in  use, 

however,  machines  applying  pressure  hydraulically, 
and  others  in  which  the  pressure  is  exerted  mechani- 
cally by  means  of  toggles  operated  by  hand  (see  Fig. 
104).  It  has  been  urged  by  some  that  the  applica- 
tion of  pressure  which  is  exerted  evenly  over  one  en- 
tire face  of  a  product  does  not  result  in  so  dense  a  unit 
as  is  possible  through  tamping,  the  contention  being 
that  this  even  pressure,  allowing  less  free  displace- 
ment of  individual  particles  than  by  tamping  with  a 
small-headed  hammer,  induces  an  arching  action, 
particularly  when  crushed  stone  is  used,  this  arching 
action  among  the  particles  of  stone  resulting  in  voids. 
There  appears,  however,  to  be  little  practical  evi- 
dence of  the  correctness  of  this  belief. 

76c.  Wet-cast    Method. — Wet -cast 
concrete  products  are  not  easily  defined  nor  are  the 

Fig.  103. — Hand  tamp  block  machine.  „     .  ,  .  ,        ,      •   .     ,i  m  i  rm 

factors  which  enter  into  them  easily  outlined,  ihere 
is  more  variation  in  the  equipment  used  and  in  the  methods  pursued  in  wet-cast  work  than  in 
the  other  two  methods.  The  quantity  of  water  varies  a  great  deal  in  wet-cast  work,  as  be- 
tween the  consistency  used  in  sand  molds  and  that  used  in  metal  molds,  for  instance.  With 
sand  molds,  it  is  possible  to  use  a  very  high  percentage  of  water  in  the  mix,  providing  the 
mixture  is  constantly  agitated  before  being  deposited  in  the  molds,  because  the  excess  moisture 


Fig.  104. — Pressure  block  machine. 


is,  in  large  measure,  taken  up  by  the  sand  of  the  mold.  The  use  of  a  very  wet  mixture  in 
metal  gang  molds  (Fig.  105),  or  in  a  fairly  tight  mold  of  any  kind,  would  result  in  a  poor  prod- 
uct, due  to  the  fact  that  much  of  the  moisture  could  not  readily  escape  and  would  be  almost 
sure  to  result  in  a  porous  product.    The  tendency  to  be  overcome  is  the  use  of  two  much  water. 

77.  Consistency. — The  consideration  of  the  various  processes  of  manufacture  has  involved 
some  thought  of  consistency  which,  in  a  measure,  defines  those  processes.    It  is  now  fairly  well 


5ec.  2-78] 


GENERAL  METHODS  OF  CONSTRUCTION 


149 


istablished  in  the  concrete  field  that  the  ideal  consistency  is  in  that  mixture  which  will  barely 
•etain  its  shape  when  the  forms  are  removed  immediately  after  the  concrete  has  been  deposited 
md  pressed  into  shape.  This  is  just  a  little  wetter  than  can  readily  be  used  in  dry-tamp  ma- 
;hines.  It  is  just  a  little  wetter  than  is  ordinarily  used  in  pressure  machines  and  it  is  a  great 
leal  drier  than  the  mixture  which  is  ordinarily  used  in  the  wet-cast  concrete.  Since,  however 
various  other  conditions  which  contribute  to  the  production  of  good  concrete  are  more  suscep- 
ible  of  control  in  the  case  of  factory  work  than  in  field  work,  the  concrete  products  manufac- 
;urer  has  a  somewhat  wider  latitude  in  the  matter  of  consistency. 

;      Concrete  products  manufacturers  using  dry-tamp  equipment  have  constant  difficulty  with 

employees  in  trying  to  get  them  to  use  a  mixture  of  the  wettest  consistency  which  it  is  possible 

;o  use  in  the  mold  boxes  of  their  machines. 

rhe  drier  the  mix,  granting  that  it  is  just  wet 

;nough  to  stick  together  under  tamping,  the 

;asier  it  is  to  remove  the  product  from  the  mold 

vithout  damage.    The  quantity  of  water  which 

^ives  the  mixture  an  ideal  consistency  resulting 
;n  water  marks  on  the  outside  of  the  product 

vhen  it  is  removed  from  the  mold  will,  it  is  gener- 

illy  contended  in  the  field,  cause  the  product  to 

stick  to  the  face  plates,  resulting  in  damaged 
products  and  in  retarding  the  work.  This  stick- 
:  ng  is  undoubtedly  due  to  a  combination  of  the 

tvater  and  fineness  of  the  facing  material  in  caus- 
i  ng  a  suction  on  the  face  plate  which  mars  the 
:"resh  product.  A  wetter  mixture  with  a  slightly 
;  coarser  facing  material  is  not  so  liable  to  cause 

damage  in  removal  from  the  mold. 

The  results  of  dr}^  mixtures  are  not  nearly  so        Fig.  105. — Metal  gang  molds  mounted  on  car. 

Dad  as  might  be  expected.    When  the  products 

ire  removed  from  the  molding  room  promptly  and  put  into  a  steam  curing  room  where  a  warm 
itmosphere  saturated  with  moisture  does  not  permit  the  evaporation  of  any  of  the  moisture 
ivhich  has  entered  into  the  block  in  the  first  place,  very  good  products  can  be  obtained. 

Mixtures  so  wet  that  they  would  give  very  unsatisfactory  results  under  ordinary  conditions 
live  high-class  products  when  poured  into  sand  molds.  A  recent  tendency  among  sand-cast 
stone  manufacturers  is  toward  less  water  and  toward  longer  mixing,  the  additional  mixing 
serving  in  the  place  of  so  great  an  excess  of  water  in  obtaining  a  smoothly  flowing  mixture. 
High  crushing  strengths  and  a  high  degree  of  density  are  obtained.  Numerous  architects  show 
a,  preference  for  the  manufactured  product  over  the  natural  product  because  of  less  tendency 
to  discolor  through  the  absorption  of  moisture  and  dirt.  Where  a  mixture  is  poured,  however, 
into  a  rigid  and  non-absorptive  mold,  as  in  the  use  of  steel  gang  molds,  in  block  and  brick  manu- 
facture, it  is  important  that  the  moisture  content  be  kept  down  just  as  low  as  is  possible  consist- 
ent with  a  ready  flow  of  the  material  into  the  forms  and  around  the  cores. 

78.  Commercial  Molds. — Commercial  molding  equipment  is,  for  the  most  part,  very  sim- 
ple, the  essential  requirement  being  a  mold  box  from  which  the  product  can  be  readily  removed 
when  shaped.  An  idea  which  has  been  almost  inseparable  from  concrete  block  from  the  incep- 
tion of  the  molding  machinery  for  its  production,  is  that  it  shall  provide  a  partially  hollow 
wall.  This  is  very  clearly  shown  in  Fig.  106.  The  various  sketches  show  how  the  designers 
of  different  machines  have  varied  the  provisions  for  air  space  either  in  the  unit  itself  or  in  the 
wall  as  the  block  are  laid  up.  The  block  shown  at  A,  B,  C,  D  and  /  are  in  one  class,  being 
complete  units  in  each  case  providing  the  entire  wall  thickness.  At  E  are  two  separate  thin- 
«^all  slabs  which,  when  laid  in  the  wall,  are  held  by  metal  ties.  The  unit  shown  at  H  is  for 
light  residence  or  other  light  wall  construction,  providing  the  plain  outer  wall  surface  on  what 


150 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-79 


is  here  shown  as  the  upper  side  of  the  sketch.  The  projecting  lugs  provide  a  base  for  attaching 
furring  strips  for  lath  and  plaster.  Blocks  F  and  G  each  consists  of  two  separate  parts  held  by- 
metal  ties,  cast  in  the  blocks.  The  broad  U-shape  block  J  is  designed  for  an  interlocking 
arrangement  as  laid  in  the  wall,  the  straight  faces  of  this  block  forming  both  interior  and 
exterior  wall  surfaces,  giving  a  complete  and  continuous  air  space  in  the  wall.  The  block 
shown  at  K  is  for  a  similar  construction,  the  lug  on  the  block  giving  the  desired  bond  between 
the  two  sides  of  the  wall.  Still  another  type  of  block  has  three  rows  of  vertical  ducts,  and  two 
horizontal.  The  center  row  is  filled  with  slush  concrete  as  laid  up  and  provides  for  reinforcing 
rods. 

The  hollow  space  serves  to  economize  in  material,  to  make  a  lighter,  more  easily-handled 
building  unit,  to  provide  as  laid  up  in  the  wall,  either  a  series  of  vertical  air  ducts,  as  in  the  block 
shown  at  A,       C,  D  and  /,  or  a  more  nearly  continuous  air  space  throughout  the  wall,  as  in 

the  block  shown  at  E,  F,  G,  H,  J  and 

'rV'  °  "V?     ^nn  rS        i%^L£^%^'p    H  A  'r\  r^°rs''r\^?  ^'  varied  manner  of  provid- 

,  ^  ,  hi,  j:uO:y:l^  /jDl^J^'l,  |0;UQl);Q;^  ing  air  space  in  the  wall  lies  the  chief 
A  B  c  D  difference  between  many  of  the  ma- 

3        ,  '  '  •  ^««33>><^iP    liA:/.  "  r^^  i^  chines  on  the  market. 

J    ^  Y  .    .  ft-,     c?^S-<S^       |j  y  79.  Operation  of  Machines.— In 

the  operation  of  the  machines,  con- 


sidering  more  particularly  the  mold 
boxes,  the  general  type  shown  in 
Fig.  103  is  made  either  to  make 

Fig.  106.— Horizontal  cross-sections  of  representative  types  of       ^^^ck  face  down,  face  Up,  Or  with  the 

concrete  block.  face  at  the  side.    If  block  are  to  be 

made  with  a  special  face  design,  as 
for  instance,  the  lamentable  example  of  the  rock-face  block  which  is  poorly  conceived  as  an 
imitation  of  pitch-face  stone,  then  the  face  plate,  which  is  to  give  this  design,  is  usually  at  the 
bottom.  If  the  face  of  the  block,  however,  is  to  be  faced  with  a  separate  mixture  of  material  for 
a  special  texture  or  color,  then  the  machine  will  be  of  either  the  face-down  type  or  face-up 
type.  If  block  are  to  be  produced  solely  for  structural  purposes,  without  face  design,  or  with- 
out a  facing  material  used  on  the  face  side,  the  so-called  stripper  machines  have  given  very 
satisfactory  results.  In  these  machines,  the  block  is  produced  upright  in  the  mold  just  as  it  is 
used  in  the  v/all  and  the  cores  of  the  machine  are  introduced  and  removed  by  upward  and  down- 
ward movements.  The  sides  of  the  block  are  thus  always  perpendicular  to  the  bed  of  the 
machine,  hence  the  block  is  stripped  out  of  the  mold  with  a  troweling  action.  Other  types 
of  machines  tip  the  block  over  before  it  is  removed  on  the  pallet. 

In  some  machines  the  cores  are  removed  with  a  downward  motion  after  the  block  has  been 
tipped  over.  The  common  way,  however,  is  to  withdraw  the  cores  while  the  block  is  still  face 
down,  leaving  the  hollow  spaces  lying  in  horizontal  position.  After  the  cores  are  removed  a 
block  is  turned  over  on  the  pallet.  All  this  is  done  by  the  movement  of  two  levers,  one  to 
remove  cores  and  one  to  tip  over  the  mold  box,  or  by  automatic  mechanism  which  is  set  in 
motion  by  one  lever  movement. 

One  of  the  pressure  machines  has  a  sort  of  track  of  equal  length  on  each  side  of  the  pressure 
head  (see  Fig.  104).  Mold  boxes  travel  on  this  track,  one  box  at  each  end.  The  box  is  filled 
clear  to  the  top,  if  it  is  to  be  a  plain  block,  or  if  it  is  to  be  a  faced  block  the  backing  material 
is  struck  off  at  a  depth  of  }i  in.  below  the  top  and  the  facing  material  is  put  on  and  struck  off. 
The  box  is  then  rolled  on  the  track  to  the  center  of  the  machine  under  the  pressure  head. 
When  the  levers  are  released,  the  box  is  rolled  back  to  its  first  position.  A  pallet  is  placed  on 
top  and  clamped  in  position.  The  box  is  then  turned  over  and  lowered  so  that  the  pallet  rests 
upon  a  stand  placed  to  receive  it.    The  block  is  thus  released  face  downward  on  the  pallet. 

79a.  Tamping. — In  the  use  of  machines  in  which  block  are  compacted  by  means 
of  tamping,  this  tamping  is  done  in  three  ways:  (1)  by  hand  solely;  (2)  by  hand-operated  pneu- 


Sec.  2-80] 


GENERAL  METHODS  OF  CONSTRUCTION 


151 


natic  tampers;  or  (3)  by  means  of  machine  tampers  suspended  above  the  mold  box.  Hand- 
^amping  is  most  common,  the  common  type  of  tamper  (Fig.  107)  being  a  double-ended  instru- 
ment with  a  center  bar  for  a  handle,  and  with  one  narrow  spade-like  head  and  one  broad  flat 
lead,  the  narrow  head  being  used  beween  cores  and  the  broad  head  over  the  full  block  area 
Defore  and  after  the  cores  are  introduced.  In  hand  work,  everything  depends  upon  the  oper- 
itor  and  most  manufacturers  maintain  that  the  operator  relaxes  his  efforts  to  a  considerable 
extent  toward  the  end  of  the  day.  In  spite  of  this,  a  man  who  is  accustomed  to  this  work  gives 
3xcellent  results  with  hand-tamping. 

Machines  for  tamping  have  to  be  built  to  withstand  severe  jarring.  They  are  supported 
either  by  a  framework  from  the  floor  of  the  factory  or  suspended  from  a  framework  above. 
5uch  tampers  have  several  feet  at  the  ends  of  plungers  so 

arranged  as  to  fit  the  type  of  machine  in  use.  These  ff^ — I  pr^Tl 
I  plungers  strike  the  concrete  with  equal  force  over  the  ^ 

sntire  open  area  of  the  mold.     The  plungers  are  so  ad-  Fig.  io7. — Hand  tamp. 

:iusted  as  to  be  responsive  to  the  depth  of  the  material 

|.n  the  mold  box,  so  that  the  length  of  stroke  varies  as  the  mold  box  is  filled, 
j  80.  Gang  Molds  for  Wet-cast  Products. — A  type  of  equipment  for  making  wet-cast 
jproducts  that  is  coming  into  more  general  use  consists  of  gang  molds.  One  kind  is  mounted 
ipon  cars  (Fig.  105),  which  are  run  on  tracks  to  receive  the  concrete  at  the  mixer,  and  from  there 
io  curing  tunnels.  Another  kind  is  located  in  such  a  way  throughout  a  stretch  of  floor  as  to 
'equire  the  mixed  concrete  to.be  brought  to  the  molds.  This  process  thus  involves  either  the 
,jse  of  a  very  large  number  of  individual  molds  in  which  the  products  must  remain  arranged 
.jver  a  very  large  casting  area  for  from  12  to  48  hr.,  or  else  it  involves  the  use  of  molds  set  up 
n  such  a  way  that  they  may  be  conveyed  to  a  curing  place  when  they  are  filled.  When  the 
i products  have  become  hard,  the  molds  are  simply  taken  down  by  a  removal  of  the  core  pieces, 
sides  and  division  plates,  and  are  oiled  and  set  up  again,  either  on  platform  or  car. 
81.  Materials. 

« 

81a.  Cement — Storage  and  Conveying. — As  a  rule  concrete  products  manufac- 
turers are  satisfied  to  use  any  standard  brand  of  Portland  cement,  which  can  usually  be  de- 
pended upon  to  conform  to  the  specifications  of  the  American  Society  for  Testing  Materials. 
There  is,  however,  a  disposition  among  some  manufacturers,  particularly  those  making  a  high 
^lass  of  trim  stone  and  more  particularly  also  where  a  rather  wet  mixture  is  used,  to  select  their 
brand  of  cement  with  some  care.  Some  of  these  manufacturers  believe  that  some  brands  have 
1  tendency  to  cause  crazing,  which  is  one  of  the  bugbears  of  the  concrete  stone  manufacturer. 
No  manufacturer  has  been  found,  however,  who  can  explain  just  exactly  the  reason  for  his  pref- 
9rence  for  one  brand  over  another,  except  so  far  as  his  experience  has  seemed  to  show  that  the 
use  of  one  brand  resulted  in  less  crazing  than  another.  There  is  a  belief  among  some  manu- 
facturers that  a  cement  which  has  been  aged  much  longer  than  is  ordinarily  demanded  is  desir- 
able in  concrete  stone  manufacture  and  it  is  said  that  this  older  cement  is  less  likely  to  give 
hair-checking  or  crazing.  In  other  respects,  the  quality  of  cement  required  in  concrete  products 
manufacture  scarcely  differs  from  that  in  general  concrete  work. 

In  a  small  plant  the  cement  is  ordinarily  stored  on  a  platform  as  near  as  possible  to  the 
level  of  the  hopper  which  feeds  the  mixer.  This  may  be,  in  some  plants,  at  the  second  floor 
level,  chutes  being  used  for  cement  as  well  as  aggregates,  or  it  may  be  at  a  level  between  the 
first  and  second  floor,  determined  by  the  level  of  the  mixer  itself.  If  stored  in  bags  on  the  second 
floor  level,  an  elevator  of  some  kind  is  provided  unless  the  plant  is  so  small  as  not  to  warrant 
the  use  of  equipment  of  this  kind.  It  is  possible,' sometimes,  to  have  a  railway  siding  on  a 
trestle  and  to  use  gravity  conveyors  with  ball-bearing  rollers  to  carry  pallets  bringing  bags  of 
cement.  With  an  arrangement  of  this  kind,  the  cement  is  brought  into  the  storage  space 
direct  from  the  car  with  very  little  handling.  In  another  plant  the  track  may  be  slightly 
above  the  level  of  the  floor  on  which  the  mixer  stands;  or,  even  with  it  on  the  same  level,  it  is 
possible  to  build  a  platform  at  the  level  of  the  car  floor  and  to  pile  bags  of  cement  in  such  a 


152 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-816 


way  that  they  may  be  emptied  into  a  cart  filled  with  gravel  from  a  bin  along  the  side  and  dumped 
into  a  mixer  which  stands  just  under  the  platform. 

Bulk  cement  has  not  been  used  extensively  in  products  manufacture  but  has  been  very 
successfully  used  by  a  few.  The  cement  may  be  scraped  from  the  door  of  the  car  into  a  chute 
feeding  into  the  bottom  of  an  elevator  boot,  the  elevator  lifting  the  cement  into  a  bin  in  the 
top  of  the  plant  from  which  it  falls  by  gravity  into  a  measuring  box  above  the  mixer  hopper. 
In  another  plant  the  cement  has  been  loaded  from  the  car  to  wheelbarrows,  handled  over  a 
runway  to  the  hopper  of  a  mixer.  Where  the  output  of  the  plant  is  large  enough  and  it  has 
been  possible  to  hold  a  car  to  use  up  its  entire  contents,  this  handling  of  the  cement  has  been 
very  economical.  When  this  has  not  been  possible,  the  cement  has  been  dumped  from  the  wheel- 
barrows into  a  bin  close  to  the  mixer  from  which  it  is  shoveled  into  the  mixer  hopper. 

816.  Aggregates — Kind  and  Quality. — In  the  main,  the  aggregates  used  in  the 
general  field  of  concreting,  are  suitable,  except  as  to  size,  for  concrete  products  manufacture. 
In  general,  fine  materials  are  used  throughout  the  concrete  products  field.  Better,  cheaper 
products  can  of  course  be  made  when  larger  aggregate  can  be  used,  the  maximum  size  equal 
to  one-half  the  smallest  dimension  of  the  product. 

Aside  from  quality  as  to  cleanness,  hardness,  and  so  on,  the  concrete  products  manufacturer 
has  been  most  concerned  with  the  consistency  of  the  mixture  with  which  the  size  and  quality 
of  the  aggregate  have  a  great  deal  to  do.  A  very  dry  mixture  on  one  hand  and  a  very  wet  mix- 
ture on  the  other — both  of  them  more  common  in  the  field  of  products  manufacture  than  any 
intermediate  mixture — have  both  been  an  influence  in  favor  of. rather  fine  materials.  Most 
manufacturers  using  dry-tamp  equipment  appear  to  be  convinced  that  coarse  materials  cannot 
be  successfully  used  in  a  mixture  containing  little  water  because  of  a  tendency  of  coarse  mate- 
rials to  fall  out  of  the  product  on  removal  from  the  molds  and  to  cause  a  high  percentage  of 
breakage. 

Crushed  limestone,  especially  when  there  is  a  rather  high  percentage  of  fine  material,  un- 
doubtedly permits  the  use  of  more  water  than  does  sand.  It  is  still  a  question  whether  or  not 
the  excess  of  moisture  used  in  a  mixture  of  such  material,  becomes  available  for  the  hydration 
of  the  cement  in  the  curing  period  which  follows  the  molding. 

The  prevalent  belief  is  that  a  high  percentage  of  fine  materials  should  not  be  used,  the 
usual  specifications  being  that  a  percentage  no  higher  than  5  or  10%  passing  a  100-mesh  screen 
shall  be  used  in  the  fine  aggregate. 

The  most  desirable  qualities  in  concrete  building  units  are,  of  course,  strength  and  the 
quality  of  resisting  the  attacks  of  the  elements,  to  the  end  that  they  will  not  disintegrate  the 
concrete  nor  spoil  its  beauty  through  absorption  of  discolorative  agents. 

Bank-run  and  crusher-run  materials  should  not  be  used.  It  is  important  that  a  concrete 
products  manufacturer's  output  be  of  even  quality.  To  this  end  he  should  maintain  a  constant 
supply  of  an  aggregate  of  uniformly  high  quality,  grading  in  size  from  fine  to  coarse.  Any 
amount  of  tamping  or  pressing,  or  care  in  puddling  and  pouring,  or  in  placing  the  concrete, 
is  entirely  unavailing  if  these  operations  have  not  been  preceded  by  scrupulous  care  in  the  choice, 
grading,  and  mixture  of  the  materials,  as  essential  to  securing  density  in  the  product.  It  is 
strongly  recommended  in  connection  with  this  chapter  that  reference  be  had  to  the  chapter 
on  "Aggregates"  in  Sect.  1  and  the  chapter  on  ''Proportioning"  in  Sect.  2,  as  these  chapters 
treat  in  detail  of  the  selection  and  grading  of  the  materials  in  order  to  obtain  the  best  results. 
No  manufacturer  should  determine  his  proportions  arbitrarily  but  should  first  examine  or  have 
examined  samples  of  the  material  which  he  proposes  to  use  and  which  he  has  reason  to  believe 
will  come  to  him  in  unvarying  quality.  To  make  sure  that  this  quality  is  unvarying,  frequent 
tests  should  be  made  to  determine  the  grading  which  should  precede  any  decision  as  to  the  pro- 
portions in  the  mixture. 

82.  Mixing. — No  one  in  the  concrete  field  has  a  wider  latitude  in  selecting  mixing  equip- 
ment than  the  concrete  products  manufacturer.    His  plant  is  stationary,  the  requirements  of 


Sec.  2-82o] 


GENERAL  METHODS  OF  CONSTRUCTION 


153 


the  plant  are  more  or  less  regular;  and  he  has  no  problems  of  getting  about,  here  and  there, 
under  varying  conditions. 

82a.  Mixers — General  Type. — The  commonest  types  of  mixers  in  concrete 
products  plants  are  those  with  the  simple  cylindrical  drums  in  which  a  comparatively  dry  mix- 
I  ture  of  concrete  ordinarily  is  turned  out,  and  the  continuous  mixer,  for  a  long  time  much  despised 
in  the  general  field.    In  many  concrete  products  factories  where  a  wet  mixture  is  being  turned 
^  out  in  large  quantities,  types  of  mixers  are  used  similar  to  those  found  in  large  construction 
'  work  in  the  field.    In  addition  to  these  types,  the  small  cylindrical  mixer  for  handling  facing 
materials  is  common  in  almost  every  concrete  products  factory.    There  are  frequently  two  or 
three  of  these  so  that  they  may  be  used  for  facing  mixtures  of  various  kinds  without  change. 
In  connection  with  the  mixers  employed  there  is  one  thing  which  is  perhaps  unique  in  the  prod- 
ucts field  and  that  is  the  adaptation  of  some  of  the  best-known  makes  of  continuous  mixers  to 
the  specific  needs  of  the  factory  in  which  they  are  used.    Local  mechanical  ability  in  each  case 
I  has  been  able  to  set  up  these  machines  so  as  to  give  very  satisfactory  results.    Not  only  has 
'  the  flow  of  dry  materials  been  fixed  under  close  control  but  the  water  is  added  in  definite 
quantity  to  give  a  continuous  flow  of  a  like  mixture.    It  is  almost  invariable  that  the  use  of  a 
continuous  mixer  in  a  concrete  products  factory  requires  the  erection  of  bins  and  hoppers  over 
those  with  which  the  machine  is  equipped. 

j  826.  Mixing  Dry  and  Mixing  Wet. — It  is  coming  to  be  more  general  practice  to 

Imix  the  concrete  materials  dry  in  one  mixer  and  to  add  the  water  in  a  second  mixer.  In  a  plant 
where  stone  of  a  very  high  quality  is  manufactured,  materials  are  stored  on  the  second  floor. 
They  are  shoveled  into  a  car  in  definite  proportions  with  the  cement  on  top.  This  car  is  shoved 
along  the  track  in  front  of  the  bins  from  which  the  materials  are  obtained  and  is  dumped  into 
a  cylindrical  drum  mixer  where  the  materials  are  mixed  dry.  They  are  then  dropped  through 
'  a  chute  to  a  continuous  mixer  on  the  first  floor  where  the  water  is  added,  the  quantity  of  water 
being  very  carefully  gaged  to  give  a  like  consistency  all  the  time. 

Long  and  thorough  mixing  is  particularly  important  in  concrete  products  manufacture 
where  a  homogeneous  mixture  of  like  color  throughout  is  particularly  desirable.  Mixing  the 
materials  dry  and  then  adding  water  in  another  mixer  is  almost  sure  to  make  for  greater 
thoroughness  in  a  combination  of  the  materials. 

82c.  Agitation  Subsequent  to  Mixing  in  Wet-cast  Work. — Where  materials  are 
mixed  wet  for  casting  in  sand  molds,  it  is  highly  important  that  the  agitation  of  the  mixture  be 
continued  so  as  to  prevent  segregation  of  the  materials.  Even  in  mixtures  where  the  size  of 
stone  is  little  more  than  in.,  it  is  impossible  in  the  wet  mixture  which  is  used,  to  prevent  rhis 
stone  settling  to  the  bottom  of  the  receptacle  as  it  is  poured  out  from  the  mixer.  For  this  reason 
it  is  common  practice  to  provide  some  means  of  keeping  this  mix  agitated  up  to  the  time  it 
is  placed  in  the  molds.  In  the  largest  plants  this  is  done  in  an  auxiliary  mixer  travelling  on  an 
overhead  crane,  driven  by  an  electric  motor — really  a  mixer  in  itself.  It  takes  the  materials 
from  the  mixer  proper,  keeps  them  constantly  agitated  until  the  mix  is  deposited  through  a 
pipe  3  or  4  in.  in  diameter  to  molds  in  a  sand  bed.  In  smaller  plants  where  such  equipment 
seems  unwarranted,  it  is  common  to  use  a  large  wooden  cask  either  swung  from  a  travelling 
hoist  or  mounted  on  a  truck  moving  about  on  tracks  through  the  casting  area.  A  workman 
simply  turns  a  crank  operating  paddles  to  keep  the  mixture  agitated  while  it  is  being  run  off 
through  a  spigot  into  the  molds. 

82(i.  Mixing  Facing  Materials. — There  are  small  cylindrical  drum  mixers  specially 
provided  for  mixing  facing  materials  in  small  batches.  Thorough  mixing  of  the  facing  mixture  is  ■ 
highly  desirable  so  that  there  may  be,  in  the  case  of  special  aggregates  or  the  use  of  color  in  any 
form,  a  thorough  distribution  of  the  material  in  order  that  it  will  not  be  spotted  or  in  any  way 
uneven  either  in  color  or  in  texture.  In  the  coarse-textured  concrete  stone,  which  is  becoming 
more  popular,  the  mixture  used  is  comparatively  lean  in  cement  and  thorough  mixing  is,  there- 
fore, necessary  to  be  sure  of  cementing  the  particles  in  place.    These  products  are  afterward 


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brushed  and  it  is  important  that  the  mixing  be  thorough  so  as  to  be  sure  of  embedding  the  stone 
particles. 

83.  Placing. — In  a  small  concrete  products  plant  where  perhaps  but  two  hand-operated 
block  machines  are  used,  and  where  only  two  men  may  be  employed  at  this  work,  it  is  not 
uncommon  to  operate  the  mixer  for  a  short  period;  pile  up  a  batch  of  concrete  in  front  of  the 
two  machines  and  shovel  it  from  the  floor  direct  in  the  machines,  each  workman  serving  him- 
self at  this  labor.  This,  however,  is  not  the  way  of  the  modern  concrete  products  plant  which 
does  away  as  much  as  possible  with  wasteful  hand  methods,  and  by  increasing  the  capacity 
and  output  of  the  plant  and  increasing  the  quantity  of  machinery  used,  lowers  the  cost  of  the 
product  and  in  most  cases  improves  its  quality. 

83a.  Buckets  and  Hoppers. — In  the  majority  of  concrete  products  factories, 
the  mixed  concrete  is  conveyed  from  the  mixer  by  a  bucket  travelling  by  a  trolley  system  to  serve 
the  trim  stone  department  and  a  row  of  block  machines.  From  this  travelling  bucket  the  con- 
crete is  deposited  in  4  to  5-cu.  ft.  batches  in  hoppers  feeding  to  sloping  tables  just  behind  the 
block  machines  (Figs.  108  and  109),  the  operators  of  the  machines  scraping  the  mixed  concrete 
into  the  mold  boxes  with  very  little  lost  effort. 


Fia.  108. — Factory  layout.    (Block  department  in  background.) 

R  =  Curing  rooms. 

S  =  Second  floor,  or  rather  an  intermediate  floor  above  curing  rooms  where  a  battery  of  mixers  (5)  are  located: 
E  =  Elevator  for  boxes  of  mixed  facing  material. 

B  =  Bucket  (a  part  of  an  electric  monorail  system)  for  delivering  mixed  concrete  to  machines  and  at  bankers. 
H  =  Hoppers  to  receive  mixed  concrete. 
C  =  Block  car. 

In  a  large  factory,  where  there  are  several  block  machines,  and  a  large-dimension  stone 
department,  there  is  a  battery  of  mixers  at  an  intermediate  level  between  the  first  floor  and  the 
second  floor,  so  arranged  that  the  raw  materials  come  in  by  conveyor  belting  at  the  level  of  the 
hoppers  over  the  various  continuous  mixers.  The  mixed  concrete  is  fed  into  buckets  which  are 
hooked  to  a  monorail  system  operated  electrically  so  that  any  workman  anywhere  in  the  large 
molding  room  can  have  a  box  of  mixed  concrete  delivered  to  him  suited  to  his  special  work,  j 
by  means  of  tracks  and  switches  controlled  from  the  starting  point.  The  empty  buckets  are 
then  returned  to  be  refilled.  This  is  an  elaborate  system  and  an  expensive  installation.  Few 
existing  factories  probably  have  an  output  to  warrant  it.  In  a  factor}'-  making  but  one  type 
of  units  a  conveyor  belt  brings  the  mixed  material  from  mixer  to  machines. 

The  market  offers  machinery  which  couples  the  block  machine  with  elevating  equipment 
and  delivers  concrete  direct  from  the  mixer  to  a  hopper  in  the  top  of  the  machine  and  drops  it  as 
required  into  the  mold  box  under  the  tampers.  Such  equipment  is  usually  coupled  with  machine 
tampers. 


ec.  2-83ftJ 


GENERAL  METHODS  OF  OONSTRVCTlON 


155 


836.  Wheelbarrows.— It  is  far  more  common  in  factories  which  put  most  of 
heir  effort  on  dimension  stone,  to  find  that  concrete  is  handled  chiefly  in  wheelbarrows.  One 
f  the  largest  wet-cast  stone  factories  in  the  East,  and  one  of  the  largest  factories  making  dry- 
amp  dimension  stone  in  the  Middle  West,  make  use  of  wheelbarrows  in  transporting  the 
lixed  concrete  to  the  molds.  In  the  case  of  the  wet  concrete,  four  pails  are  carried  in  a  barrow, 
'he  situation  is  quite  different,  however,  in  various  localities  in  respect  to  labor,  and  the  situa- 
ion  is  also  affected  by  the  fact  that,  in  a  factory  making  dimension  stone  which  is  to  sell  in 
ompetition  with  natural  stone,  the  actual  labor  in  molding,  tamping,  and  finishing  is  much 
More  per  cubic  foot  of  concrete  than  is  the  ordinary  standard  product  made  in  machines.  The 
ulk  of  the  concrete  handled  is,  therefore,  of  less  consequence  than  where  standard  units  are  the 
hief  products. 

83c.  Pallets.— The  pallets  used  in  standard  block  machines  and  brick  machines 
re  commonly  of  two  kinds— wood  and  iron.    The  pallets  stand  repeated  changes  from  wet  to 

':ry  and  are  subject  to  severe  wear.  If  iron  pallets  are  neglected,  they  become  coated  with  rust 
nd  concrete  so  as  to  be  useless.    It  is  recommended  that  to  keep  iron  pallets  in  proper  con- 

jlition  they  should  be  kept  coated  with  paraffine  oil,  or  that  they  be  dipped  in  a  mixture  of 


Fig.  109. — Block  machines  with  hoppers  above  are  shown  in  the  background  and  block  cars  in  the  foreground, 
^ote  the  two  floor  levels.  The  cars  run  on  tracks  into  pits  so  that  four  decks  can  be  loaded  without  too  high  a 
each.    The  empty  "decks"  from  the  car  at  the  left  are  placed  on  the  car  at  the  right  as  it  is  piled. 

ierosene  and  axle  grease,  when  the  concrete  can  easily  be  wiped  off  at  the  end  of  each  day's 
rvork.  The  same  treatment  is  recommended  for  the  metal  parts  of  the  block  machine.  An- 
)ther  manufacturer  suggests  that  iron  pallets  be  dipped  in  a  solution  of  1  part  lard  oil  and  1 
3art  kerosene,  to  keep  the  pallets  clean  and  to  prevent  rusting.  With  wood  pallets,  the 
hfiiculties  are  from  swelling,  splintering,  warping  and  so  on.  It  is  necessary  to  use  wood  which 
s  as  little  subject  to  warping  as  possible,  and  have  the  pallets  well  treated  in  order  to  overcome 
varp  so  far  as  it  can  be  done.  It  is  pointed  out  that  pallets  should  not  be  made  of  one  solid 
jiece  but  of  strips  not  more  than  4  in.  wide,  with  slightly  open  joints  to  allow  for  some  expan- 
lion.  Some  manufacturers  recommend  dipping  wood  pallets  into  hot  linseed  oil.  Difficulty 
rom  slight  swelling  of  the  pallets  is  not  important  except  in  machines  where  pallets  must  fit 
^ery  accurately  as  is  not  the  case  with  most  tamp  machines.  There  are  machines,  however, 
vhere  the  pallets  must  fit  with  great  nicety  and  in  such  cases  considerable  difficulty  has  been 
ixperienced  in  getting  a  pallet  which  will  resist  the  severe  treatment.  One  manufacturer 
uffering  such  conditions  finallj^  adopted  a  combination  wood  and  metal  pallet. 

Most  blocks  are  delivered  on  a  pallet  right  side  up,  face  perpendicular  as  they  will  be  laid 


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[Sec.  2-83d 


in  a  wall.  The  condition  of  the  pallet  in  this  case  is  not  so  important.  Where,  however,  the 
block  is  turned  over  face  down  and  delivered  on  a  pallet  in  that  position,  it  is  very  important, 
particularly  for  face  block,  that  the  pallet  be  very  true,  and  metal  pallets  are  recommended 
for  such  work  where  a  true,  smooth  face  is  required.  For  rough-textured  block,  this  is,  of 
course,  not  necessary, 

^Zd.  Bankers. — Practically  all  dimension  stone  is  made  in  special  molds,  these 
molds  resting  on  heavy  plank  pallets,  supported  in  turn  by  bankers  which  may  be  of  reinforced 
concrete  to  minimize  vibration.  Such  bankers  are  used  in  factories  where  dimension  stone  is 
made  by  the  dry-tamp  process.  For  work  of  this  kind,  the  placing  of  the  concrete  is  much 
slower  than  with  wet-cast  work,  as  the  facing  materials  have  to  be  built  up  vertically  2  or  3  in.  at 
a  time  on  such  faces  of  the  stone  as  are  to  be  exposed,  besides  placing  on  the  bottom,  and  the 
backing  must  be  tamped  in  as  the  facing  is  brought  up.  Thus  for  the  convenience  of  the 
workmen  the  mold  is  placed  on  bankers  at  a  height  which  is  convenient  for  his  work. 

84.  Curing. — In  from  20  min.  to  1  hr.  after  water  has  been  added  and  the  mixing  of  con- 
crete completed,  this  mixture  must  be  placed  and  it  must  not  only  be  so  handled  subsequently 
as  not  to  disturb  the  hardening  process  but  it  must  be  kept  in  a  condition  which  will  aid  that 
process.  Conditions  for  curing  must  be  such  that  the  product  will  not  be  rapidly  dried,  yet 
as  temperature  influences  the  hardening — heat  quickening  it,  cold  retarding  it,  and  freezing 
interrupting  the  hardening  process  for  the  period  in  which  the  low  temperature  continues — it 
is  important  that  these  things  be  considered  in  caring  for  products  when  they  have  been  molded  : 
or  cast. 

The  problems  of  curing  do  not  present  themselves  as  so  serious  a  matter  to  the  manufacturer 
of  wet-cast  stone  as  to  the  manufacturer  of  dry-tamp  products.  In  the  wet-cast  work  where 
there  is  already  an  excess  of  moisture,  sufficient  heat  is  practically  the  only  essential,  with  con- 
ditions which  will  prevent  too-rapid  drying.  In  tamp  products,  and  for  the  most  part  in  pressed 
products  where  the  moisture  entering  the  mixture  is  only  just  about  (or  even  a  little  less  than) 
that  actually  required  for  thorough  hydration,  it  is  very  important  that  none  of  this  moisture 
be  permitted  to  escape  before  complete  hydration. 

In  curing  wet-cast  stone,  block,  and  brick  made  in  gang  molds  on  cars,  one  method  is  to 
move  these  cars  on  tracks  to  curing  tunnels  which  are  heated  by  steam.  The  tunnels  are  made 
of  concrete  and  just  high  enough  to  admit  loaded  cars.  They  are  heated  to  give  a  rapid  hard- 
ening of  the  concrete.  The  cars  are  usually  removed  24  hr.  after  they  are  placed  in  the  tunnels, 
the  molds  are  taken  down,  and  the  products  are  carefully  piled  under  sheds.  The  molds  are 
oiled,  set  up  again  on  the  cars  and  returned  to  the  mixer  to  be  refilled.  In  other  wet-cast  work, 
where  gang  molds  on  cars  are  not  employed,  or  where  other  molds  are  used  with  a  wet  mixture 
on  a  large  casting  floor,  it  is  common  to  leave  these  molds  in  place  until  the  product  is  suffi- 
ciently hard  to  be  handled.  The  molds  prevent  a  rapid  escape  of  moisture  in  the  early  stages  i 
of  hardening,  and  particularly  is  this  true  in  sand  cast  work,  where  the  sand  is  always  damp 
from  having  absorbed  the  excess  moisture  of  the  mixture. 

84a.  Natural  Curing. — The  recommendations  in  the  old  "Standard  Practice" 
of  the  American  Concrete  Institute  with  respect  to  natural  curing  are  usually  regarded  as  sound. 
They  are  as  follows: 

Natural  Curing. — The  concrete  products  shall  be  protected  from  the  sun  and  strong  currents  of  air  for  a  period 
of  at  least  7  days.  Throughout  this  period  they  shall  be  sprinkled  at  such  intervals  as  is  necessary  to  prevent  dry- 
ing, and  maintained  at  a  temperature  of  not  less  than  50°F.  Such  other  precautions  shall  be  taken  a^  to  enable  the 
hardening  to  take  place  under  the  most  favorable  conditions.  Products  must  not  be  removed  from  the  yard  until 
they  are  21  days  old. 

Where  products  are  cured  in  this,  way,  it  is  necessary  that  racks  or  cars  be  used  so  that 
block  on  the  pallets  may  be  piled  up  in  tiers.    As  standard  practice  requires  that  products  be  \ 
sprinkled  for  7  days,  it  is  obvious  that  there  must  be  curing  shed  space  for  7  days'  output  and 
a  very  large  yard  storage  space  in  order  to  keep  products  until  21  days  old.    Building  regula- 


I 


5ec.  2-846]  GENERAL  METHODS  OF  CONSTRUCTION  157 

ions  in  numerous  cities  require  that  products  be  at  least  30  days  old  when  cured  in  this  way, 

\  vithout  regard  to  the  crushing  strength. 

Inasmuch  as  this  method  of  curing  would  require  the  use  of  a  very  large  number  of  cars 

,  )n  which  to  tier  up  the  products,  it  is  common,  when  natural  curing  is  used,  to  apply  the  rack 
;ystem  of  storage.  It  will  be  obvious  that  this  can  be  used  only  in  rather  small  plants.  The 
•acks  are  usually  built  of  2  by  4's,  each  rack  16  to  20  ft.  long.  One  rack  can  thus  readily 
iccommodate  26  blocks  8  by  8  by  16  in.  These  racks  can  be  piled  about  four  high.  Four 
•Qws  of  racks  will  thus  accommodate  about  400  blocks. 

:  With  natural  curing,  the  products  are  either  moved  on  cars  and  placed  upon  racks,  or  are 
;arried  on  pallets  direct  from  the  machine  to  the  racks.  This  latter  method  can  only  be  used 
n  the  smallest  plants  because  the  labor  of  carrying  the  block  the  distance  required  by  racking 

I  n  a  large  plant  would  make  the  cost  excessive. 

Sometimes  products  are  made  which  are  too  large  or  too  heavy  or  of  too  awkward  shape 

;  or  removal  to  curing  sheds.  Until  hardening  has  progressed  to  a  considerable  extent  precau- 
ion  should  be  taken  to  see  that  these  products  are  kept  under  suitable  conditions  to  attain 

!  strength.  When  left  in  the  molding  room,  the  products  should  be  covered  with  wet  cloths 
md  the  cloths  kept  wet.  This  applies  particularly  to  tamp  products  where  the  molds  are 
-emoved  a  day  or  so  after  manufacture.    Sprinkling  may  be  done  systematically  and  thoroughly 

\N\ih.  a  nozzle,  which  gives  a  fine,  well-diffused  spray.    The  nearer  the  spray  approximates  a 

'ioating  mist  the  more  thoroughly  it  will  do  the  work,  reaching  all  the  surface  of  products 
stored  in  tiers  on  racks  or  cars. 

!  Where  the  products  are  removed  to  sheds  and  cured  in  the  natural  way,  it  is  obvious  that 
jonsiderable  labor  will  be  required  to  use  the  hose  on  the  products  and  it  would  be  difficult  to 
ase  the  hose  in  any  effectual  way.  It  is  common,  therefore,  to  install  permanent  sprinklers 
m  the  curing  sheds. 

In  an  Eastern  factory  turning  out  high-class  products  from  wood  and  plaster  molds,  the 
time  for  the  products  to  remain  in  the  molds  is  from  5  hr.  for  small  units  up  to  24  to  48  hr.  for 
the  larger  and  more  complicated  pieces.  Until  the  molds  are  removed  it  is  not  necessary  to 
ipply  additional  water  to  prevent  the  escape  of  the  moisture  contained  in  the  product  because 
there  is  considerable  water  used  in  the  mix.  As  soon  as  the  molds  are  removed,  sprinkling 
oegins,  using  a  fine  spray.  This  factory,  which  is  of  old  construction,  has  wooden  columns 
ibout  10  ft.  apart  in  each  direction.  Pipes  have  been  placed  so  that  there  is  a  water  outlet  at 
3very  column.  A  man  is  kept  busy  all  day  sprinkling  the  products  and  another  man  continues 
the  work  at  night.    Great  care  is  taken  to  keep  the  products  moist  until  they  dry  out  evenly. 

In  some  ornamental  work,  manufacturers  frequently  make  use  of  total  immersion  of  prod- 
acts  to  cure  them.  It  is  common  in  such  cases  to  cover  the  product  with  wet  cloths  just  as 
soon  as  it  has  been  removed  from  the  mold  and  allow  it  to  remain  in  this  way  until  it  has  at- 
tained sufficient  strength  to  be  handled  and  placed  in  the  tank.  Other  manufacturers  do  not 
use  the  immersion  system  but  simply  use  the  wet  cloths. 

846.  Steam  Curing. — General  practice  in  steam  curing  makes  use  of  a  wet  steam 
and  a  low  pressure  to  create  a  dense  warm  fog  with  all  the  moisture  which  can  be  introduced  at  a 
temperature  in  the  curing  rooms  between  100°  and  130°F.  While  common  practice  in  the  field 
does  not  warrant  the  use  of  high-pressure  steam  and  while  investigations  with  high-pressure 
steam  in  curing  have  not  gone  far  enough  to  suggest  its  adoption  on  a  commercial  basis,  there 
has  been  some  investigation  tending  to  show  that  steam  under  pressure  up  to  80  lb.  can  be 
ased  with  success.  This  steam  has  to  be  employed  in  steam-tight  compartments.  The  ordi- 
aary  curing  rooms  of  the  concrete  products  plant  are  not  steam-tight.  They  are  wide  enough 
to  accommodate  the  cars  which  usually  run  on  24-in.  track  and  high  enough  to  permit  four 
decks  of  standard  block  to  be  piled  on  the  cars,  leaving  some  room  for  the  accommodation  of 
special  products  to  which  it  may  be  necessary  to  give  steam-curing  treatment.  The  curing 
tunnels  of  the  plant  are  usually  about  60  to  90  ft.  long,  built  of  concrete  block,  with  arched  or 
"  A-shaped  "  ceiling— preferably  a  ceiling  made  by  applying  Portlant-cement  plaster  to  a  ribbed 


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[Sec.  2-846 


reinforcing  mesh.  The  ceihng  is  built  so  as  to  carry  the  condensed  moisture  of  the  room 
to  the  sides  and  away  from  the  fresh  products  which  dripping  would  damage.  Curing 
rooms  are  sometimes  built  wide  enough  to  accommodate  two  or  even  three  tracks,  so  laid  out 
that  in  the  case  of  very  wide  products  to  be  admitted  to  a  curing  room,  only  the  middle  track 
can  be  used,  allowing  plenty  of  room  for  the  projection  of  the  products  at  the  sides.  At  one 
end  the  curing  rooms  usually  open  into  the  molding  department  as  convenient  as  possible  to 
the  machines  supplying  the  greatest  number  of  products  to  be  cured,  and  the  other  end  fre- 
quently opens  into  a  passageway  connecting  with  the  yard,  or  to  the  yard  direct. 

The  construction  of  the  doors  has  given  concrete  products  manufacturers  considerable 
difficulty  from  time  to  time,  due  to  the  fact  that  metal  doors  rust,  unless  kept  in  perfect  condi- 
tion, wooden  doors  swell  with  the  steam  on  one  side  while  they  remain  dry  and  of  their  original 
size  on  the  other  side,  and  canvas  curtains  are  very  short-lived.  These  curtains  roll  up  and 
are  fastened  at  the  sides,  usually,  with  carriage  buttons.  In  using  them,  allowance  has  to  be 
made  for  shrinkage.  Galvanized  sheet  metal  for  doors  lightly  framed  with  wood,  or  small 
angle  irons,  have  given  satisfaction. 

The  following  recommendations  of  the  American  Concrete  Institute  with  respect  to  steam 
curing  were  made  some  time  ago  but  are  still  considered  as  representing  good  practice. 

The  products  shall  be  removed  from  the  molds  as  soon  as  conditions  will  permit  and  shall  be  placed  in  a 
steam-curing  chamber  containing  an  atmosphere  of  steam  saturated  with  moisture  for  a  period  of  at  least  48  br. 
The  curing  chamber  shall  be  maintained  at  a  temperature  between  100°  and  130°F.  The  products  shall  then  be 
removed  and  stored  for  at  least  8  days.    (This  does  not  apply  to  high-pressure  steam  curing.) 

From  an  excellent  discussion  of  the  proper  use  of  steam  in  curing  concrete  products,  the 
following  by  W.  M.  Kinney  in  Concrete  is  quoted: 

The  principal  object  in  curing  concrete  products  with  steam  is  to  accelerate  the  hardening  by  means  of  heat 
without  endangering  the  concrete  through  loss  of  moisture  by  evaporation.  Saturated  steam  will  provide  not  only 
heat  but  sufficient  moisture  to  insure  against  injury  from  drying. 

In  the  early  history  of  concrete  products  manufacture  it  was  customary  to  use  exhaust  steam  for  heating  the 
curing  chamber,  but  as  a  sufficient  quantity  was  not  always  to  be  procured,  the  natural  resort  was  to  use  steam  direct 
from  the  boiler.  The  records  show  that  in  many  cases  large  quantities  of  good  concrete  came  to  grief  due  to  its 
drying  action,  which  was  not  at  that  time  explained. 

Especially  difficult  is  the  maintenance  of  a  sufficient  quantity  of  steam  in  a  boiler  at  low  pressure  to  heat 
sufficiently  any  number  of  curing  rooms.  Coupled  with  this  difficulty  is  the  danger  of  the  pressure  rising  con- 
siderably above  that  necessary  for  proper  curing.  With  this  in  view  we  have  been  recommending  steam  under 
pressure,  that  is,  around  30  to  45  lb.,  provided  it  be  admitted  through  water. 

The  most  satisfactory  way  of  admitting  steam  in  this  manner  is  through  a  perforated  pipe  embedded  in  a 
trough  of  water  running  through  the  center  or  along  the  sides  of  the  curing  chamber.  The  floor  should  be  so  sloped 
that  any  water  or  condensation  on  the  products  or  on  the  walls  of  the  curing  chamber  will  be  returned  to  the  trough 
for  re-evaporation.  In  this  manner  the  trough  is  automatically  kept  full  of  water  and  we  have  yet  to  record  a  case 
of  trouble  when  this  method  of  curing  was  employed.  All  of  the  heat  which  the  steam  contains  on  being  emitted 
is  taken  up  immediately  by  the  water  and  the  result  shown  by  evaporation.  The  temperature  of  the  water  is  at 
the  boiling  point  due  to  the  fact  that  steam  is  continually  being  forced  through  it  and  what  heat  is  taken  up  by  the 
water  is  used  in  evaporating  the  water.  This  water  evaporated  at  212°F.  is  just  as  useful  in  warming  the  room  as 
is  the  steam  at  the  same  temperature. 

To  explain  the  drying  action  of  steam  under  pressure  when  admitted  to  the  curing  chamber,  let  us  assume  that 
we  are  taking  steam  from  a  boiler  operating  at  30-lb.  gage  pressure.  The  temperature  of  the  steam  in  the  boiler 
is  252°  atmospheric  pressure.  It  is,  of  course,  understood  that  steam  under  atmospheric  pressure  and  having  a 
temperature  of  252°  is  in  an  abnormal  condition  which  we  technically  call  superheated.  This  steam  is  in  a  similar 
condition  to  that  which  would  be  obtained  if  water  vapor  at  212°  were  heated  up  to  252°  away  from  contact  with 
water.  Naturally  the  first  thing  that  steam  in  this  condition  does  is  to  avail  itself  of  the  first  opportunity  to  reach 
normal  conditions  and  the  most  ready  way  is  to  absorb  water  from  anything  in  its  vicinity  which  is  so  possessed. 
The  result  is  a  drying  out  of  the  concrete  products  which  happen  to  be  stored  in  the  vicinity. 

Another  method  of  introducing  steam  into  curing  rooms  is  described  by  A.  E.  Cline  as 
follows : 

The  simplest  way  is  to  have  a  main  pipe  over  the  top  of  the  curing-room  doors,  then  from  this  lead  a  separate 
IH-in.  pipe  to  each  room.  Run  this  along  one  of  the  walls  close  to  the  floor  but  with  slant  enough  to  drain  to  the 
farther  end.    Join  each  length  with  a  T,  having  the  third  hole  of  the  T  reduced  to  }4  in.  and  turn  this  at  right  angles 


ec.2-85]  GENERAL  METHODS  OF  CONSTRUCTION  159 

5  the  wall.  The  1  J^-in.  pipe  can  be  reduced  to  1  in.  at  half  the  length  of  the  room,  and  this  on  a  supposition  that 
lie  curing  room  is  80  ft.  long.  If  using  steam  for  power,  have  this  main  pipe  connected  with  the  exhaiLst  during 
he  day  and  with  the  boiler  at  night.  If  the  boiler  pressure  at  night  is  greater  than  10  lb.  it  is  best  to  have  a 
sducing  valve  in  the  main  line  as  high  pressure  is  not  wanted. 

85.  Special  Molds. — Although  the  commercial  market  affords  a  wide  range  of  machines  for 
(lolding  various  concrete  units  and  a  large  number  of  special  molds — not  only  for  sills,  lintels, 
,nd  so  on,  used  in  building,  but  for  various  ornamental  objects  and  special  architectural  pieces 
-the  progressive  concrete  products  manufacturer  no  longer  considers  that  his  plant  is  fully 
quipped  until  he  has  a  department  for  making  molds  to  meet  the  demands  of  architects  in 
urning  oiit  dimension  stone  according  to  special  designs  as  may  be  required. 

85a.  Wood  Molds. — ^The  material  most  commonly  used  in  making  these  molds 
or  dimension  stone  is  wood  and  a  large  plant  will  have  an  extensive  wood-working  department 
vith  power  saws,  planers,  etc.,  for  cutting  down  the  labor  cost.  By  far  the  greater  part  of 
limension-stone  work  in  most  factories  will  be  made  in  wood  molds — preferably  white  pine, 
rhis  will  include  sills,  lintels,  belt  courses,  cornices  and  so  on.  In  general,  for  a  plain  piece  of 
v^ork  the  mold  consists  of  side  planks  resting  on  a  pallet  with  end  pieces  fitting  inside  (see 
ng.  110). 

All  pieces  have  to  be  carefully  finished,  all  small  holes  or  cracks  filled,  ordinarily  with 
)laster,  the  entire  work  shellacked  and  then  oiled  before  use.  By  clamping  the  side  pieces 
irmly,  the  end  pieces  are  held  in  place  on  the  outside  against  cleats. 
vVhen  the  facing  mixture  has  been  placed  on  the  bottom  of  the  mold 
md  up  the  front  side  and  part  way  on  the  ends,  as  the  case  requires, 
he  backing  follows.  When  it  is  tamped  all  the  way  up,  the  work  is 
itruck  off  at  the  top  and  a  plank  very  carefully  bedded  on  top  by  means 
)f  a  layer  of  bedding  sand.  This  plank  is  then  clamped  in  place,  the 
damps  passing  over  the  bottom  pallet  and  the  entire  work  is  turned 
)yer  so  that  when  the  mold  pieces  are  released  the  stone  is  right  side  up. 


Clarr'p-'' 

F 

r 

ion 


laving  been  tamped  in  place  in  an  up-side-down  position.    It  is  not  yig.  no.— Cross-sect 
lecessary  to  use  the  bedding  sand  on  very  small  products  which  will  bed        simple  wood  mold, 
•eadily  on  a  smooth  plank  surface. 

In  wet-cast  work  in  which  the  molds  cannot  be  removed  immediately,  it  is  common  to 
ise  a  large  casting  floor  smoothly  finished  with  concrete.  This  is  shellacked  and  oiled  as  an 
)rdinary  mold  surface  would  be  treated  and  on  it  are  set  up  side  rails  for  plain  work,  with  the 
lecessary  insert  pieces  and  dividing  partitions  to  produce  the  plain  units  in  necessary  lengths. 
Sometimes  for  greater  convenience  the  bottom  of  these  molds  is  provided  in  a  bench  or  table 
rvith  a  concrete  slab  top. 

Where  long  side  rails  are  necessary  channel  irons  of  proper  widths  can  be  used  to  advan- 
:age.  Properly  cleaned  and  oiled  they  will  give  long  service  and  the  principal  thing  to  recom- 
.-nend  them  is  the  fact  that  they  do  not  warp  as  wood  does  frequently  unless  the  grain  is  very 
leavily  filled  and  the  surface  shellacked  and  oiled,  nor  do  they  spring  out  of  line  from  the  weight 
Df  the  concrete.  This  is  something  that  has  to  be  carefully  considered  in  long  work,  where 
3ven  a  slight  wind  due  to  the  springing  of  the  form  frequently  prevents  the  use  of  the  stone  on 
aice  fitting  work. 

The  market  affords  a  great  many  standard  molds  made  of  metal  for  various  ornamental 
pieces  and  standard  architectural  units.  Manufacturers  who  are  catering  to  discrimmatmg 
architects  will  not  depend  upon  standard  units,  however,  but  will  be.  prepared  to  meet  the  de- 
signs of  architects. 

856.  Plaster  Molds.— Plaster  molds  are  very  extensively  used  in  concrete  stone 
manufacture.  In  fact,  plaster  is  used  not  only  in  making  molds  but  in  making  models,  and 
Qot  only  in  plaster  molds  themselves  but  in  making  molded  inserts  for  wood  and  metal  molds. 
Fig.  Ill  shows  how,  by  means  of  a  template  of  thin  metal,  stiffened  by  a  wood  frame  operated 
on  a  smooth  oiled  surface,  it  is  possible  to  make  moldings  for  various  purposes  in  mold  manu- 


160 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-85c 


facture.  The  template  is  guided  by  a  straight-edge  and  moves  on  the  table,  pushing  aside  the 
soft  plaster,  except  in  the  desired  section  described  by  the  template.  Similar  work  requiring 
curved  outline  is  handled  by  mounting  a  template  at  the  end  of  a  pivoted  arm  at  such  a  length 
as  to  describe  the  required  arc.    The  template  then  has  a  circular  movement. 

Plaster  is  readily  used  in  making  models  from  architects'  drawings.  When  this  is  done 
the  plaster  is  cast  in  a  large  block  from  which  the  model  can  be  carved  with  knives  and  suitable 
chisels  after  the  details  have  been  outlined  with  a  pencil  on  the  various  faces  of  the  block.  The 

plaster  model  is  then  shellacked  and  oiled  and  the  mold  made 
over  this  model,  the  mold  also  being  made  of  plaster. 

Flat  panels  in  moderate  relief  without  undercut  may  be 
cast  in  draw  molds.  The  model  should  be  framed  with  wood 
strips  or  clay  ''fences"  to  control  the  plaster.  It  should  then 
be  given  two  coats  of  shellac  (orange)  and  when  dry,  should  be 
greased,  using  a  mixture  of  1  part  stearine  and  2  parts  kerosene 
(combined  hot).  If  a  clay  model  is  being  reproduced,  grease 
moiding.  with  lard  oil.    Sift  plaster  into  a  pan  half  full  of  water,  until 

plaster  lies  about  an  inch  below  the  surface  of  the  water.  Stir 
thoroughly.  When  it  has  thickened  to  a  creamy  consistency,  apply  to  model,  going  over 
the  entire  surface  thinly  at  first  and  jarring  the  model  which  is  best  supported  by  a  rigid 
frame.  The  jarring  eliminates  bubbles  and  pinholes.  Then  pour  in  the  plaster,  reinforc- 
ing as  may  be  necessary  with  strips  of  burlap,  excelsior  or  wood  frame  for  heavy  work.  Jars, 
urns,  Capitols  and  similar  objects  must  have  piece  molds,  the  model  surface  being  divided 
by  clay  fences  against  which  the  plaster  is  applied.  When  a  section  of  plaster  mold  is  hard, 
the  fence  is  removed  and  notches  are  cut  in  the  plaster  edge  to  key  the  adjoining  mold  sec- 


FiG.  112. — Plaster  molds.    The  dark  modeled  part  is  the  plaster  model.     The  parts  A  and  B  are  the  first  two 

pieces  of  a  plaster  mold. 

tion  (see  Fig.  112).  The  edges  are  then  shellacked  and  greased  for  ready  separation  of 
the  mold  parts.  When  the  parts  are  set  up  for  casting  the  concrete,  the  mold  previously  shel- 
lacked and  greased  is  held  by  rope  or  by  chain  and  turnbuckle,  or  by  clamps,  as  the  size, 
weight,  or  shape  of  the  work  may  necessitate  (see  Fig.  113). 

85c.  Glue  Molds. — The  use  of  gelatin  or  glue  molds  is  necessary  in  all  work 
where  there  is  intricate  undercut  in  the  model  to  be  reproduced,  it  not  being  possible  to  remove 
a  rigid  mold  over  these  undercuts  unless  a  plaster  mold,  for  instance,  is  made  in  many  pieces 
to  join  at  the  undercut  and  thus  pull  away.    When  a  glue  mold  is  to  be  made,  the  model  is 


Sec.  2-85rf] 


GENERAL  METHODS  OF  CONSTRUCTION 


161 


greased  and  covered,  first  with  paper  and  then  with  modeUng  clay  to  the  thickness  necessary 
for  the  thickness  of  the  glue  mold.  This  clay  covering  is  then  greased  and  plaster  is  applied 
over  it,  to  form  a  shell  with  a  hole  or  several  holes  at  the  top  with  air  vents  at  various 
heights.  This  is  illustrated  in  Fig.  114,  the  lion  head  being  the  model  to  be  reproduced.  The 
space  immediately  around  it  is  first  filled  with  clay  and  over  this  is  the  plaster  shell  with 
a  funnel  at  the  top.    When  the  plaster  mold  is  hard  it  is  removed  and  the  clay  and  paper 


Fig.  114.— Mak- 
ing a  glue  mold. 


Fig.  113. — Plaster  mold  with  plank  pallets  clamped  on  top  and  bottom  being  turned  over  on  banker  after  tamping 
full,  before  release  of  mold  parts  from  the  fresh  product. 

cleaned  from  the  model.  The  plaster  shell  and  model  are  shellacked  and  oiled  again  and  the 
shell  is  then  fitted  in  place  over  the  model  and  the  space  between  the  model  and  the  shell 
is  filled  with  the  glue,  the  vent  holes  being  stopped  with  clay  as  the  shell  is  filled.  For 
ready  handling,  the  plaster  shell  is  usually  divided  in  a  number  of  pieces,  together  with  the 
glue  mold,  the  division  being  made  with  a  knife.  Glue  should  be  of  the  best  quality  and  should 
be  melted  in  a  double  receptacle  with  very  little  water  used  in  the  vessel  with 
the  glue.    Over-heating  takes  the  '  life"  or  elasticity  out  of  the  glue. 

S5d.  Combination  Molds. — The  manufacturer  who  has  a  well- 
developed  model  and  mold  department  will  have  workers  in  wood,  in  clay,  and 
in  plaster,  and  men  also  familiar  with  the  making  and  use  of  glue  or  gelatin 
molds.  As  the  work  progresses,  a  resourcefulness  in  meeting  special  require- 
ments will  lead  the  manufacturer  to  make  combinations  of  various  mold- 
making  materials  as,  for  instance,  plaster  inserts  in  wood  molds,  and  small  glue  molds  in  con- 
nection with  plaster  molds  to  take  care  of  small  areas  of  undercut  in  the  model  to  be  reproduced. 

85e.  Waste  Molds. — Ornamental  pieces,  especially  when  there  is  to  be  consid- 
erable duplication  and  rapid  work  is  necessary,  are  sometimes  made  in  so-called  "waste" 
molds  of  plaster.  If  the  model  is  intricate,  a  glue  mold  is  made  first  and  in  the  glue  mold  a 
glue  model  is  cast.  From  the  glue  model  as  many  duplicate  molds  are  made  of  plaster  as  there 
are  pieces  to  be  cast.  When  the  concrete  has  become  hard  within  the  plaster  mold,  the  plaster 
is  cut  away  and  the  concrete  surface  cleaned.  Panels,  without  undercut,  are  reproduced  in 
a  similar  way  without  the  necessity  for  first  making  a  glue  model. 

86.  Sand  Molds  and  Casting  in  Sand. — Sand-molding  of  concrete  has  not  been  in  exten- 
sive use  except  by  a  few  manufacturers  particularly  in  the  East,  until  recently.  Patents 
covering  important  features  of  sand-molding  are  just  about  to  expire. 

For  ordinary  work  the  sand,  or  the  mixture  of  sand  and  stone  dust  with  a  little  loam  or 
other  ingredients  to  make  the  sand  particles  adhere,  as  in  iron  foundries,  is  used  in  large  beds 
on  a  big  casting  floor.    The  sand  is  packed  around  models;  the  models  are  so  made  that  they 
can  be  withdrawn  at  the  top  and  the  molds  are  filled  with  a  very  thoroughly  mixed  concrete 
11 


162 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-87 


at  a  flowing  consistency  in  which  there  are  usually  no  particles  larger  than  3^^  in.  and  most  of 
the  aggregates  much  smaller  than  this.  Less  water  is  used  than  the  consistency  might  suggest. 
The  ideal  mix  has  no  free  water.  The  mixture  is  constantly  agitated  after  leaving  the  mixer 
proper  so  as  to  prevent  segregation  of  materials.  Mixing  frequently  is  continued  for  from  10 
to  15  min.  which  greatly  facilitates  the  smoothness  of  the  flow.  Ordinarily,  the  concrete  is 
deposited  through'a  spout  and  some  means  adopted  (as  for  instance  holding  a  small  board  near 
the  bottom  of  the  mold)  to  prevent  injury  to  the  sand  mold  by  the  heavy  stream  of  concrete. 
To  preserve  the  edges  at  the  back  of  this  stone,  which  is  usually  the  surface  upward,  and  to 
permit  subsequent  troweling  of  this  upward  surface,  it  is  common  to  use  wood  strips  placed  in 
the  sand  to  give  a  more  stable  edge  against  which  to  work.  It  is  customary  to  fill  the  sand 
molds  throughout  one  floor  area;  allow  an  hour  for  the  very  wet  mixture  to  stiffen  and  settle 
and  then  trowel  the  upper  surfaces,  filling  in  a  little  additional  concrete  on  the  backs  of  the  stones 
where  it  has  settled. 

When  balusters,  capitols,  and  similar  pieces  are  to  be  made,  liaving  no  large  flat  surface 
to  which  the  model  parts  will  ''draw"  on  the 
upper  side  of  the  sand  bed,  it  is  necessary  to  use 
the  flask  method.  A  box  for  each  of  two  or  more 
portions  of  a  pattern  supports  the  sand  for  a  sec- 
tion of  the  flask.    The  boxes  are  assembled  to 


Arch  stone  -  T^vo  or  three  piece  pattern  ^ 
depending  on  direction  or 'draw" 


Nof-e:-  Incasepaffem  >i 
IS  drawn  -Trorri  sand  as 
shown  by  arrow  'A'  wood 
box  IS  not  required  and 
pattern  split  in  three 


^  parrs  as  shown 
by  solid  lines 

-<.  • 


V/ood 
box. 


1 


Note  -  In  case pattern  is  drawn  as  shown  . .  

by  arrow  'B'  if  is  split  as  shown  by 
dotted  lines  and  wood  box  is  usedi^'  " 
to  take  care  of  check  ^^^-v 


Nails  removed  before 
pattern  is  complexly 
moulded  ■•.  .  i{  . 


Fig.  115. — Splitting  pattern  for  making  sand  mold. 


Fig.  116. — Two  ways  of  splitting  a  pattern. 


complete  a  mold.  The  sand  is  sometimes  mixed  with  a  very  small  percentage  of  plaster  to 
give  stiffness  to  the  mold. 

A  great  deal  of  the  skill  in  successful  stone  manufacture  with  sand  molds  is  in  making  the 
models,  around  which  the  sand  must  be  packed.  Take  for  instance  a  stone  like  that  illustrated 
in  lig.  115.  The  molded  surface  at  the  right  is  to  be  down  and  the  model  drawn  from  the  sand 
in  the  direction  indicated  by  the  arrow.  It  is  necessary,  therefore,  to  make  a  four-piece  pattern 
as  indicated  by  the  numbers  1,  2,  3,  and  4.  The  parts  are  held  lightly  when  first  made  by  nails 
as  shown  in  Fig.  116,  which  shows  two  ways  of  splitting  a  pattern  somewhat  similar  to  that  in 
Fig.  115.  The  nails  are  loosened  when  the  pattern  is  packed  into  the  sand.  Note  the  small 
pattern  part  at  4  in  Fig.  115.  It  is  the  custom  among  many  manufacturers  to  eliminate  the 
undercut  in  such  a  small  part  in  making  a  pattern,  it  being  cheaper  in  such  a  case  to  let  the  stone 
cutter  put  in  the  undercut  after  the  concrete  is  hard.  If  a  great  number  of  these  pieces  were  to 
be  made,  it  would,  in  most  cases,  be  cheaper  to  make  the  pattern  complete  to  avoid  so  much 
stonecutting. 

There  is  a  tendency  in  practically^  all  sand-cast  concrete,  for  some  of  the  sand  in  the  sur- 
rounding bed  to  be  held  by  the  cement  and  so  leave  lumps  and  uneven  places  on  the  casting. 
Surface  treatment  of  sand-cast  concrete  stone  is,  therefore,  necessary,  in  most  cases. 

87.  Surfaces. 

87a.  Face  Design  in  Standard  Units. — Design  of  units  is  a  matter  best  left  to 
the  judgment  of  architects  who  are  specialists  in  such  matters.  Some  early  manufacturers  of 
block  machinery  and  of  concrete  block  were  led  astray  by  the  ease  with  which  the  face  of  a 
block  could  be  cast  to  imitate  anything.  Face  plates  were  supplied  to  imitate  pitch-face  stone, 
cobble  stone,  bush-hammered  stone,  tooled  stone  and  with  all  sorts  of  panels  and  borders. 
Not  satisfied  with  this,  manufacturers  of  block  and  special  stone,  still  drunk  with  the  plastic 
possibilities  of  so  tractable  a  material,  impressed  it  with  the  designs  of  rubber  matting  and 
pressed-steel  ceilings.    These  errors  the  industry  is  outgrowing.    The  most  persistent  crime 


'   Sec.  2-876] 


GENERAL  METHODS  OF  CONSTRUCTION 


1G3 


against  good  taste  is  a  rock-face  block  which  is  bad  chiefly  because  it  does  not  imitate  success- 
fully one  of  the  least  desirable  types  of  natural  stone.  This  much  should  be  of  record  in  this 
connection.  If  block  makers  will  now  devote,  as  many  of  them  are  doing,  as  much  thought  to 
making  concrete  look  like  itself  as  their  predecessors  have  to  making  it  look  like  the  least  desir- 
able natural  stone,  a  great  future  seems  probable  for  the  manufacturers  of  the  material. 

In  making  special  units,  the  manufacturer  will  do  well  to  follow  the  designs  which  archi- 
tects work  out  for  him.  In  making  standard  units,  he  will  more  frequently  have  the  architects 
on  his  side  if  he  eliminates  face  designs  and  makes  a  plain  unit  whose  title  to  beauty  is  in  the 
honesty  of  its  appearance,  in  the  tones  and  colors  of  its  exposed  aggregates,  or  in  the  light  and 
shade  of  a  rugged  texture. 

87b.  Facing  Materials. — Most  concrete  block  and  special-dimension  stone  is 
not  of  the  same  mix  throughout.  When  such  stone  is  made  of  a  dry-tamp  mixture,  it  is  a  simple 
matter  to  face  it,  on  the  surfaces  which  are  to  be  exposed,  using  a  special  aggregate  which  will 
give  the  desired  qualities  in  color  and  texture  in  the  finished  product.  The  facing  mixture  can 
be  backed  up  with  plain  concrete.  When  stone  is  cast  in  sand  molds — in  fact,  in  the  manu- 
facture of  most  wet-cast  stone — the  conditions  in  the  work  necessitate  that  the  concrete  shall 
be  the  same  all  the  way  through.  In  such  work,  therefore,  facing  mixtures  are  not  used.  There 
are  some  exceptions  to  this  rule  in  the  use  of  commercial  equipment  for  the  manufacture  of  con- 
crete block  in  gang  molds.  One  exception  is  in  the  coating  of  face  plates  with  a  thin  film  of 
glue  on  which,  after  the  glue  has  become  sufficiently  thick  and  sticky,  the  facing  aggregate, 
with  no  cement,  is  sprinkled  so  as  to  form  a  complete  layer  over  the  face  plate.  This  plate, 
placed  in  the  bottom  of  a  mold  is  filled  with  a  wet  mixture  of  concrete.  The  water  loosens  the 
glue  and  the  facing  aggregate  bonds  with  the  wet  backing.  Another  method  of  facing  a  wet- 
cast  material  is  in  gang  molds  in  which  the  product  is  made  face  up.  The  molds  are  filled  with 
a  slushy  mixture,  not  quite  to  the  surface,  then  the  facing  mixture  is  spread  on  after  the  backing 
concrete  has  partially  hardened.  This  is  troweled  into  place  on  the  surface  In  general, 
with  regard  to  facing  mixtures,  it  is  common  to  make  them  of  a  1 : 2  proportion  of  cement  and 
a  special  aggregate,  or  1:23'^  or  1:3,  depending  not  only  upon  the  grading  of  the  mixture  but 
upon  the  effect  desired  in  smoothness  or  roughness  in  the  product.  Materials  commonly  used 
include  special  sand,  in  white,  buff,  and  so  on,  crushed  marbles  in  the  more  choice  work,  crushed 
granite,  trap  rock,  even  crushed  cobble  stones  (which  are  within  the  reach  of  almost  anybody 
in  a  glacial  country),  and  crushed  limestone.  Micaspar  crystals,  so-called,  are  used  by  many 
manufacturers  in  producing  a  gray  granite  effect  in  either  dark  or  light  shades.  Other  facing 
materials  are  on  the  market  containing  mica  which  gives  a  sparkle  and  life  to  the  finished  product. 
It  has  been  very  common  for  most  manufacturers  to  use  fine  sand  for  facing  material,  particu- 
larly in  tamp  work,  and  to  make  a  special  effort  to  get  a  very  smooth,  fine  face  on  their  products. 
Some  architects  are  encouraging  work  in  another  direction  by  the  interest  which  they  have 
shown  in  products  having  a  rough  texture.  This  is  secured  by  using  coarser  aggregates  not  so 
well  graded — that  is,  not  so  much  fine  material  to  fill  up  all  the  spaces — and  with  just  as  little 
cement  as  can  be  depended  upon  to  bind  the  aggregates  thoroughly  in  the  face.  It  is  common 
in  such  work  to  use  1 : 3  mixtures  and  to  use  facing  aggregates  as  large  as  }4  in.  The  results 
which  can  be  produced  in  this  way  are  limitless  and  their  effectiveness  depends  largely  upon 
the  taste  and  judgment  of  the  manufacturer.  The  use  of  yellow  marble  or  black  marble 
(crushed  trap  rock  is  frequently  used  in  place  of  black  marble),  red  granites,  and  so  forth,  lead 
to  possibilities  in  colors  in  concrete  stone  which  only  need  experiment  to  prove. 

If  a  smooth  block  or  polished  finish  is  desired,  the  product  should  be  made  on  as  smooth 
a  surface  as  possible  so  that  there  will  be  few  projections  to  work  down.  Where  a  well-graded 
aggregate  of  a  polishable  material  is  used— as,  for  instance,  granite  or  marble— and  this  material 
is  well  distributed  over  the  surface  area  with  few  spaces  between,  it  is  possible  to  polish  a  con- 
crete product  just  as  the  granite  or  marble  itself  is  polished.  A  recent  development  in  the  manu- 
facture of  concrete  stone  hes  in  the  direction  of  obtaining  a  smooth  surface  by  means  of  a  sheet 
of  very  heavy  paraffined  paper  of  glossy  finish,  which  is  placed  in  the  bottom  of  the  mold  of 
whatever  kind  is  used;  the  facing  material  being  placed  in  on  top  of  this  and  the  backing  tamped 


I 


164 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-87c 


behind  it.  This  gives  a  very  smooth  surface  which  requires  only  a  minimum  of  rubbing  to 
give  an  excellent  finish. 

Aside  from  the  special  methods  and  devices  in  obtaining  various  products  which  have 
already  been  described,  facing  mixtures  are  used  chiefly  with  tamped  products.  In  such  work, 
the  facing  mixture  is  generally  a  relatively  dry  mixture,  placed  on  the  bottom  or  face-side  of 
the  mold  box,  and  the  backing  tamped  in  behind  it.  When  it  is  necessary  to  fill  up  the  facing 
material  on  the  side  of  a  mold  of  any  kind,  this  can  be  done  by  piling  it  up  2  or  3  in.  at  a  time 
and  filling  in  the  backing  behind  it,  or  it  may  be  done  by  the  use  of  a  thin  piece  of  metal  of  a 
size  equal  to  the  side  of  the  mold  which  is  to  be  faced.  With  the  use  of  this  dividing  plate  the 
facing  mixture  is  placed  on  one  side  and  the  backing  on  the  other,  the  plate  being  gradually 
raised  as  the  two  are  tamped  together  to  form  a  bond.  This  facing  mixture,  while  relatively 
dry,  must  neither  be  too  dry  nor  too  wet.  It  must  be  just  sticky  enough  to  hold  its  position  when 
pressed  into  shape. 

Whenever  a  facing  mixture  is  used,  it  is  desirable  to  finish  the  work  in  such  a  way  that  the 
special  aggregates  of  whatever  nature  are  used,  are  exposed  to  lend  color  and  to  give  better 
texture  to  the  work  by  the  removal  of  the  cement  which  covers  the  surfaces,  leaving  the  cement 
in  the  matrix  to  bind  the  aggregates  in  their  position.  Various  methods  for  finishing  the  stone, 
not  only  that  which  is  faced  with  a  special  mixture,  but  also  that  which  is  of  like  character 
throughout,  will  be  considered. 

87c.  Colors. — Great  care  should  be  exercised  in  the  selection  of  colors.  They 
cannot  be  used  in  rich  mixtures  without  destroying  a  great  deal  of  the  binding  value  of  the 
cement  with  which  they  are  mixed,  and  the  strongest  colors  cannot  be  obtained  unless  rich 
mixtures  are  used.  For  both  these  reasons  there  has  been  some  tendency  to  discourage  the 
use  of  mineral  colors  in  cement  mixtures. 

J.  H.  Jackson,  authority  on  colors,  writes  in  Concrete  as  follows: 

Mineral  colors  of  the  highest  degree  of  purity  are  the  only  ones  to  use  in  coloring  cement.  The  permanency 
of  shade  or  color  obtained  depends  upon  the  elimination  by  the  color  manufacturer  of  anything  in  the  color  that 
the  cement  itself  will  destroy.  Few  contractors  realize  that  the  more  intense  and  brilliant  are  the  colors,  the  more 
quickly  they  fade,  and,  in  more  instances  than  one,  help  to  disintegrate  the  concrete,  for  none  of  the  mineral  colors 
useful  in  cement  work,  is  found  naturally  brilliant  and  the  addition  of  chemically  prepared  colors  or  the  treatment 
of  native  colors  chemically  to  give  them  intensity  is  a  positive  detriment  under  all  conditions.  All  true  cement 
colors  will  withstand  the  acid  treatment  (1  part  acid,  5  parts  to  6  parts  water),  scrubbing  and  troweling,  but  in 
polishing  after  setting  and  trowel  polishing  before  setting,  special  care  should  be  taken  when  yellow,  green  and 
similar  colors  are  used  for  the  metallic  polishing  is  likely  to  darken  the  color.  Never  give  a  smooth  finish  to  outside 
concrete  when  color  is  used. 

The  standard  proportions  for  colors  generally  used  are  6  to  QVz  lb.  of  color  to  every  100  lb.  of  cement.  The 
amount  of  color  can  be  increased  slightly  if  a  deeper  shade  is  desired,  but  you  should  not  use  more  than  10  lb.  of 
color  to  every  100  lb.  of  cement,  for  an  excess  of  color  reduces  the  binding  power  of  the  cement. 

A  table  of  color  quantities  and  the  results  by  L.  C.  Sabin  from  his  ''Cement  and  Concrete" 
is  as  follows: 

Colored  Mortars 

Colors  given  to  Portland-cement  Mortars  Containing  2  Parts  River  Sand  to  1  Cement 

Weight  of  dry  coloring  matter  to  100  lb.  cement 


Dry  material 
used 


Lamp  black  

Prussian  blue  

Yellow  ochre  

Ultramarine  blue  

Burnt  umber ....... 

Venetian  red  

Chatt.  iron  ore  

Red  iron  ore  


M  lb. 


Light  slate  

Light  green  slate  .  .  .  . 
Light  green  


Licrht  pinkish  slate .  .  . 

Slate,  pink  tinge  

Light  pinkish  slate.  .  . 
Pinkish  slate  


1  lb. 


Light  gray  

Light  blue  slate 


Light  blue  slate  

Pinkish  siate  

Bright  pinkish  slate.  . 

Dull  pink  

Dull  pink  


2  lb. 


Blue  gray. 
Blue  slate 


Blue  slate  

Dull  lavender-pink. .  . 

Light  dull  pink  

Light  terra-cotta  .... 
Terra-cotta  


4  lb. 


Dark  blue  slate 
Bright  blue  slate 
Light  buff 
Bright  blue  slate 
Chocolate 
Dull  pink 
Light  brick  red 
Light  brick  red 
 J 


Sec.  2-87(^1 


(mNEUAL  METHOD.'^  OF  CON^HTRIJCTION 


165 


Coloring  by  absorption  is  described  in  the  Concrete  by  Adolph  Schilling: 

To  color  in  reds  and  in  browns  use  sulphate  of  iron  in  a  solution  of  1  lb.  of  sulphate  to  1  gal.  of  water;  for 
greens  1  lb.  sulphate  of  copper  to  3  gal.  water.  The  older  the  concrete  the  longer  the  bath  must  continue.  It 
must  be  borne  in  mind  that  the  coloring  stops  to  a  very  great  extent  the  hardening  of  the  concrete.  Therefore, 
it  is  necessary  to  permit  the  concrete  to  attain  such  strength  as  is  necessary  in  the  ornamental  work  before  im- 
mersing it.  Immersion  may  continue  for  a  few  minutes  or  for  several  days,  depending  upon  the  age  of  the  con- 
crete and  upon  the  depth  of  color  desired.  The  effects  may  be  varied  by  using  an  aggregate  which  is  not  highly 
absorptive  so  that  this  stands  out  while  the  matrix  surrounding  it  is  colored.  Effects  can  be  heightened  in  elaborate 
designs  by  "picking  out"  certain  parts,  coloring  them  with  a  brush  with  cement  stains. 

Rough-textured  work  is  sometimes  beautified  by  having  stain  stippled  on  or  brushed  over  the  high  points. 
The  manufacturer,  of  course,  will  always  have  to  use  his  judgment  in  the  application  of  these  colorings.  The  great 
danger  is  in  overdoing. 

Aside  from  the  use  of  white  cement  to  obtain  light  colors  in  concrete,  it  is  possible  to 
make  an  ordinary  gray  cement  surface  lighter  by  rubbing  with  a  concrete  brick  made  of  fine 
materials.    The  work  should  be  kept  wet  while  being  rubbed. 

A  method  of  obtaining  white  surfaces  is  described  by  John  Oursler,  in  Concrete,  as  follows : 

A  wash  made  of  1  lb.  of  concentrated  lye,  4  lb.  of  alum  and  5  gal.  of  water,  with  enough  cement  added  to  make 
the  wash  of  a  good  consistency  for  spreading  with  a  brush,  has  been  used  to  give  a  white  surface. 

87c?.  Spraying. — One  method  for  removing  the  surface  film  of  concrete  block 
and  special  stone  where  there  is  a  special  facing  mixture,  is  the  spraying  method,  described  in 
Concrete  by  the  early  user  of  the  method,  E.  J.  Thompson: 

Immediately  upon  removing  the  block  from  the  machine,  place  it  where  there  will  be  a  good  light  on  the  face 
and  spray  it,  using  a  fine  vapor  spray,  such  as  is  used  in  spraying  fruit  trees.  The  outlet  holes  in  such  sprays  are 
about  the  size  of  an  ordinary  pin,  and,  for  the  best  results,  should  be  used  in  connection  with  a  water  pressure  of 
40  lb.  or  more.  This  spray  nozzle  attached  to  a  length  of  j2-in.  hose  is  all  the  equipment  needed.  The  spraying  is 
a  simple  operation.  It  can  be  done,  after  a  little  practice,  by  any  intelligent  laborer.  The  effect  of  the  spray, 
which  lasts  only  momentarily,  is  to  wash  off  the  surface  film  of  cement  and  expose  the  aggregate  (see  Fig.  117). 
The  spraying  must  not  be  continued  until  the  surface  begins  to  run  or  furrow,  but  just  a  little  practice  teaches  the 
operator  when  to  stop. 

Some  manufacturers  prefer  spraying  their  products  when  they  are  lying  face  up;  others 
prefer  to  have  them  with  the  face  perpendicular.  The  perpendicular  method  is  the  commonest, 
but  the  face-up  method  has  a  tendency  to  leave  all  the  cement  on  the  surface,  to  wash  it  into 
the  pores.  One  manufacturer  who  advocates  this  method  urges  that  it  not  only  exposes  the 
aggregate  but  makes  tke  face  of  the  product  more  dense.  When  this  work  is  done  on  standard 
concrete  block,  it  is  done  very  rapidly  and  adds  very  little  to  the  cost  of  the  block. 

87e.  Brushing. — Brushing  the  surfaces  of  concrete  stone  in  standard  and  special 
units  is  particularly  desirable  where  a -rough-textured  effect  is  desired  (see  Figs.  117  and  118). 
It  is  commonly  used  where  a  graded  aggregate,  with  larger  particles  than  is  ordinarily  used 
in  facing  mixtures,  is  employed.  The  brushing  is  done,  ordinarily,  while  the  product  is  com- 
paratively green,  using  a  fiber  brush  with  stiff  bristles  and  using  considerable  water  while 
the  brushing  is  in  progress.  Care  must  be  taken  that  brushing  is  not  started  too  soon  so  that 
the  face  of  the  products  will  be  damaged,  and  on  the  other  hand,  the  work  must  be  done  before 
the  product  is  too  hard,  or  the  work  becomes  expensive.  The  manufacturer  will  find  that  the 
time  for  brushing  depends  a  great  deal  upon  the  conditions  of  curing.  For  surfaces  which  have 
been  allov\^ed  to  become  partially  hardened,  a  brush  about  4  in.  wide  made  by  clamping  together 
a  number  of  sheets  of  wire  cloth  has  been  found  more  effective  than  the  wire  brushes  which  are 
ordinarily  sold  for  this  purpose.  Care  must  be  taken  in  brushing  not  to  injure  the  edges  of 
the  products.  Sometimes  it  is  desirable  for  the  operator  to  use  a  small  frame  or  at  least  a 
straight-edge  to  protect  the  edges  of  the  product  while  brushing. 

Fig.  119  shows  three  views  of  turning  stand  for  handling  green  concrete  block  to  be  brushed. 
This  stand  is  used  for  handling  products  which  are  delivered  on  pallets  face  down.  A  block 
on  pallet  is  placed  on  stand  as  in  the  first  position.    The  shelf  is  turned  over,  so  that  the  block 


166 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-87/ 


rests  on  its  side  as  in  the  second  position.  The  shelf  which  first  supported  the  block  is  then 
turned  down  leaving  the  face  exposed  for  brushing  or  other  treatment. 

Where  steam-curing  is  employed,  it  is  common  to  run  the  block  into  the  steam  rooms  for 
a  few  hours  and  out  again,  when  the  brushing  is  done,  and  the  products  are  returned  to  the  cur- 
ing rooms. 

87/.  Rubbing. — Rubbing,  as  a  finish  in  concrete  stone,  is  commonly  used  where 
a  limestone  finish  is  desired.  In  wet-cast  work  when  air  bubbles  and  slight  imperfections  occur 
on  the  surfaces  of  concrete  stone,  it  is  the  usual  practice  to  pour  on  the  surface  a  creamy  grout 


of  cement  and  water.  This  is  rubbed  in  first  with  a  brush  or  swabbed  on  with  a  cloth,  and  a 
few  minutes  later  rubbed  in  with  a  small  wood  block.  When  hard,  the  stone  is  rubbed  down 
with  abrasives.  The  rubbing  removes  the  effect  of  the  painted  surface.  It  is  common  to  use 
cement  brick  made  with  very  fine  material  in  rubbing  concrete  work.  Ordinary  commercial 
abrasives  are  also  employed. 

For  finishing  marble  concrete  which  may  be  cast  in  large  blocks  and  cut  up  by  gang  saws 
into  slabs,  or  cast  in  thin  sections  in  pressure  machines  as  for  floor  tiles,  the  methods  are  like 
those  in  factories  where  natural  marble  is  handled.    The  pieces  are  first  smoothed  down  on  a 

revolving  rubbing  bed,  sand  and  water  being 


First  position  Second  position       Third  position 

Fig.  119. — Three  views  of  turning  stand  for  handling 
green  concrete  block  to  be  brushed. 


fed  to  the  grinding  surface.  Then  power- 
operated  carborundum  discs  are  employed, 
or  a  second  rubbing  bed  with  a  finer  grit, 
for  a  dull  gloss  surface,  or  when  a  polish 
is  desired,  the  work  going  under  hand  or 
power-operated  mops,  employing  oxalic  acid 
and  putty  powder  in  the  process. 

87gr.  Tooling. — In  considering 
the  tooling  of  concrete  stone  in  various  sur- 
face treatments  now  put  on  it,  there  might 
be  considered  all  of  the  methods  which  are  common  to  the  finishing  of  natural  stone.  The 
))est  quality  of  manufactured  stone  admits  of  the  same  treatments  as  are  given  to  natural 
stone,  with  similar  results.  The  means  at  the  disposal  of  the  manufacturer  of  high-class  con- 
crete stone  include  the  ordinary  hand  work  with  rasps  and  chisels,  bush  hammers,  crandalls, 
planers,  polishers,  and  so  on.  To  make  possible  the  use  of  tools  of  this  kind  in  obtaining 
satisfactory  finish,  it  is  necessary  that  the  concrete  have  a  uniform  texture,  with  no  aggregd,tes 
of  unusual  hardness;  that  is,  the  materials  shall  be  of  a  like  character  throughout.  The  aggre- 
gates used  in  such  work,  ordinarily  pass  a  3^-in.  screen.    They  include  crushed  limestone, 


Sec.  2-87// J 


GENE  HAL  METHODS  OF  CONSTRICTION 


167 


marble,  granite,  and  trap  rock.  While  faced  products  are  fre(iuently  tooled,  it  is  more  common 
to  find  such  finishing  methods  applied  to  products  which  are  of  like  character  throughout. 

The  use  of  pneumatic  tools  in  bush-hammering  and  crandalling  concrete  surfaces  is  becom- 
ing more  common  and  resulting  in  great  economy  over  the  use  of  hand  tools.  A  finish  in  parallel 
grooves,  very  common  on  natural  stone,  is  put  on  concrete  stone  using  power  equipment  which 
revolves  a  gang  of  thin  carborundum  wheels  mounted  together,  so  that  considerable  surface 
is  covered  at  one  time.  Methods  of  cutting  which  are  common  in  the  natural  stone  field  and 
which  are  used,  though  are  not  so  common  in  the  concrete  stone  industry,  include  the  cutting 
up  of  large  slabs  of  stone  by  means  of  saws  which  make  deep  grooves,  so  that  a  slab  is  easily 
split  up  on  the  job  just  before  the  stone  is  laid,  thus  preserving  the  edges  and  keeping  theni 
clean  and  sharp. 

For  fine  ornamental  details  and  for  finishing  undercuts  which  are  not  easily  included  in 
patterns  and  molds,  expert  stone  carvers  are  employed  in  some  of  the  best  plants  making  a 
high  quality  of  concrete  stone. 

87/i.  Mosaics. — The  subject  of  the  surface  treatment  of  concrete  would  not  be 
complete  without  the  mention  of  the  possibilities  which  lie  in  the  use  of  mosaics  in  large  and 
small  ornamental  surfaces.  These  may  be  glued  into  a  mold  on  strips  of  paper  where  the 
concrete  surface  is  to  be  flush  with  the  mosaic  itself;  or  the  inlay,  consisting  of  tile  or  bits  of 
marble  or  other  stone,  may  be  set  in  places  which  have  been  provided  in  the  products  when  cast. 
After  the  product  is  complete  and  before  the  curing  period  is  entirely  ended,  the  grooves  or 
spaces  left  where  inlays  are  to  be  inserted  are  thoroughly  wet  and  grouted  in  to  hold  the  inlays 
in  place. 

87i.  Efflorescence. — Efflorescence  is  ordinarily  considered  in  connection  with 
surfaces  because  it  is  a  surface  disfiguration.  The  cause,  however,  goes  far  back  of  the  surface 
treatment  and  lies  in  the  fact  that  the  concrete  mixture  is  not  so  dense  as  should  be  obtained. 
Efflorescence  is,  in  reality,  a  disfiguration  which  is  common  to  brick,  to  concrete  and  to 
natural  stone.  It  occurs,  as  a  direct  result  of  porosity  in  the  material  on  which  it  appears. 
An  impervious  substance  is  not  subject  to  efflorescence.  When  a  substance  is  porous,  water 
which  is  absorbed  dissolves  certain  salts  found  in  the  material;  as  for  instance  in  concrete 
block  and  brick,  the  salt  which  is  dissolved  is  principally  lime  carbonate.  A  concrete  product 
which  soaks  water  like  a  sponge  after  a  rain,  subsequently  dries  out  generally  from  exposure 
to  the  sun.  In  drying  out,  any  salt  solution  is  brought  to  the  surface  and  left  there  when  the 
water  evaporates.  The  best  remedy  is  in  prevention  by  maintaining  a  dense  mixture.  Efflo- 
rescence can  usually  be  removed  with  a  solution  of  muriatic  acid  and  water  although  this  is 
not  always  successful. 

87j.  Air  Bubbles. — Air  bubbles,  like  efflorescence,  are  a  part  of  the  subject  of 
density.  They  are  formed  when  there  is  insufficient  care  in  placing  the  concrete.  A  wet 
mixture  should  be  spaded  against  the  forms  so  that  these  little  air  pockets  will  not  form.  They 
are  also  prevented  by  tapping  the  molds,  or  by  vibrating  platforms,  actuated  sometimes  by 
machinery.  The  object  of  such  equipment,  however,  is  not  so  much  to  avoid  the  pinholes, 
which  become  surface  blemishes,  as  to  produce  a  dense  concrete  by  consolidating  the  mass. 

The  removal  of  air  bubbles  is  frequently  accomplished  by  tooling  the  surface  when  the 
concrete  is  removed,  and  sometimes  it  is  done  by  filling  the  surface  a  cement  paste  being  rublx^d 
in,  as  is  described  in  connection  with  rubbed  surfaces. 

87/c.  Crazing. — Crazing,  or  the  formation  of  hair-cracks  in  the  surface  of  con- 
crete stone,  is  more  frequently  encountered  in  wet  mixtures  than  in  dry  mixtures;  is  more 
common  in  rich  mixtures  than  in  lean  mixtures;  and  it  is  said  by  some  manufacturers  that  the 
tendency  to  surface  crazing  diminishes  greatly  when  a  well-aged  cement  is  used.  The  writer 
has  never  known  but  one  manufacturer  using  a  wet  mixture  of  concrete  who  claimed  entire 
freedom  from  crazing  in  his  products.    This  manufacturer  uses  a  graded  mixture  of  trap  rock. 

The  reason  for  the  hair-checking  is  in  the  greater  tendency  of  the  surface  of  concrete  stone 
to  undergo  temperature  changes,  leaving  the  interior  of  the  stone  comparatively  unaffected. 


168 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  2-88 


These  surface  cracks  do  not  cause  any  structural  harm,  as  they  extend  scarcely  more  than 
2  in.  into  the  stone.  They  are  entirely  removed  in  ordinary  tooling  treatments  to  which 
much  of  the  wet-cast  stone  (in  which  crazing  is  most  common)  is  subjected.  While  these 
cracks  are  believed  by  some  manufacturers  to  be  characteristic  of  the  very  rich  surface  skin  of 
cement  which  forms  on  spaded  mixtures  of  concrete  or  on  very  rich  mixtures  of  fine  material, 
other  manufacturers  find  that  even  in  tooling  this  thin  mortar  skin  on  the  surface,  the  crazing 
is  not  entirely  done  away  with  as  it  may  craze  again  later  on.  Its  only  disadvantage  is  in  the 
fact  that  it  provides  minute  lodging  spaces  for  dirt.  It  does  not  seem  possible  to  say  just  how 
this  crazing  can  be  avoided  in  concrete  stone,  because  it  is  maintained  by  many  manufacturers 
that  two  pieces  of  stone  made  in  the  same  way,  from  the  same  batch  and  cured  in  the  same  way, 
will  not  show  the  same  results,  one  piece  being  covered  in  a  short  time  with  surface  cracks  and 
the  other  piece  entirely  free  from  them.  A  manufacturer  of  concrete  monuments  says  that  he 
obviates  surface  crazing  by  keeping  his  products  buried  in  damp  sand  for  30  days  after  manu- 
facture. In  manipulating  the  drier  mixtures  of  concrete,  manufacturers  frequently  insist  that 
workmen  shall  not  trowel  the  surfaces  of  products  after  they  are  molded,  this  troweling  having 
a  tendency  to  bring  the  fine  cement  particles  to  the  surface  and  result  in  crazing, 

88.  Specifications  of  the  American  Concrete  Institute. — Newly  adopted  (1917)  specifi- 
cations and  building  regulations  of  the  American  Concrete  Institute  for  manufacture  and 
use  of  concrete  architectural  stone,  building  block  and  brick  provide  as  follows: 

1.  Concrete  architectural  stone  and  building  blocks  for  solid  or  hollow  walls  and  concrete  brick  made  in 
accordance  with  the  following  specifications  and  meeting  the  requirements  thereof  may  be  used  in  building  con- 
struction. 

2.  Tests. — Concrete  architectural  stone,  building  blocks  for  hollow  and  solid  walls  and  concrete  brick  must 
be  subjected  to  (a)  compression  and  (b)  absorption  tests.  All  tests  must  be  made  in  a  testing  laboratory  of  recog- 
nized standing. 

3.  Ultimate  Compressive  Strength. — (a)  In  the  case  of  solid  stone,  blocks,  and  brick,  the  ultimate  compressive 
strength  at  28  days  must  average  fifteen  hundred  (1500)  lb.  per  sq.  in.  of  gross  cross-sectional  area  of  the  stone  as 
used  in  the  wall  and  must  not  fall  below  one  thousand  (1000)  lb.  per  sq.  in.  in  any  case. 

(b)  The  ultimate  compressive  strength  of  hollow  and  two-piece  building  blocks  at  28  days  must  average  one 
thousand  (lOOO)  lb.  per  sq.  in.  of  gross  cross-sectional  area  of  the  block  as  used  in  the  wall,  and  must  not  fall  below 
seven  hundred  (700)  lb.  per  sq.  in.  in  any  test. 

4.  Gnoss  Cross-sectional  Areas. — (a)  Solid  concrete  stone,  blocks  and  brick.  The  cross-sectional  area  shall 
be  considered  as  the  minimum  area  in  compression. 

(b)  Hollow  building  blocks.  In  the  case  of  hollow  building  blocks,  the  gross  cross-sectional  area  shall  be 
considered  as  the  product  of  the  length  by  the  width  of  the  block.  No  allowance  shall  be  made  for  the  air  space 
of  the  block. 

(c)  Two-piece  building  blocks.  In  the  case  of  two-piece  building  blocks,  if  only  one  block  is  tested  at  a 
time,  the  gross  cross-sectional  area  shall  be  regarded  as  the  product  of  the  length  of  the  block  by  one-half  of  the 
width  of  the  wall  for  which  the  block  is  intended.  If  two  blocks  are  tested  together,  then  the  gross  cross-sectional 
area  shall  be  regarded  as  the  product  of  the  length  of  the  block  by  the  full  width  of  the  wall  for  which  the  block  is 
intended. 

5.  Absorption. — The  absorption  at  28  days  (being  the  weight  of  the  water  absorbed  divided  by  the  weight 
of  the  dry  sample)  must  not  exceed  ten  (10)  %  when  tested  as  hereinafter  specified. 

6.  Samples. — At  least  six  samples  must  be  provided  for  the  purpose  of  testing.  Such  samples  must  represent 
the  ordinary  commercial  product.  In  cases  where  the  material  is  made  and  used  in  special  shapes  and  forms  too 
large  for  testing  in  the  ordinary  machine,  smaller  specimens  shall  be  used  as  may  be  directed.  Whenever  possible, 
the  tests  shall  be  made  on  full-sized  samples. 

7  Compression  Tests. — Compression  tests  shall  be  made  as  follows:  The  sample  to  be  tested  must  be  carefully 
measured  and  then  bedded  in  plaster  of  Paris  or  other  cementitious  material  in  order  to  secure  uniform  bearing 
in  the  testing  machine.  It  shall  then  be  loaded  to  failure.  The  compressive  strength  in  pounds  per  square  inch 
of  gross  cross-sectional  area  shall  be  regarded  as  the  quotient  obtained  by  dividing  the  total  applied  load  in  pounds 
by  the  gross  cross-sectional  area,  which  area  shall  be  expressed  in  square  inches  computed  according  to  Art.  4. 

When  such  tests  must  be  made  on  cut  sections  of  blocks,  the  pieces  of  the  block  must  first  be  carefully  meas- 
ured. The  samples  shall  then  be  bedded  to  secure  uniform  ])caring,  and  loaded  to  failure.  In  this  case,  however, 
the  compressive  strength  in  pounds  per  square  inch  of  net  area  must  be  obtained  and  the  net  area  shall  be  re- 
garded as  the  minimum  bearing  area  in  compression.  The  average  of  the  compressive  strength  of  the  two  portions 
of  blocks  shall  be  regarded  as  the  compressive  strength  of  the  samples  submitted.  This  net  compressive  strength 
shall  then  be  reduced  to  compressive  strength  in  pounds  per  square  inch  of  gross  cross-sectional  area  as  follows: 

The  net  area  of  a  full-sized  block  shall  be  carefully  calculated  and  the  total  compressive  strength  of  the  block 


Sec.  2-88] 


GENERAL  METHODS  OF  CONSTRUCTION 


169 


will  be  obtained  by  multiplying  this  area  by  the  net  compressive  strength  obtained  above.  This  total  gross  com- 
pressive strength  shall  be  divided  by  the  gross  cross-sectional  area  as  figured  by  Art.  4  to  obtain  the  compressive 
strength  in  pounds  per  square  inch  of  gross  cross-sectional  area. 

When  testing  other  than  rectangular  blocks,  great  care  must  be  taken  to  apply  the  load  at  the  center  of 
(,1  gravity  of  the  specimen. 

I  8.  Absorption  Tests. — The  samples  shall  be  first  thoroughly  dried  to  a  constant  weight  at  a  temperature  not 

to  exceed  two  hundred  and  twelve  (212)  degrees  Fahrenheit,  and  the  weight  recorded.  After  drying,  the  sample 
shall  be  immersed  in  clean  water  for  a  period  of  48  hr.  The  sample  shall  then  be  removed;  the  surface  water  wiped 
off,  and  the  sample  reweighed.    The  percentage  of  absorption  shall  be  regarded  as  the  weight  of  the  water  absorbed 

|!  divided  by  the  weight  of  the  dry  sample  multiplied  by  one  hundred  (100). 

i  9.  Limit  of  Loading. — (a)  Hollow  walls  of  concrete  building  blocks.    The  load  on  any  hollow  walls  of  concrete 

blocks,  including  the  superimposed  weight  of  the  wall,  shall  not  exceed  one  hundred  and  sixty-seven  (107)  lb.  per 
sq.  in.  of  gross  area.  If  the  floor  loads  are  carried  on  girders  or  joists  resting  on  cement  pilasters  filled  in  place  with 
slush  concrete  mixed  in  proportion  of  one  (1)  part  cement,  not  to  exceed  two  (2)  parts  of  sand  and  four  (4)  parts 
of  gravel  or  crushed  stone,  said  pilasters  may  be  loaded  not  to  exceed  three  hundred  (300)  lb.  per  sq.  in.  of  gross 

i  cross-sectional  area. 

I  (6)  Solid  walls  of  concrete  blocks.    Solid  walls  built  of  architectural  stone,  blocks  or  brick  and  laid  in  Port- 

i[  land-cement  mortar  or  hollow  block  walls  filled  with  concrete  shall  not  be  loaded  to  exceed  three  hundred  (300) 
j  lb.  per  sq.  in.  of  gross  cross-sectional  area. 

10.  Girders  and  Joists. — Wherever  girders  or  joists  rest  upon  walls  in  such  a  manner  as  to  cause  concentrated 
loads  of  over  four  thousand  (4000)  lb.  the  blocks  supporting  the  girders  or  joists  must  be  made  solid  for  at  least 
eight  (8)  in.  from  the  inside  face  of  the  wall,  except  where  a  suitable  bearing  plate  is  provided  to  distribute  the  load 
over  a  sufficient  area  to  reduce  the  stress  so  it  will  conform  to  the  requirements  of  Art.  9. 

When  the  combined  live  and  dead  floor  loads  exceed  sixty  (60)  lb.  per  sq.  ft.,  the  floor  joists  shall  rest  on  a 
steel  plate  not  less  than  three-eighths  {%)  in.  thick  and  of  a  width  Vi  to  1  in.  less  than  the  wall  thickness.  In 
lieu  of  said  steel  plate  the  joists  may  rest  on  a  solid  block  which  may  be  three  (3)  or  four  (4)  in.  less  in  wail  thick- 
ness than  the  building  wall,  except  in  instances  where  the  wall  is  eight  (8)  in.  thick,  in  which  cases  the  solid  blocks 
shall  be  the  same  thickness  as  the  building  wall. 

11.  Thickness  of  Walls. — (a)  Thickness  of  bearing  walls  shall  be  such  as  will  conform  to  the  limit  of  loading 
given  in  Art.  9.  In  no  instance  shall  bearing  walls  be  less  than  eight  (8)  in.  thick.  Hollow  walls  eight  (8)  in. 
thick  shall  not  be  over  sixteen  (16)  ft.  high  for  one 

story,  or  more  than  a  total  of  twenty-four  (24)  ft.  for  TabLE  I 

two  stories. 

(6)  Walls  of  residences  and  buildings  com- 
monly known  as  apartment  buildings  not  exceeding 
four  stories  in  height,  in  which  the  dead  floor  load 
does  not  exceed  sixty  (60)  lb.  or  the  live  load  over 
sixty  (60)  lb.  per  sq.  ft.,  shall  have  a  minimum  thick- 
ness in  inches  as  shown  in  Table  I. 

12.  Variation  in  Thickness  of  Walls. —  (a) 
Wherever  walls  are  decreased  in  thickness  the  top 
course  of  the  thicker  wall  shall  afford  a  solid  bear- 
ing for  the  webs  or  walls  of  the  course  of  the  con- 
crete block  above. 

13.  Bonding  and  Bearing  Walls. — Where  the  face  wall  is  constructed  of  both  hollow  concrete  blocks  and 
brick,  the  facing  shall  be  bonded  into  the  backing,  either  with  headers  projecting  four  (4)  in.  into  the  brickwork, 
every  fourth  course  being  a  header  course,  or  with  approved  ties,  no  brick  backing  to  be  less  than  eight  (8)  in.  thick. 
Where  the  walls  are  made  entirely  of  concrete  blocks,  but  where  said  blocks  have  not  the  same  width  as  the  wall, 
every  fifth  course  shall  overlap  the  course  below  by  not  less  than  four  (4)  in.  unless  the  wall  system  alternates  the 
cross  bond  through  the  wall  in  each  course. 

14.  Curtain  Walls. — For  curtain  walls  the  limit  of  loading  shall  be  the  same  as  given  in  Art.  9.  In  no  in- 
stance shall  curtain  walls  be  less  than  eight  (8)  in.  in  thickness. 

15.  Party  Walls. — Walls  of  hollow  concrete  blocks  used  in  the  construction  of  party  walls  shall  be  filled  in 
place  with  concrete  in  the  proportion  and  manner  described  in  .Art.  9. 

16.  Partition  Walls.— UoUow  partition  walls  of  concrete  blocks  may  be  of  the  same  thickness  as  required 
in  hollow  tile,  terra-cotta  or  plaster  blocks  for  like  purposes. 


No. 
of 
stories 

Base- 
ment, 
inches 

First 
story, 
inches 

Second 

story, 

inches 

Third 
story, 
inches 

Fourth 

story, 

inches 

1 

8 

8 

2 

10 

8 

8 

3 

12 

12 

10 

8 

4 

16 

12 

10 

10 

8 

SECTION  3 

CONSTRUCTION  PLANT 
PREPARATION  OF  CONCRETE  AGGREGATES 

1.  Preparation  of  Crushed -stone  Aggregate. — The  preparation  of  crushed-stone  aggregate 
has  grown  to  be  an  industry  of  such  size  that  marked  refinements  in  methods  have  been  in- 
troduced in  recent  years  in  the  better  plants.  The  general  scheme,  however,  is  (1)  the  breaking 
down  of  the  ledge,  by  one  means  or  another,  into  pieces  which  can  be  readily  handled  and  fed 
into  crushing  machinery;  (2)  the  breaking  of  these  larger  pieces  in  crushers  of  one  type  or  another ; 
and  (3)  the  separation  of  the  crushed  material  into  various  sizes. 

la.  Preparation  of  Site  for  Quarrying. — When  a  ledge  is  located  for  quarrying, 
it  is  necessary  to  strip  off  the  overburden  in  order  to  expose  clean  rock  and  to  prevent  the  work- 
ings from  being  filled  with  dirt  and  debris.  Quarrying  is  carried  on  in  morc-or-less  distinct 
levels  one  above  another,  the  overburden  being  stripped  back  a  distance  from  the  top  and  the 
ledge  quarried  down  a  convenient  depth,  gradually  working  backward  into  the  face.  A  lower 
terrace  will  then  be  started,  working  backward  for  a  distance,  until  the  vertical  face  of  the  first 
portion  is  encountered.  Successive  levels  may  be  quarried  in  this  way,  the  top  ledge  being 
successively  stripped  back  to  greater  distances  and  the  lower  ledges  being  worked  again  in  the 
same  sequence.  It  is  usually  sought  to  quarry  inward  from  the  side  face  of  a  ledge  whose  top 
is  a  considerable  distance  above  the  side  of  the  crushing  plant,  in  order  that  the  rock  may  be 
brought  within  reach  by  gravity. 

16.  Quarrying. — The  general  method  of  quarrying  is  to  bring  rock  down  by 
charges  of  explosive  set  off  in  holes  drilled  in  the  rock  ledge.  These  holes  are  put  down  to  the 
depth  to  which  the  rock  is  to  be  split.  The  requisite  amount  of  powder  is  charged  into  the 
hole,  covered  by  sand,  and  fired  by  means  of  a  fuse  or  by  electricity.  In  larger  operations 
charges  in  a  line  of  drilled  holes  are  fired  simultaneously  by  electricity.  Gunpowder  is  the 
explosive  mostly  used,  although  nitroglycerine  and  dynamite  are  often  preferred  both  because 
of  the  larger  quantity  of  rock  which  can  be  brought  down  per  batch  and  also  because  of  the 
shattering  effect  of  these  quick-acting  explosives.  Various  refinements  in  minor  details  are  of 
great  importance  and  have  a  distinct  bearing  on  the  effect  of  the  explosive  charge.  Even  such 
an  apparently  small  matter  as  the  form  of  the  bottom  of  the  drill  hole  has  a  very  marked  effect. 
When  bored  with  a  hand  drill,  the  hole  is  triangular  at  the  bottom  and  the  blast  in  such  a  hole 
will  break  rock  in  three  directions.  Explosives  in  a  squared  bottom  hole  have  a  more  distinctly 
lateral  effect.  An  expert  rock  man  will  shoot  approximately  that  portion  of  the  rock  which  he 
desires  to  bring  down. 

Ic.  Drills. — The  jumper  is  a  drill  similar  to  that  used  for  drilling  holes  for  plug 
and  feather  work  in  dimension-stone  quarries,  except  that  it  is  larger  and  longer.  It  is  usually 
held  by  one  man,  who  rotates  it  between  the  alternate  blows  from  hammers  in  the  hands  of 
two  other  men.  Churn  drills  are  long  heavy  drills  measuring  from  6  to  8  ft.  in  length.  They 
are  raised  by  a  workman,  let  fall,  caught  on  the  rebound,  raised  and  rotated  a  little  and  then 
dropped  again,  thus  cutting  a  hole  without  being  driven  by  hammer.  They  are  more  econom- 
ical than  jumpers  as  they  cut  faster  and  make  larger  holes.  Machine  rock  drills  bore  much 
more  rapidly  than  hand  drills  and  are  more  economical  in  most  operations  for  preparing  rock 
for  concrete  aggregate,  where  the  w^ork  is  of  sufficient  magnitude  to  justify  the  preliminary  out- 
lay. They  drill  in  any  direction  and  can  often  be  used  in  boring  holes  so  located  that  they 
could  not  be  bored  by  hand.    They  are  worked  either  by  steam  or  by  compressed  air,  and  may 

in 


172 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  Z-ld 


be  either  percussion  or  rotary.  The  action  of  a  percussion  drill  is  the  same  as  that  of  a  churn 
drill  already  described,  a  piston  moved  by  steam  or  compressed  air  being  attached  to  the  drill 
in  such  manner  as  to  make  a  stroke  at  every  complete  movement  of  the  piston,  an  automatic 
device  rotating  the  drill  slightly  at  each  stroke.  Rotary  drills  may  be  either  shot  drills  or  dia- 
mond drills  and  they  are  more  often  used  for  prospecting  than  for  drilling  holes  for  explosives, 
inasmuch  as  in  their  use  a  core  is  obtained  which  is  of  value  mainly  as  mdicating  the  strata 
penetrated. 

Id.  Stone  Crushers. — Crushers  are  of  two  general  kinds:  jaw  crushers  and  gyra- 
tory crushers.  The  former  type  is  better  adapted  to  small  or  portable  plants,  while  the  latter 
is  used  in  larger  operations.  A  convenient  size  of  jaw  crusher  for  a  portable  plant  is  about 
10  by  16  in.  This  will  crush  from  50  to  100  cu.  yd.  per  day,  depending  upon  the  size  of  the  stone 
to  be  crushed. 

Both  types  of  crushers  have  means  for  regulating  openings  so  that  by  using  a  proper  open- 
ing together  with  a  proper  crushing  plate,  almost  any  size  of  crusher  product  can  be  obtained, 
the  size  being  limited  by  a  small  opening  at  the  crusher-plate  end  of  the  machine.  The  output 
of  any  crusher  will  depend  to  a  large  extent  upon  the  plant  arrangement.  Necessarily  also, 
the  more  finely  a  stone  is  crushed  the  more  work  must  be  done  upon  it  and  the  less  the  output. 
In  deciding  upon  the  type  of  crusher  to  be  installed  at  any  plant,  it  is  best  to  get  comparative 
estimates,  costs,  and  tables  of  weight  and  output  from  manufacturers  of  various  types  of  ap- 
paratus, balancing  the  advantages  of  one  against  those  of  another  and  finding  the  machine  best 
adapted  to  the  purpose  in  mind.  Machinery  of  this  kind  is  constantly  being  improved  and 
changed  in  type,  so  that  accurate  data  representative  of  the  latest  practice  is  difficult  to  give. 

le.  Screening  and  Grading  of  C|-ushed  Stone. — As  stone  comes  from  the 
crusher,  it  is  carried  by  some  elevating  means,  usually  a  bucket  elevator,  to  revolving  screens 
fixed  over  bins.  Elevating  and  screening  plants  can  be  furnished  in  either  portable  units 
(in  which  case  they  are  so  arranged  that  they  can  be  readily  dismantled  for  transportation) 
or  in  fixed  units  with  the  machinery  more  massive.  The  usual  type  of  screen  is  a  rotary  screen 
inclined  on  its  longitudinal  axis,  screens  of  various-size  holes  disposed  successively  throughout 
its  length  forming  the  screen  barrel.  The  stone  as  received  from  the  elevating  buckets  is  fed 
into  the  fine  screen  end.  Through  the  openings  in  this  screen  the  very  fine  materials,  dust, 
etc.,  are  taken  off;  and  as  the  stone  progresses  down  the  screen  barrel,  the  several  sizes  fall 
into  bins  arranged  below  them,  from  which  they  are  drawn  off  into  conveyances  as  required. 
The  storage  bins  vary  in  size  from  those  having  a  capacity  of  13  tons  to  those  having  a  capacity 
of  50  tons.  In  some  of  the  modern  types  of  bins,  provisions  are  made  so  that  a  bin  may  be 
raised  to  a  height  sufficient  to  permit  wagons  being  driven  under  gate  spouts. 

1/.  Washing  Crushed  Stone. — Crushed  stone  is  often  covered  with  a  tenacious 
film  of  dust  of  which  it  is  very  hard  to  get  rid.  Although  seldom  if  ever  done,  it  would  be 
advantageous  to  wash  stone  after  crushing  and  screening,  inasmuch  as  this  dust  is  of  such  size 
that  it  is  impossible  to  coat  it  with  cement,  and  so  tenacious  that  it  prevents  the  cement  from 
being  in  contact  with  the  aggregate. 

Ig.  Crushed  Limestone. — ^Limestone  crushes  with  a  flaky  fracture  and  a  con- 
siderable amount  of  dust.  If  the  finer  screenings  are  to  be  used,  it  is  well  to  roll  them  between 
rollers,  inasmuch  as  this  flaky  fracture  renders  them  extremely  friable  and  unsuited  to  the 
production  of  concretes  impervious  to  water  or  of  high  strength. 

2.  Screening  of  Sand  and  Gravel. — Screening  of  sand  and  gravel  may  be  done  by  hand  or 
by  machinery.  Hand-screening  is  adapted  to  small  jobs  and  light  work.  Power-screening  is 
adapted  to  handling  larger  quantities  of  material.  Screening  of  gravel  or  sand  containing  large 
amounts  of  coarse  material  can  be  done  more  cheaply  by  mechanical  than  by  hand  means, 
using  either  revolving  screens  or  fixed  screens  placed  upon  an  incline.  The  type  of  screening 
equipment  is  largely  determined  by  location  and  natural  topography,  and  the  availability  of 
power.  Revolving  screens  are  most  effective  and  economical  for  large  quantities,  the  material 
being  conveyed  by  bucket  elevators  to  the  screens  and  then  falling  into  bins  provided  with 
gates  convenient  for  unloading. 


Sec.  3-3] 


CONSTRUCTION  PLANT 


173 


Large  and  elaborate  plants  for  screening  of  sand  and  gravel  are  being  installed  in  increasing 
numbers  in  situations  where  dredging  of  these  materials  from  river  beds  is  practicable.  Many 
of  these  plants  are  now  turning  out  aggregate  of  exceedingly  high  quality,  the  screening  and 
grading  operation  being  incidental  to  the  elevation  of  this  material.  Necessarily  also  these 
materials  are  washed  while  being  screened  and  graded. 

3.  Washing  of  Sand  and  Gravel. — Gravel  is  not  infrequently  coated  with  a  tenacious  film 
of  material  which,  if  not  removed,  may  greatly  reduce  the  strength  of  the  concrete.  Sand  also 
is  not  infrequently  contaminated  with  clay,  loam,  or  slit  coatings  of  organic  matter.  Such 
coatings  are  responsible  for  a  great  deal  of  difficulty  and  many  defects  in  concrete;  and  their 
removal,  while  not  easy  even  by  washing,  is  decidedly  essential. 

Various  means  have  been  proposed  for  washing  sand  and  gravel.  Attempts  have  been 
made  to  wash  them  in  piles  with  a  hose  but  this  is  always  difficult  and  usually  impossible  to 
carry  out  properly,  inasmuch  as  the  materials  washed  from  the  upper  layers  are  carried  down 
by  the  stream  of  water  to  the  lower  portions,  where  they  are  rarely  dislodged.  Another  scheme 
is  shoveling  sand  into  one  end  of  a  V-trough,  washing  it  down  with  a  hose  and  endeavoring 
to  carry  off  the  finer  materials  in  the  runoff  water.  For  large  quantities  of  material  a  combina- 
tion of  a  trough  of  this  kind  with  an  ejector  has  been  successfully  used.  A  concrete  mixer  has 
also  proven  adaptable  to  this  kind  of  work,  water  being  turned  in  and  the  mixer  allowed  to 
overflow  while  the  drum  is  in  rotation.  Necessarily  all  of  these  processes  are  somewhat  ex- 
pensive and  add  to  the  cost  of  the  aggregate,  but  where  tests  indicate  that  the  quality  of  concrete 
will  be  seriously  affected  by  uncleanness  of  sand  or  stone,  it  should  be  undertaken  without 
hesitation  even  at  the  increased  cost. 

HANDLING  AND  STORAGE  OF  MATERIALS 

4.  General  Considerations. — The  handling  of  materials,  and  their  storage  and  disposal  is 
of  great  economic  importance  in  concrete  work.  Hundreds  of  tons  are  removed,  loaded,  trans- 
ported, unloaded,  piled  and  elevated  oftentimes  to  considerable  heights  before  the  making  of 
concrete  has  begun;  and  all  this  material  as  concrete  must  be  rehandled  one  or  more  times 
before  it  is  delivered  to  forms.  The  engineering  problems  prior  to  placement  are,  therefore, 
highly  important ;  and  their  adequacy  not  only  determines  rate  of  progress,  but  their  efficiency 
may  decide  whether  there  is  to  be  a  quick  turnover  or  a  slow  one,  with  corresponding  profit  or 
possibly  loss. 

It  is  axiomatic  that  gravity  should  be  employed  in  such  work  whenever  possible  by  utiliz- 
ing natural  advantages  of  site  to  the  fullest  extent.  It  should  also  be  borne  in  mind  that  there 
is  approximately  twice  the  quantity  of  stone  to  be  handled  as  sand;  and  twice  the  quantity  of 
sand  as  cement.  In  planning  a  job,  careful  routing  and  proportionate  disposal  of  these  materials 
should  therefore  receive  early  and  adequate  attention. 

It  is  also  trite  and  almost  unnecessary  to  say  that  suflficient  storage  room  should  be  pro- 
vided for  supplies  of  materials,  ample  to  insure  continuous  prosecution  of  work  when  desired. 
Shipments  may  be  held  up  through  any  number  of  unexpected  and  unforseen  happenings,  so 
that  unless  there  is  reserve  supply,  a  shutdown  must  result.  Specifications  often  stipulate 
that  a  certain  reserve  quantity  of  material  shall  be  maintained  on  the  job,  but  even  where  this 
salutary  provision  is  omitted,  contractor  and  owner's  engineer  alike,  for  their  individual  and 
mutual  protection,  should  have  regard  for  this  very  important  feature. 

It  would  seem  that  remarks  as  to  providing  proper  care  for  materials  on  delivery  to  the 
work  were  equally  unnecessary,  yet  disregard  of  these  important  matters  is  seen  every  day. 
Cement  always  reacts  with  water,  whether  such  water  comes  from  the  mixer  measuring  tank, 
or  whether  it  comes  from  rain,  or  from  condensed  steam,  or  from  dew,  or  from  water  absorbed 
from  the  ground.  Cement,  therefore,  should  always  be  stored  in  weather-tight  houses,  having 
floors  raised  at  least  6  in.  above  the  ground;  and  any  cement  directly  at  the  work  should  be 


174 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  3-5 


C/eats  short  or  cont/nuous 
nailed  io  cross  t/es>  which 


To  secure  greater  sfabiiity 
the  base  of  lower  courses 
may  be  made  three  to  four 
feet  wide  Crib  shouid  be 
set  up  as  material  is 
deposited 


kept  off  the  ground  and  carefully  covered  with  an  impervious  covering,  whether  or  not  the 
atmosphere  seems  damp,  or  rain  actually  falling,  or  the  weather  threatening. 

5i  Storage  and  Care  of  Stone. — One  of  the  essential  qualities  of  large  aggregate  for  con- 
crete is  cleanness.  Stone,  therefore,  should  not  be  dumped  indiscriminately,  so  that  when  it  is 
rehandled,  dirt  and  rubbish  are  carried  into  the  concrete.  A  thick  layer  of  sand,  or  preferably 
a  platform  of  planks  should  be  placed  on  the  ground  before  stone  is  deposited ;  and  not  only  will 
this  precaution  be  found  to  keep  the  material  clean,  but  it  furthermore  will  often  pay  for  its 
own  cost,  both  in  the  quantity  of  stone  saved  by  this  means  in  rehandling  and  also  in  assurance 
as  to  freedom  of  the  concrete  from  deleterious  foreign  matter. 

6.  Shoveling  Materials  Directly  from  Cars  to  Ground. — Where  a  siding  extends  to  the 
construction  site,  sand  and  stone  may  be  shoveled  directly  from  the  cars  to  the  ground,  which 
should  have  been  previously  smoothed.  That  portion  of  the  ground  designed  for  the  stone 
should  first  be  spread  with  a  layer  of  sand  at  least  1  in.  thick,  this  layer  serving  to  keep  the  stone 

clean  and  also  working  economy  in  subse- 
quent shoveling.  In  order  that  materials 
may  be  piled  high  and  the  track  be  kept 
may  be  spaced  about  3'c  toe  clear,  a  bulkhead  may  be  built  of  a  double 
row  of  2  by  12-in.  plank  with  1  by  3-in. 
cross-ties,  having  stops  as  indicated  in  Fig. 
1.  This  method  requires  no  fitting  or  cut- 
ting of  the  plank. 

7.  Storage  and  Care  of  Sand. — Sand 
should  not  be  dumped  directly  on  the 
ground,  but  for  like  reasons,  should  receive 
care  similar  to  that  described  for  stone. 
Although  sand  is  a  common  material — 
"common  as  dirt" — all  dirt  is  not  sand  and 
dirt  rarely,  if  ever,  makes  good  concrete.  It 
is  only  by  attention  to  such  seemingly  small  matters  that  a  job  can  be  well  organized,  made 
profitable,  and  the  best  results  secured. 

8.  Conveyance  Economics. — The  type  of  vehicle  in  which  sand  and  stone  are  conveyed 
exercises  a  large  influence  on  the  economy  of  a  job.  As  an  excellent  emploj'ment  of  gravity  to 
cut  labor  costs,  bottom-dumping  conveyances,  whether  horse-drawn  or  motor-driven,  or 
railroad  cars,  are  conspicuous  for  economy.  In  certain  situations,  of  course,  gravity  cannot  be 
employed.  In  these  the  use  of  a  locomotive  crane  with  grab  bucket  is  increasingly  prevalent; 
and  the  type  of  car  or  barge  used  to  convey  materials  within  reach  of  the  bucket  will  have  a 
pronounced  effect  on  the  amount  of  material  the  bucket  can  handle  in  a  given  time. 

As  an  example  of  comparative  conveyance  economies,  consider  the  following  with  respect 
to  two  types  of  railroad  cars: 

Two  quarries  are  located  on  different  railroads.  Railroad  "A"  is  prepared  to  supply 
only  hopper-bottom  cars;  railroad  ''B"  can  furnish  only  flat-bottom  cars.  Assume  gravity 
dump  to  be  impossible,  and  that  the  plan  of  operation  involves  unloading  the  stone  by  shovehng. 
Assume  also  that  one  quarry,  on  railroad  No.  ''A"  quotes  $1.30  per  cu.  yd.;  and  the  other,  on 
railroad  No.  B"  quotes  SI. 32  per  cu.  yd.  It  will  be  found  cheaper  in  the  end  to  order  material 
at  $1.32  per  cu.  yd.  in  flat-bottom  cars  for  the  reason  that  more  than  the  difference  in  first 
cost  can  be  saved  by  lessened  labor  in  unloading. 

The  reason  for  this  is  self-evident.  A  good  man,  under  efficient  superintendence,  can 
unload  2  cu.  yd.  per  hr.  from  a  flat-bottom  car,  as  against  1J>^  cu.  yd.  per  hr.  from  a  hopper- 
bottom  car — a  saving  of  at  least  3  cts.  per  cu.  yd. — and  this  proportional  saving  increases  as 
less  efficient  labor  is  employed.  These  figures  represent  average  results.  A  good  man  working 
under  a  yardage  or  carload  system  will  perhaps  average  50%  more  than  the  above,  but  the 


idinj 


Fig.  1. 


Sec.  3-9] 


CONSTRUCTION  PLANT 


175 


ratio  will  not  change  between  the  two  types  of  cars.  The  often -neglected  matter  of  shoveling, 
therefore,  becomes  a  matter  of  moment. 

9.  Unloading  Economies. — ^Low-side  cars  are  more  economical  for  unloading  than  high- 
side,  except  where  a  wagon  loader  (Figs.  2  and  3)  is  used.    Where  such  a  loader  is  emi)loyed, 


Fig.  2. 

the  car  side  to  which  it  is  attached  should  either  be  of  sufhcient  height  to  give  wagon  clearance, 
or  stakes  must  be  provided  to  raise  the  hopper  to  the  proper  level.  The  use  of  a  hopper  ex- 
pedites unloading  the  car,  relieving  possible  demuriage  charges  and  cutting  down  team  and 
wagon  hours.  One,  two,  or  three  hoppers  may  be  attached  to  a  singh;  car  and  one  or  more  men 
put  in  the  car  for  each  hopper,  depending 
upon  the  number  of  teams  available. 
Hoppers  should  be  filled,  ready  to  dump 
when  the  teams  range  alongside  the  car; 
and  the  more  quickly  materials  are  dis- 
charged into  wagons,  possibly  even  with- 
out stopping,  the  more  economical  will 
be  the  process. 

10.  Proper  Size  and  Type  of  Shovel. 
— Although  refinements  in  efficiency  can 
be  carried  to  extremes,  a  potent  factor 
in  securing  a  proper  output  of  work  in  so 
simple  an  operation  as  shoveling  is  a 
proper  size  and  type  of  shovel.  A  good 
worker  will  always  look  for  a  good  shovel, 
which  of  itself  is  eloquent  testimony  as 
to  the  importance  of  this  tool.  Frederick 
W.  Taylor  found  that  a  shovel  adapted 
to  a  load  of  21  lb.  gave  the  best  results. 

Such  a  shovel  corresponds  to  the  standard  No.  4  size  shovel.  The  No.  3  shovel  is  somewhat 
smaller.  The  size  of  shovel  should  always  be  chosen  with  reference  to  the  weight  of  the  ma- 
terials to  be  handled.  *    u      i  • 

The  better  the  quality  of  material  in  a  shovel,  the  longer  will  it  last.  A  shovel  is  a  con- 
veying tool  and,  at  the  same  time,  it  is  a  cutting  tool  no  less  than  a  chisel  or  a  drill.  ISo  con- 
tractor would  consider  using  an  inferior  steel  for  such  cutting  instruments,  yet  m  buying  shovels 


Fig.  3. 


176 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  3-11 


many  consider  first  cost  only,  having  little  regard  to  performance  or  endurance.  It  is  ele- 
mentary economics  to  balance  the  value  of  a  shovel  costing  $9  a  dozen  which  lasts  about  2 
months,  against  the  value  of  a  shovel  costing  15  a  dozen,  which  lasts  1  month  or  even  less,  par- 
ticularly when  its  performance,  in  addition  to  its  absolute  existence,  is  taken  into  account. 


1 


Fig.  4. 


11.  Clam-shell  Buckets. — When  gravity  dumping  is  precluded,  a  most  efficient  unloading 
device  is  the  clam-shell  bucket  (Fig.  4),  hung  from  derrick  or  locomotive  crane.  With  this 
combination  a  skilled  engineman  can  unload  a  large  quantity  of  material  in  a  day,  but  care 
should  be  taken  that  the  bucket  chosen  is  one  suited  to  the  work.    Some  buckets  tend  to  ride 


Fig. 


the  material  when  it  is  at  all  resistant,  while  others  are  so  designed  that  they  fill  to  the  capacity 
at  each  bite,  with  proportionate  efficiency  and  economy.  The  cost  of  equipment  of  this 
type  is  necessarily  large,  so  that  proportionate  care  should  be  taken  in  choosing  the  type  of 


Sec.  3-12] 


CONSTRUCTION  PLANT 


177 


bucket.  No  matter  how  excellent  the  derrick,  or  crane,  or  engine,  or  operative,  a  poor  bucket 
will  negative  them  all  and  run  up  handling  costs  at  an  alarming  rate.  An  orange-peel  bucket  is 
a  digging  rather  than  an  unloading  tool  and  is  not  well  adapted  to  the  usual  rehandling  of 
materials. 

12.  Bucket  Unloaders  and  Conveyors. — There  are  an  almost  endless  variety  of  elevating 
=  bucket  unloaders  each  suited  to  some  particular  need.    When  the  quantity  of  materials  to  be 
l]  handled  and  stored  is  considerable,  a  bucket  elevator  installation  (Fig.  5)  may  prove  very 
economical,  the  more  particularly  as  it  makes  possible  the  use  of  gravity  discharge  from  con- 
veyance  to  elevating  buckets  as  well  as  gravity  discharge  from  storage  bins  through  measuring 
I  hoppers  to  the  mixer.    The  installation  and  power  equipment  required  for  such  elevating 
|;  mechanisms  is  not  necessarily  expensive  or  extensive.    Some  lighter  types  are  shown  in  Figs. 
6  and  7,  and  from  these,  the  plant  may  range  up  to  the  heavier  types,  capable  of  handling  very 


Fig.  6. 


.  large  quantities.  In  each  individual  layout,  the  needs  should  be  studied  and  the  economy  or 
lack  of  it  determined.  No  hard  and  fast  recommendation  can  be  made  that  will  apply  to  all 
situations. 

13.  Belt  Conveyors.— In  certain  situations  an  endless  belt,  grooved  to  V-form  by  pidleys 
over  which  it  runs,  furnishes  a  rapid  and  excellent  means  of  handhng  raw  concrete  materials. 
It  cannot,  however,  raise  the  materials  so  nearly  vertically  as  can  the  bucket  conveyor,  its 
elevating  slope  being  limited  to  about  1  vertical  foot  for  every  2,^  horizontal  feet.    The  ap- 

!  pUcations  of  conveying  belts  are  without  number,  but,  as  in  the  case  of  the  bucket  conveyor,  no 
blanket  recommendation  can  be  made.  The  manufacturers  of  conveying  machinery  are  in 
position  to  advise  with  respect  to  types,  appHcability,  and  relative  economies  of  various  types 

I     of  conveyors  for  any  given  set  of  conditions,  and  should  be  consulted  for  individual  needs. 

I  14.  Storage  and  Handling  of  Sack  Cement.— Cement,  because  of  case  in  handling,  is  usu- 

i    allv  ordered  in  cloth  or  paper  sacks,  each  holding  94  lb.   Cloth  sacks  are  less  liable  to  rupture 


178 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  3-15 


than  are  paper  sacks,  but  their  cost  is  greater.  When  sack  cement  is  received,  a  chain  of  laborers 
is  formed  between  cars  and  storage  house,  each  man  shouldering  one  sack.  Economies  in  such 
procedure  may  be  introduced  by  insuring  ready  entrance  and  exit  both  to  cars  and  to  storage 


Fig.  7. 


houses,  with  adequately  wide  gang  planks  to  cars,  so  that  confusion  and  interference  may  be 
prevented.  The  speed  at  which  men  will  work  is  then  a  question  of  the  personality  and  driving 
force  of  the  superintendent  or  foreman. 


Fig.  8. — Proper  method  of  bundling  cement  sacks. 

Upper  left:  A  bundle  of  50  cement  sacks  laid  out  flat  with  2  ropes  40  in.  long,  under  the  pile,  and  with  a  longer 
rope  of  about  8  ft.,  resting  on  top. 

Upper  right:  The  first  operation  in  bundling  is  to  bring  two  of  the  ropes  over  the  pile,  as  shown,  tying  tightly. 

Lower  left:  After  the  short  ropes  have  been  tied,  the  bundle  is  turned  over,  and  the  long  rope  brought  around 
and  crosses  in  the  middle  of  the  bundle,  engaging  first  the  shorter  ropes. 

Lower  right:  Bundle  of  50  cement  sacks  tied  and  tagged  ready  for  shipment. 

15.  Bundling  and  Storage  of  Empty  Cement  Sacks. — Inasmuch  as  each  cement  sack  has  a 
return  value  of  10  cts.,  it  is  important  that  none  should  be  lost,  damaged,  or  destroyed.  Fur- 


Sec.  3-16] 


CONSTRUCTION  PLANT 


170 


thermore,  the  cleaning,  bundling,  and  shipping  of  these  sacks  becomes  an  operation  of  impor- 
tance on  large  jobs.  Much  cement  is  lost  when  bags  are  insufficiently  shaken,  and  this  retained 
cement  further  adds  to  the  weight  and  bulk  of  sacks  bundled  for  return.  The  proper  method 
of  bundling  sacks  for  return  shipment  is  shown  in  P'ig.  8.  In  showing  a  bundle  of  50  sacks,  it 
has  been  with  the  purpose  of  emphasizing  the  greater  convenience  in  handling  with  equal  ad- 
vantages as  a  counting  unit  of  the  50-sack  bundle,  rather  than  the  100-sack  bundle. 

16.  Storage  and  Handling  of  Water. — In  most  instances  water  in  pipes  is  within  reach  of 
a  concrete  job.  Where  this  is  not  so  and  water  must  be  pumped,  reservoirs  of  adequate  capacity 
properly  protected  against  contamination  should  be  supplied.  From  such  reservoirs,  water 
can  be  distributed  in  pipes  to  be  used  as  needed.  The  storage  of  water  is  so  simple  and  so  easily 
carried  out  that  the  needs  of  each  individual  situation  are  of  greater  determining  importance 
than  any  particular  type  of  pumping  or  distributing  apparatus. 

17.  A  Typical  Installation. — Fig.  9  illustrates  storage  arrangements  and  handhng  facilities 
as  installed  in  connection  with  a  large  building  for  the  Singer  Manufacturing  Co.  at  Elizabeths- 
port,  N.  J.    The  available  storage  space  in  this  instance  was  a  narrow  strip  20  ft.  wide  between 


Elevation 

Fig.  9. 


the  railroad  track  and  the  building,  of  which  the  work  in  question  formed  an  extension.  A 
trench  was  made,  extending  the  length  of  this  available  space,  and  this  was  sheathed  and 
converted  into  a  tunnel  by  a  covering  of  2-in.  plank.  In  the  bottom  of  the  trench  was  laid  a 
suitable  track  for  the  operation  of  a  skip  car.  Gn  the  ledger  pieces  were  mounted  two  saw- 
toothed  measuring  hoppers,  fitted  with  wheels. 

Materials  were  unloaded  from  the  cars  and  piled  over  the  trench,  sand  and  stone  in  alter- 
nate piles.  The  saw-toothed  measuring  hoppers  were  kept  continually  against  the  toe  of  the 
sand  and  stone  piles  to  faciUtate  charging"  by  breaking  down  of  the  face  of  the  piles.  Four 
men  in  this  way  handled  the  materials  for  about  30  cu.  yd.  of  concrete  per  hr.  Materials 
were  automatically  dropped  from  the  measuring  hoppers  into  the  skip  car  as  it  passed  below 
the  hoppers  on  its  way  to  the  mixer.  The  A-frame  shown  in  Fig.  10  has  been  used  to  good 
advantage  as  a  substitute  for  the  trench.  With  this  arrangement  one  man  only  was  needed  to 
charge  the  measuring  hopper. 


Sec.  3-18] 


CONSTRUCTION  PLANT 


181 


CONCRETING  PLANT 

18.  Plant  Economics. — Necessarily  much  of  the  plant  for  the  handling  and  storage  of 
materials  must  be  considered  as  a  part  of  the  concreting  plant  proper.  The  economies  of  the 
whole  plant  therefore  depend  upon  the  individual  and  collective  economies  of  its  elements. 
The  main  factors  affecting  these  are  first  cost,  cost  of  installation,  cost  of  operation,  cost  of  main- 
tenance, cost  of  removal,  salvage,  and  interest  on  the  investment. 

18a.  First  Cost. — First  cost  of  plant  includes  many  items  in  addition  to  prices 
for  machinery.  Bonus  for  quick  delivery,  where  equipment  is  required  in  a  hurry;  express 
charges;  tracing  charges;  and  a  hundred  other  items  all  swell  the  quoted  figures.  And  it  is  not 
always  best  to  consider  first  cost  too  closely.  A  plant  that  is  cheapest  in  first  cost  may  not  be 
the  most  economical;  and  labor  losses  due  to  delay  speedily  offset  differences  in  price  betw^een 
good  and  poor  equipment.  Furthermore,  low  costs  of  operation  and  maintenance  with  higher 
salvage  returns  still  further  reconcile  any  disparit}'-. 

186,  Cost  of  Installation. — Cost  of  installation  varies  with  the  character  of  the 
plant,  cost  of  labor,  location  of  the  work  and  a  variety  of  factors  which  must  be  separately 
considered  for  each  situation. 

18c.  Cost  of  Operation. — Cost  of  operation  depends  both  upon  plant  arrangement 
and  upon  organization.  The  concreting  plant  should  be  of  a  type,  size,  capacity,  and  arrangement 
to  permit  continuous  operation  during  working  hours,  assuming  an  organization  so  coordinated 
as  to  make  this  possible  and  desirable ;  and  the  character  and  arrangement  of  plant  will  depend 
to  a  large  extent  upon  local  conditions,  such  as  contour  of  the  ground,  class  of  construction, 
manner  in  which  materials  are  delivered  to  the  site,  total  yardage  to  be  placed,  time  limit,  bonus, 
penalty  and  other  financial  considerations  which  permit  the  use  of  equipment  more  or  less 
expensive  and  elaborate.  In  addition,  attention  must  be  given  to  the  time  of  the  year  during 
which  the  work  is  to  be  done,  the  normal  temperature  at  that  season  for  the  particular  locality, 
and  the  amount  of  land  available  for  plant  and  material,  since  storage  is  always  a  factor  in 
operation. 

18d.  Cost  of  Maintenance. — Cost  of  maintenance  includes  upkeep  of  machines, 
repairs,  oil,  etc.,  this  being  greater  or  less  according  to  the  mechanical  excellence  of  the  plant 
and  to  its  disposition  and  treatment. 

18e.  Cost  of  Removal. — Cost  of  removal  includes  clearing  the  site  of  the  plant 
and  its  appurtenances  after  completion  of  the  work.  This  cost  will  vary,  according  as  more  or 
less  of  the  plant  is  sold  or  junked,  with  proportionate  lessening  of  care  and  labor  required  in 
loading  on  cars,  and  of  transportation. 

18/.  Salvage. — The  salvage  value  of  machinery  is  always  problematical.  It 
usually  is  worth  what  can  be  obtained  for  it.  Certainly,  depreciation  on  contractor's  machinery 
is  very  large  and  most  estimates  of  salvage  value  should  be  liberally  discounted. 

19.  Balancing  the  Plant.— The  general  layout  of  the  work  will  probably  be  the  determining 
factor  in  the  choice  of  means  adopted  for  carrying  out  each  portion  of  the  work.  The  total 
yardage  of  concrete  will  also  have  a  pronounced  effect,  possibly  suggesting  two  or  more  separate 
installations  of  medium  size,  or  a  single  installation  of  greater  size,  or  a  number  of  smaller 
mixers  placed  on  different  parts  of  the  work.  Various  factors  must  be  balanced  one  against 
the  other  and  various  layouts  planned,  with  a  following  through  from  delivery  of  raw  materials 
to  delivery  of  concrete  in  the  forms,  with  juggling  of  one  scheme  with  another  until  the  most 
advantageous  result,  consistent  with  allowable  cost,  is  secured.  Careful  plannmg  of  plant 
before  starting  the  job  is  well  repaid  in  results,  and  a  well-balanced  plant  is  far  more  profitable 
than  one  poorly  balanced.  Installation  of  a  mixer  of  double  the  capacity  of  the  charging 
facilities,  or  of  a  fraction  of  the  capacity  of  the  handling  facilities  for  the  mixed  materials  is 
sheer  waste. 

20.  Typical  Plants.— Some  typical  examples  of  plants  which  have  proven  successful  in 
service,  are  given  in  the  following  paragraphs: 


182 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  3-20 


Fig.  11  shows  an  arrangement  on  the  work  of  Cramp  &  Co.,  Philadelphia.  It  will  be  noted 
that  materials  are  delivered  in  bottom-dump  wagons  upon  the  incline,  and  pass  by  way  of 
bucket  elevator  to  the  bins  above  the  mixer.  Once  in  the  bins,  it  is  a  gravity  process  through 
measuring  hopper  to  mixer.    Messrs.  Cramp  &  Co.  report  289  cu.  yd.  with  this  plant  in  8)^  hr., 


with  a  crew  of  eight  men,  and  covering  all  handling  from  wagons  and  cement  storage  to  delivery 
bin  on  hoist  tower.    The  mixer  is  }i-yd.  capacity. 

Fig.  12  illustrates  an  arrangement  adopted  by  the  Turner  Construction  Co.  on  the  Bush 
Stores,  South  Brooklyn.  Materials  were  delivered  to  the  work  in  standard  cars,  and  unloaded 
by  shovel  into  special  hoppers  as  indicated.    These  hoppers  were  readily  portable,  and  each 


Sec.  3-20]  CONSTRUCTION  PLANT  183 

I 

I  hopper  had  a  capacity  for  approximately  1  cu.  yd.  Materials  were  drawn  off  as  required  into 
I  cars  with  a  capacity  of  6  cu.  ft.,  and  wheeled  to  the  mixer  which  was  set  at  a  lower  level  so  that 
!!  the  fixed  hopper  was  on  a  level  with  the  ground.  The  bumping  post  A  facilitated  discharge 
I  of  carts  into  the  hopper.    Carts  were  wheeled  up  against  the  bumper  when  a  slight  lift  on  the 

handles  did  the  trick.  ^ 

Fig.  13  illustrates  the  plant  used  in  the  erection  of  the  buildings  for  Foster  Armstrong  Co. 

at  Despatch,  N.  Y.  The  work  on  these  buildings  was  carried  on  through  the  winter  months 
.  and  the  bins  indicated  provided  the  readiest  means  for  heating  the  materials  to  the  desired 
fj  temperature  of  90  to  100°F.  An  auxiliary  measuring  tank  took  care  of  the  salt  solution  used 
ij  in  the  concrete  mixture.    Steam  coils  also  served  to  warm  the  water  used  in  mixing  the  concrete. 

When  mixed,  the  concrete  was  placed  immediately;  in  no  case  more  than  10  min.  elapsed, 
i   When  the  concrete  had  been  placed,  it  was  protected  against  the  action  of  frost  by  a  solid  wood 

covering,  blocked  up  at  least  6  in.  above  the  surface  of  the  floor  in  a  manner  to  permit  free 


Fig.  12. 


circulation  of  air  beneath  the  covering.  Heat  was  introduced  beneath  the  floor  (or  in  the 
case  of  ground  floors,  beneath  the  board  covering)  by  means  of  steam  coils  and  salamanders, 
provision  being  made  for  the  escape  of  sufficient  steam  beneath  the  covering  to  prevent  prema- 
ture drying  out  of  the  concrete.  Salamanders  were  sprinkled  freely  with  water,  thus  producing 
the  necessary  amount  of  moisture,  and  small  openings  were  left  in  the  floor  slab  to  permit 
the  warm  air  to  circulate  over  the  upper  surface  of  the  floor.  The  sides  of  the  floor  were  pro- 
tected by  canvas  curtains  which  extended  downward;  to  the  floor  next  below. 

There  were  placed  beneath  the  floor  and  beneath  the  panels  on  top  of  the  floor,  at  intervals 
of  10  ft.,  self -registering  thermometers,  which  in  no  case  showed  lower  than  32°.  This  tempera- 
ture was  maintained  until  the  test  cubes  which  had  been  allowed  to  set  on  the  floor  and  beneath 
the  top  covering  showed  the  strength  used  as  a  basis  for  the  design. 

The  extra  plant  involved  in  carrying  on  winter  work  involves  considerable  outlay,  and  work 
in  freezing  weather  should  not  be  undertaken  without  a  thorough  understanding  of  all  that  is 
involved. 

Fig.  14  indicates  a  more  or  less  elaborate  plant,  designed  fof  hirgc  work,  or  for  crarnjx'd 


184 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  3-20 


quarters.  Tbe  plant  consists  of  a  suitable  bucket  elevator,  designed  to  handle  the  entire 
aggregate.  This  elevator  discharges  the  materials  into  trough  screens  as  indicated.  While 
passing  through  these  screens,  the  coarse  materials  are  washed  by  a  flow  of  water  applied  at  the 
head,  and  the  sand  is  still  more  thoroughly  washed  by  passing  through  the  water  boot  and  in- 
clined worm.  The  washed  materials  are  discharged  from  the  first  flight  of  trough  screens  upon 
inclined  troughs  leading  to  a  fixed  measuring  hopper  at  the  mixer.    The  lower  end  of  the 


Pivot  on  which  , 
bucket  tuma  for 
discharging 


Trapvdoors  for 
tfnloadlngY^grs 


Steel  Bucket  for  ^ 
hoisting  concrete 


Pivot  for  bucket- 


Gates  for         i  \ 

'discharging  sand 
and  gravel  not  showi 


2 


^veliL^ 


3rd  .tloor  leVel 


2nd  Irtoor  level 


Front  guldo 


-  Crab  for 
hoisting  hue 


hi  ii 


/^jlansome^j    j  | 
"-jpatenteilii    .  | 
^    '^^'|ooncretei  !L- 
^     1i  miier,  |jLr<j 

lull 


1  rJ,  '? 


|iTr?it;Tr;H7rr^i 
I  !i  !;        \  • 


Fig.  13. 


troughs  is  fitted  with  a  gate  to  control  the  flow.  Such  excess  material  as  cannot  be  cared  for 
by  the  measuring  troughs  falls  to  the  ground  in  piles  as  indicated.  Two  belt  conveyors  operat- 
ing in  tunnels  beneath  the  piles  permit  ready  draft  against  these  reserve  piles,  delivering  materi- 
als to  the  original  elevator,  and  thence  to  the  measuring  troughs.  With  such  a  plant  it  is  a 
simple  matter  to  handle  upward  of  50  cu.  yd.  per  hr.  with  four  men. 


Sec.  3-20]  .  CONSTRUCTION  PLANT  lg5 

Figs.  15  and  16  illustrate  two  set-ups  of  practically  the  same  plant,  and  illustrate  forciblv 
the  importance  of  proper  arrangement.  With  the  arrangement  shown  in  Fig.  16,  17  mei. 
handled  72  cu.  yd.  in  43^  hr.    With  the  arrangement  shown  in  Fig.  15,  15  men  handled  87  cu! 


Fig.  14. 

yd.  in  43^  hr.,  a  saving  of  approximately  13  cts.  per  cu.  yd.  In  Fig.  15  the  runway  and  plat- 
form are  too  small,  with  the  result  that  the  men  interfere  with  each  other,  and  cannot  work  to 


Fig.  15. 


advantage.  Furthermore,  the  use  of  the  feed  chute  involves  assembly  of  the  batch  in  the 
mixer  drum.  Water  was  fed  to  the  machine  a  bucketful  at  a  time,  requiring  an  extra  man  for 
this  purpose.    In  Fig.  16  a  charging  hopper  is  substituted  for  the  feed  chute,  and  both  platform 


186 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  3-21 


and  runway  are  increased  in  size.  Water  is  fed  to  the  mixer  through  a  pipe,  and  all  operating 
levers  are  controlled  by  one  man.  Provision  is  also  made  to  take  care  of  any  material  working 
down  beneath  the  mixer,  with  the  result  that  wear  and  tear  on  journals,  etc.,  is  reduced. 


Side  Ele-Yat'ioa 

Fia.  16. 


The  difference  in  cost  of  the  two  arrangements  amounted  to  $59.  The  illustrations  are 
taken  from  actual  experience,  and  indicate  results  secured  under  different  superintendents. 

21.  Machine  vs.  Hand-m.ixing. — Except  in  relatively  small  quantities,  hand-mixing  of 
concrete  is  not  to  be  economically  considered.    Furthermore,  hand-mixing  is  inferior  to  ma- 


chine-mixing, with  no  comparison  in  quantity  output.  The  province  of  a  mixing  machine  is 
essentially  the  thorough  incorporation  of  materials — one  of  the  fundamentals  in  the  production 
of  sound,  enduring  concrete.  Mixing,  therefore,  should  be  accorded  the  respect  due  its  impor- 
tance, and  the  best  possible  means  chosen  for  its  accomplishment. 


Sec.  3-22] 


CONST  R  UCTION  PL  A  N  T 


187 


I  22.  Types  of  Mixers. — The  general  types  of  mixers  which  have  endured  and  are  on  the 

I  market  at  the  present  time  may  be  classified  as  drum  mixers,  trough  mixers,  gravity  mixers, 

i  and  -pneumatic  mixers. 

i  22a.  Drum  Mixers. — Drum  mixers  (Fig.  17)  are  essentially  of  a  typo,  differing 

I  mainly  in  excellence  of  mechanical  construction  and  arrangement.    The  action  of  all  of  them 


Fig.  is. — Low  charging  drum  mixer. 


is  about  the  same  so  far  as  mixing  is  concerned,  the  operation  being  accomplished  by  agitation, 
lifting,  and  pouring  of  the  several  materials  by  blades  and  scoops  attached  to  the  inside  of  the 
mixer  drum.  With  the  exception  of  tilting  mixers,  discharge  of  the  materials  from  the  drum 
is  accomplished  by  inserting  a  trough  into  one  side  of  the  drum,  in  such  position  as  to  catch 
the  concrete  as  it  is  poured  from  the  mixing  buckets.  Minor  differences  in  charging  mechan- 
isms and  arrangements  are  to  be  noted  in  different  makes,  but  the  action  of  all  is  essentially 


Fig.  19. — Small  pot  mixer. 


the  action  of  a  churn,  in  which  capacity  they  would  function  if  filled  with  cream.,  instead  of 
with  stone,  sand,  cement,  and  water. 

Of  the  low-charging  mixers,  the  mixer  shown  in  Fig.  18  is  typical.  Small  pot  mixers 
such  as  shown  in  Fig.  19  are  excellent  for  small  work. 

226.  Trough  Mixers.— Trough  mixers  are  paddle  mixers  of  one  type  or  another. 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  3-22c 


They  may  be  batch  mixers  of  theshovcUng  type  (Fig.  20), or  continuous  mixers  (Fig.  21),  in  which 
a  sectional  screw  rotates  in  an  open  trough.  Continuous  mixers  have  not  met  with  general 
favor  as  have  batch  mixers  since  many  engineers  object  to  these  mixers  on  the  grounds  of 
uncertainty  of  mixing  operation. 

22c.  Gravity  Mixers. — Gravity  mixers  are  essentially  a  series  of  large  funnels 
or  pans  suspended  one  above  another  with  bottom  gates  which  can  be  opened  successively, 
permitting  materials  to  flow  from  one  into  the  other  with  incidental  mixing  to  a  greater  or 


Fig.  20. — Batch  mixer  of  the  shoveling  type. 

less  extent.  Gravity  mixers  are  often  urged  in  preference  to  power-driven  mixers  on  grounds 
of  cheapness  in  operation  and  low  first  cost,  permitting  their  being  scrapped  when  worn;  but 
many  engineers  do  not  advocate  their  use  because  of  the  inherent  uncertainty  of  their  mixing 
operation  and  oftentimes  the  requirement  of  deterimental  quantities  of  water  to  prevent  the 
mass  sticking  in  the  pans. 

22d.  Pneumatic  Mixers. — Pneumatic  mixers  have  been  developed  by  various 
inventors.    At  the  present  time  there  are  two  main  types  on  the  market.    In  some  of  these 


Fig.  21. — Continuous  mixer. 


machines  premixing  is  had  before  delivery,  either  mechanically  or  by  the  agitation  of  air  pres- 
sure, while  in  others  the  charge  is  introduced  into  a  chamber,  dependence  for  mixing  being  placed 
on  what  may  happen  in  transit  through  pipes  under  the  delivering  air  pressure.  Pneumatic 
mixers  have  their  own  particular  field — that  of  placing  concrete  in  forms  where  access  is  par- 
ticularly difficult — but  because  of  the  large  compressor  plant  which  must  be  installed  for 
each  mixer,  and  for  other  reasons  which  are  valid  and  of  importance  in  many  classes  of  work, 
their  use  is  relatively  restricted. 


Sec.  3-23] 


CONSTRUCTION  PLANT 


189 


23.  Machine  Mixing. 

23a.  Time  of  Mixer  Operations. — Considering  the  concreting  plant  proper  as 
an  installation  for  mixing  together  raw  materials  to  form  concrete,  the  plant  cycle  can  be 
considered  as  complete  in  three  operations,  viz.,  charging,  mixing,  and  discharging. 

In  charging  and  discharging  the  mixer,  a  time  limit  is  imposed  both  by  the  physical  laws 
governing  the  flow  of  materials  from  one  container  to  another,  and  also  (in  the  case  of  power- 
loading,  or  side-loading  hoppers  in  particular)  by  the  physical  limitations  of  operatives  and  of 
the  mechanism  itself.  As  plant  refinements  are  given  consideration  (particularly  with  regard 
to  the  gravity  loading  of  measuring  or  charging  hoppers  from  overhead  bins)  this  loading 
time  is  diminished;  but  when  a  side-loading  hopper,  or  a  measuring  hopper  is  charged  by  wheel- 
barrows, the  time  is  lengthened  more-or-lcss  according  to  the  perfection  of  the  runway  arrange- 
ments and  the  speed  at  which  the  men  work. 

In  the  following  table  is  given  the  result  of  timing  of  different  types  of  mixers  on  different 
'  classes  of  work.  These  studies  were  made  both  with  a  seconds  clock,  motion  picture  camera, 
and  with  a  stop-watch,  and  are  the  summary  of  a  large  number  of  observations.  From  this  it 
will  be  seen  that  the  loading  periods  vary  greatly;  that  the  unloading  periods  have  an  equally- 
great  variation;  that  the  mixing  periods  are  usually  dependent  upon  the  time  taken  in  loading 
and  unloading;  and  that  successive  operations  overlap,  the  endeavor  of  the  mixer  man  being 
to  get  out  his  material  on  as  near  a  batch-a-minute  schedule  as  is  possible.  In  a  number  of 
instances  it  will  be  noted  from  this  table,  such  a  procedure  gives  a  negative  mixing  time. 


Summary  of  Timing  Data  on  Concrete  Mixers 
Time  given  in  minutes  and  seconds. 


Run 

Kind  of 
mixer 

Loading 
means 

Load- 
ing 

Un- 
loading 

Actual 
mixing 

Actual 
total 

Loading 
and 
unloading, 
total 

Time  of 
mixing 
batch, 
minimum 
schedule 

1 

Lakewood,  1  yd.  .  . 

Batch  hopper . 

0:51 

0:59 

0:11 

2:02 

1:50 

—0:50 

2 

Koehring,  1  yd ...  . 

Batch  hopper . 

0:36 

0:34 

0:42 

1:51 

1:10 

—0:10 

3 

Smith,  3^  yd  

Batch  hopper . 

0:15 

0:19 

0:25 

1:01 

0:34 

+0:26 

4 

Foote,  3^  yd  

Side  loader .  .  . 

0:16 

0:17 

0:20 

0:54 

0:33 

+0:27 

5 

Foote,  K  yd..  . .  .  . 

Side  loader.  .  . 

0:23 

0:27 

0:25 

1:15 

0:50 

+0:10 

6 

Chain  Belt,  K  yd. . 

Side  loader .  .  . 

0:07 

0:35 

0:28 

1:10 

0:42 

+0:18 

7 

Koehring,  K  yd. .  . 

Side  loader .  .  . 

0:12 

0:32 

0:21 

1:05 

0:44 

+0:16 

8 

Lakewood,  1  yd .  .  . 

Side  loader .  .  . 

0:11 

1:02 

1:11 

2:25 

1:12 

—0:12 

9 

Ransome,  1  yd. .  .  . 

Batch  hopper. 

0:35 

0:40 

1:40 

2:57 

1:15 

—0:15 

10 

Ransome,  yi  yd. .  . 

Side  loader .  .  . 

0:08 

0:12 

0:54 

1:10 

0:20 

+0:40 

11 

Chain  Belt,  3'^  yd. 

Side  loader.  .  . 

0:13 

0:27 

0:11 

0:51 

0:40 

+0:20 

12 

Ransome,  3^  yd. .  . 

Side  loader.  .  . 

0:18 

0:38 

0:46 

1:32 

0:56 

+0:40 

13 

Side  loader .  .  . 

0:17 

0:29 

0:20 

1:06 

0:46 

+  0:14 

0:21 

0:33 

0:28 

1:29 

0:53 

+0:70 

Average,  omitting  8  and  9  

0:19 

0:29 

0:17 

1:17 

0:49 

+0:11 

Note. — Mixer  8  had  very  poor  blading.  Mixer  9  was  fed  by  derrick  bucket.  Long  mix- 
ing due  to  inability  to  get  raw  material  and  to  dispose  of  mixed  concrete. 

236.  Time  of  Mixing. — Insufficient  time  is  given  to  the  mixing  operation  itself 
in  most  commerical  work.  Too  long  a  period  may  possibly  be  indulged,  but  it  usually  is  not; 
and  no  fear  need  be  entertained  of  injuring  the  concrete  by  a  mixing  interval  up  to  and  in- 
cluding 30  min.  The  mixing  operation  proper  comprehends  not  only  admixture  of  materials, 
but  also  reaction  between  cement  and  water  with  distribution  of  the  products  of  this  reaction 


190 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  3-23c 


over  the  surfaces  of  sand  and  stone.  The  time  required  for  such  thorough  incorporation,  and, 
to  a  certain  extent,  for  the  hastening  of  the  reaction  between  cement  and  water,  depends  upon 
the  adequacy  of  the  blading  and  cleanness  of  the  mixer.  Oftentimes  mixers  are  put  on  work 
with  the  drum  (Fig.  22)  half-choked  with  concrete  or  full  of  holes,  or  the  blading  so  worn  that 
they  cannot  handle  the  materials.  Necessarily  such  mixers  will  not  produce  the  same  result 
as  a  clean  mixer,  properly  bladed  and  having  a  tight  drum.  Also,  mixers  are  not  all  equally 
efficient. 

So  many  factors  enter  into  the  making  of  good  concrete,  that  a  hard  and  fast  rule  applicable 
to  all  cases  cannot  be  made,  but  in  general  it  may  be  said  30  sec.  or  even  1  min.  of  mixing  is  in- 
adequate. It  is  far  better,  when  it  is  desired  to  do  a  thoroughly  first-class  job,  to  employ 
more  mixers  even  at  a  higher  first  cost  for  equipment  and  work  them  on  a  longer  schedule,  than 
it  is  to  attempt  with  one  mixer  to  get  out  concrete  on  a  rapid-fire  schedule.  The  latter  method 
often  brings  a  chain  of  unfortunate  consequences,  for  not  only  is  the  concrete  inadequately 
mixed  and  the  cement  insufficiently  used,  but  also  excess  water  is  nearly  always  added  in  order 
to  make  the  mass  free-working  and  to  diminish  the  labor  of  mixing. 

23c.  Drum  Speeds. — Extended  experimentation  has  established  standard 
drum  speeds  for  various  sizes  of  mixers.  Engines  and  motors  as  supplied  with  them  are  so 
regulated  as  to  maintain  these  speeds  practically  constant.  Necessarily,  as  the  art  of  concrete 
making  advances,  changes  will  result,  but  the  present  rotational  speeds  of  standard  mixers 
seem  suited  to  the  requirements  of  average  practice.    Obviously,  a  slower  drum  speed  would 


Fig.  22. — Mixer  drum.  Fig.  23. — Charging  hopper  mounted  on  mixer  frame. 

result  in  less  thorough  incorporation  of  materials  and  a  greater  speed  might  cause  the  materials 
to  stick  to  the  drum  through  centrifugal  action.^    It  is  best,  therefore,  to  adhere  to  speed 
ratings  prescribed  by  manufacturers  unless  such,  speeds  are  patently  inefficient.  Inasmuch 
as  any  concrete  mixer  that  will  perform  its  operations  better  and  more  quickly  than  its  com-  , 
petitors  is  sure  to  have  correspondingly  greater  sales,  it  is  safe  to  assume  that  mixer  manu-  | 
facturers  have  adopted  for  their  product  the  maximum  speed  consistent  with  proper  operation.  I 
It  is  not  well,  therefore,  for  the  user  to  attempt  economies  by  changing  speed  of  the  mixer  drum,  j 
2Zd.  Loading  the  Mixer. — There  are  many  time  economies  that  may  be  effected  ^ 
in  loading  the  charge  of  materials  into  the  mixer.    Various  types  of  loading  mechanism  have 
been  designed  to  meet  different  conditions  of  service  and  the  time  cycle  of  each  is  different.  ■ 
A  study  of  each  type  will  show  its  adaptability  to  particular  needs.  i 

Charging  Hoppers. — Where  a  charging  hopper  mounted  on  the  mixer  frame  can  be  used, 
as  in  Fig.  23,  the  limitation  to  charging  time  is  dependent  upon  the  design  of  this  hopper,  upon 
the  slope  of  its  sides  and  upon  the  size  of  opening  from  hopper  to  drum.  Inasmuch  as  this 
type  of  charging  device  is  usually  loaded  by  gravity  from  superposed  measuring  hoppers,  like 

1  For  studies  of  nnxer  actions  see  N.  C.  Johnson;  Eng.  Rcc,  Dec.  4,  191o. 


Sec.  Z-23d] 


CONSTRUCTION  PLANT 


191 


considerations  must  be  taken  into  account  in  their  design;  and  always  there  must  be  prompti- 
tude in  releasing  of  gates,  etc.  In  some  very  large  operations  such  as  the  Elephant  Butte 
Dam,  pneumatic  opening  devices  have  been  installed  with  an  interlocking  system,  so  that  a 
sequence  of  operations  is  carried  out  with  almost  perfect  regularity  and  great  efficiency. 

Power  Loaders. — Side  loaders  or  power  loaders  are  often  attached  to  mixers  in  order  to  give 
the  advantages  of  low  loading,  as  well  as  those  of  relatively  high  discharge  of  mixed  materials. 
The  general  type  of  mechanism  employed  is  shown  in  Fig.  24.  The  type  of  loading  hopper 
or  skip  varies  with  different  manufacturers,  some  hoppers  having  a  raised  back,  requiring  a 
slight  incline  for  wheelbarrows  that  must  be  dumped  into  the  hopper,  while  others  permit 
running  wheelbarrows  directly  on  to  the  hopper  back  itself.  Through  a  friction  clutch,  the 
power  loader  is  elevated  by  the  same  motive  power  which  drives  the  mixer  drum.  Inasmuch 
as  it  is  required  to  hoist  such  loading  skips  to  a  considerable  height  before  materials  will  run 


Fig.  24. 


from  them  into  the  mixer  drum,  it  is  essential  that  sufficient  power  be  provided  to  hoist  this 
skip  rapidly,  as  otherwise  an  undue  amount  of  time  will  be  consumed  in  this  elevating  operation. 
The  mixers  of  different  manufacture  vary  widely  as  to  speed  of  hoisting;  and  it  will  generally 
be  found  that  the  more  expensive  mixers  have  a  better  and  more  rapid  hoisting  mechanism, 
in  addition  to  their  other  economies,  than  have  the  cheaper  types  of  mixing  machines. 

Low-charging  Mtxers.— Low-charging  mixers  (see  Fig.  18),  particularly  in  smaller  units, 
have  of  recent  years  been  meeting  with  favor.  In  such  mixers  the  opening  at  the  charging 
end  is  relatively  larger  than  in  other  types  of  drum  mixers  and  blading  about  this  opening  on 
the  interior  of  the  drum  is  so  disposed  as  to  draw  the  materials  within  the  drum  from  a  relatively 
small  hopper  of  low  height  into  which  they  are  charged  by  wheelbarrows.  With  such  mixers 
an  inclined  runway  platform  of  2}^  to  3  ft.  in  height  is  required.  Their  advantages,  therefore, 
consist  in  a  simplification  of  charging  and  the  absence  of  hoisting  mechanisms  rather  than  in 


192 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  3-23e 


any  particular  efficiency  of  mixing  operation.  Furthermore,  these  machines  are  relatively 
low  in  price  and  a  number  of  small  units,  gasoline  or  electric  motor-driven,  are  often  very 
advantageous  when  distributed  about  the  work.  From  a  standpoint  of  thorough  mixing  and 
flexibility  of  operation,  there  is  much  to  recommend  this  practice,  inasmuch  as  the  needs  of 
one  part  of  the  work  can  be  supplied  without  reference  to  other  parts  or  causing  an  overdraft 
on  any  one  machine  with  consequent  speeding  up  of  operations  as  is  the  case  when  all  parts 
of  the  work  are  demanding  concrete  at  the  same  time  from  a  single,  centralized  plant.  Without 
disparaging  in  any  way  the  importance  of  the  time-cost  element  in  concrete  mixing  operations, 
it  is  yet  to  be  regretted  that  considerations  of  quality  and  ultimate  satisfaction  of  the  customer, 
rather  than  first  cost,  do  not  more  often  govern  both  the  selection  of  the  plant  and  its  operation. 

23e.  Measuring  Materials. — It  is  often  taken  for  granted  that  measurement 
of  materials  for  a  concrete  batch  is  of  little  or  no  importance  and  that  it  can  be  accomplished 
in  almost  any  way.  It  is  probable  that  the  average  mix  varies  at  least  50%  in  its  proportions 
from  those  desired,  and  for  this  reason  alone  it  is  not  to  be  wondered  that  much  concrete  found 
on  every  hand  is  so  variable  in  quality. 

Materials  should  be  measured  either  in  bottomless  boxes  placed  on  wheelbarrows,  or  like 
devices,  or  else  in  a  barrow  pan  permitting  of  struck  measurement.  A  measuring  barrow  of 
known  capacity  permitting  struck  measurement  is  shown  in  Fig.  25.    At  the  same  time  these 


Fig.  25. 


barrows  are  adapted  by  reason  of  their  balance,  to  the  conveyance  of  considerable  quantities 
of  material  at  one  time.  Measuring  hoppers  of  known  capacity,  if  carefully  filled,  can  be  made 
to  function  quite  accurately;  but  where  they  are  not  struck,  or  where  there  is  pronounced 
variation  in  the  moisture  content  of  the  sand,  the  quantities  of  materials  obtained  per  batch 
will  be  found  surprisingly  variable. 

It  is  difficult  to  convince  the  average  contractor  that  economies  can  result  from  careful 
measurement.  It  may  seem  a  useless  task  to  confine  field  men  to  struck  measure  of  sand  and 
stone,  but  if  the  comparative  quantities  of  cement  required  for  accurately  proportioned  and 
inaccurately  proportioned  mixes  were  taken  into  account,  the  cost  balance  would  usually  be 
found  in  favor  of  the  careful  proportioning  and  measurement.  And  in' addition,  there  should 
be  considered  and  there  will  be  considered  with  increasing  force  with  passage  of  time,  the 
ultimate  performance  and  endurance  of  the  concrete  produced.  The  time  is  not  long  distant 
when  owners  will  demand  of  contractors  guarantees  as  to  the  quality  of  the  product  which  they 
are  to  receive  and  only  by  careful  proportioning  and  measurement  and  placing  of  the  concrete 
can  a  reasonable  basis  for  such  guarantees  be  established. 

23/.  Discharge  of  the  Mixer. — A  further  economy  of  time  can  often  be  had  by 
giving  attention  to  the  proper  and  rapid  discharge  of  materials  from  the  mixer.    Many  mixers 


Sec.  3-24] 


CONSTRUCTION  PLANT 


have  inadequate  and  insufficient  blading  due  to  having  become  worn  with  passage  of  time. 
Manj'  also  are  partially  choked  by  concrete  hardened  inside  the  drum.  Both  insufficient 
blading  and  choked  mixer  drums  mean  a  relatively  slow  discharge  of  materials  from  the  dmm 
which  cuts  into  the  essential  mixing  operation. 

24.  Transporting  and  Placing  of  Concrete. — Providing  means  for  transporting  mixed 
concrete  and  for  placing  it  properly  in  forms  is  an  art  in  itself.  These  operations  both  in  first 
cost  and  in  ultimate  effect  rank  equal  in  importance  with  the  operations  of  conveying,  pro- 
portioning, and  of  mixing  raw  materials.  In  mixed  concrete,  not  only  are  the  raw  materials 
to  be  handled  and  oftentimes  conveyed  to  considerable  distances,  but  in  addition  this  must  be 
done  at  low  unit  cost  and  in  such  a  manner  and  so  expeditiously  as  to  protect  the  mixed  mass 
from  injury. 

The  means  usually  adopted  for  the  conveyance  and  placing  of  concrete  are  some  sort  of 
bucket  or  cableway,  or  else  open  spouts  or  chutes  through  which  the  concrete  flows  by  gravity, 
or  else  in  barrows,  carts,  or  cars.  The  particular  means  adopted  in  any  case,  will  depend  upon 
the  size  of  the  operation,  upon  the  physical  conditions  attendant  and  upon  the  financial  limi- 
tations to  plant  imposed  by  commercial  considerations. 

24a.  Barrows. — As  affecting  perhaps  the  great  bulk  of  concrete  used  today, 
it  will  be  proper  to  first  consider  the  use  of  barrows  or  carts.    This  method  involves  less  original 


Fig.  26. 


plant  outlay  than  the  others  before  enumerated.  In  many  instances,  the  cost  of  installation 
of  an  elaborate  plant  would  cover  not  only  the  cost  of  the  barrows  themselves,  but  a  great 
part  of  the  entire  cost  of  distribution  of  the  concrete  by  other  means. 

The  ordinary  wheelbarrow  (Fig.  26)  having  a  flat  pan  is  not  well  adapted  to  the  distri- 
bution of  concrete.  In  such  a  barrow  a  man  can  handle  about  1 3^  to  2  cu.  ft.  of  mixed  concrete. 
This  load  he  can  wheel  about  25  ft.  every  3  min.,  the  objection  to  the  pan  wheelbarrow  being 
that  the  man's  working  rate  is  necessarily  cut  down  by  the  care  which  is  required  to  keep  the 
materials  from  slopping  over  the  sides.  Furthermore  by  the  design  of  the  barrow  a  large 
proportion  of  the  weight  of  the  load  is  on  the  man's  arms,  rather  than  on  the  wheel.  Deep 
pan  barrows  have  been  designed  to  overcome  this  difficulty,  but  have  not  wholly  accomplished 
the  desired  end. 

246.  Concrete  Carts.— Two-wheel  concrete  carts  (Fig.  27)  are  better  adapted 
to  this  work  than  wheelbarrows,  both  because  they  can  carry  a  larger  load  and  also  because  this 
load  is  balanced  on  the  wheels  themselves  with  Httle  or  no  strain  on  the  man.  The  usual 
two-wheel  concrete  car  is  of  6-cu.  ft.  capacity  in  which  about  41^  cu.  ft.  of  mixed  concrete  can 
be  carried  by  one  man. 

In  this  comparison  there  are,  however,  certain  cost  offsets  to  be  made.  Wheelbarrows 
13 


194 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  3-24r 


require  less  scaffolding  than  do  the  heavier  and  wider  carts,  so  that  the  cost  of  this  runway  must 
be  carefully  estimated.  When  runways  must  be  elevated,  the  showing  becomes  more  favorable 
for  carts,  as  bents  or  supports  for  wheelbarrows  must  be  practically  of  the  same  size  and  strength 
as  those  for  carts.    Turnouts  and  gangways  must  in  both  cases  be  of  ample  width  so  that  there 


Fig.  27. 

may  not  be  congestion  in  the  passing  of  full  and  empty  carts  going  to  and  returning  from  the 
forms. 

24c.  Buckets. — There  is  a  great  variety  in  types  of  buckets  adapted  to  the 
distribution  of  concrete.    Some  of  these  buckets  are  straight-side  skips,  as  in  Fig.  28,  adapted 


Fig.  28.— Tilting  bucket. 


Fig.  29. — Round  self-tilting  bucket. 


to  dump  by  overturning.  Others  are  bottom-dumping  buckets  operated  by  a  man  at  the  form; 
and  these  bottom-dumping  buckets  may  be  of  various  patterns,  adapted  to  some  particular 
use.    An  example  of  this  sort  of  bucket  is  shown  in  Fig.  31,  in  which  the  bottom  is  so  constructed 


Sec.  3-24rf] 


CONSTRUCTION  PLANT 


195 


as  to  form  a  long  narrow  opening,  actuated  through  a  powerful  lever  mechanism.  A  groat 
variety  of  these  devices  is  on  the  market  and  the  needs  of  each  particular  situation  must  b(; 
studied  and  met  by  as  specialized  a  product  for  that  use,  as  financial  considerations  will  permit. 

24kd.  Cableways  and  Buckets. — Cableways  usually  require  large  initial  outlay 
but  on  large  operations  they  may  be  found  very  economical.    Usually  they  consist  of  a  strong 


Fig.  30. — Bottom-dump  bucket  for  Fig.  31. — Bottom-dump  bucket  for 

large  forms.  narrow  forms. 


|i  messenger  cable  or  cables  (carried  between  either  fixed  or  movable  towers)  with  actuating 
ij  cables  to  hoist  and  earry  the  buckets  to  any  desired  spot  on  the  work.  Cableway  buckets  may 
t'  be  of  various  types,  but  that  shown  in  Fig.  33  has  proven  its  worth  in  many  constructions. 
'  The  bucket  shown  in  this  illustration  is  a  2-yd.  bucket.    Its  deep  upper  body  and  steep  sloping 

bottom  provide  capacity  and  free  flow,  while  a  gate  controlled  by  levers  regulates  the  discharge 

of  concrete. 


Fig.  32.— Tower-hoist  tilting  bucket.  Fig.  33.— Bottom-dump  cableway  bucket. 


24e.  Spouts  or  Chutes.— The  handling  of  concrete  through  spouts  or  chutes 
is  a  development  of  the  last  8  years.  This  system  at  the  present  time  is  in  more  extensive 
use  than  any  of  the  foregoing  methods  of  distribution,  with  the  possible  exception  of  distribution 


it 


196 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  3-24/ 


in  carts.  The  economic  features  of  spouting  are  undeniably  attractive.  To  raise  concrete 
vertically  in  a  tower  by  means  of  a  skip  bucket  and  engine  located  at  the  central  mixer  plant, 
then  distributing  by  gravity  through  channels  which  can  be  arranged  in  convenient  sections 
to  cover  any  area  with  a  radius  from  10  to  300  ft.  from  the  base  of  the  tower,  appeals  strongly 
both  to  engineering  and  to  business  sense.  Further,  the  ease  of  handling  by  gravity  is  usually 
greater  and  the  time  cost  per  cubic  yard  for  placing  is  usually  less  than  in  transferring  the  same 
quantity  of  material  in  hand-barrows,  in  cableway  buckets,  or  in  cars.  Yet  in  spite  of 
its  many  good  points,  the  convenience  of  spouting  has  brought  about  many  abuses. 

For  instance,  it  is  obvious  that  in  order  to  flow  readily  through  chutes,  concrete  must  be 
smooth  and  plastic,  whereas  the  materials  of  which  concrete  is  composed,  with  the  exception  of 
water,  are  all  exceedingly  sharp  and  gritty.  It  is  not  to  be  wondered  then  that  lubrication 
and  ease  of  flow  secured  by  increased  wetness,  has  encouraged  the  use  of  excess  water,  especially 
where  for  reasons  of  cost,  it  is  desired  to  erect  only  a  relatively  low  tower  causing  the  angle  of 
the  spout  to  be  comparatively  flat.  Furthermore,  many  spouting  equipments  have  been  in- 
stalled with  ease  of  distribution  alone  in  view,  the  first  cost  of  plant  and  rapid  deterioration  not 
being  taken  into  account,  so  that  saving  has  later  been  sought  by  cutting  comers  to  make 
up  for  the  initial  mistake. 

In  all  spouting  installations,  care  must  be  taken  to  have  the  chutes  at  a  workable  inclina- 
tion. Furthermore,  it  is  important  to  maintain  a  uniform  pitch  throughout  the  entire  line, 
in  order  that  the  flow  may  be  thorough  and  uninterrupted  and  not  subject  to  slackening  at  one 
part  and  accelerated  flow  in  another.  The  pitch  also  must  be  greater  when  the  material  is  to 
be  carried  to  a  considerable  distance  than  when  it  is  to  be  carried  only  a  short  distance,  for  as 
the  distance  increases,  the  friction  of  the  concrete  in  a  chute  tends  to  overcome  its  initial  mo- 
mentum. Whereas,  therefore,  a  wet  concrete  will  flow  50  ft.  with  the  pitch  of  1  in  6  it  becomes 
necessary  to  increase  this  pitch  to  1  in  4  for  a  distributing  distance  of  100  ft.,  while  a  distance 
of  300  or  400  ft.  will  require  a  pitch  of  1  in  3.  The  slopes  as  above  described  are  based  upon 
chute  rigidly  supported  having  uniform  pitch  throughout;  and  it  would  be  even  better  to  in- 
crease this  pitch  in  order  that  concretes  of  a  drier  consistency  may  be  used. 

Various  methods  have  been  proposed  for  increasing  the  ease  of  flow  of  concrete  in  chutes. 
Hydrated  lime  in  one  proportion  or  another  has  probably  proven  the  most  effective,  but  there 
is  no  standard  procedure  in  this  regard,  nor  is  the  exact  quantity  of  hydrated  lime  required  for 
any  given  concrete  prescribable  without  experimental  knowledge  of  the  aggregates  separately 
and  in  combination.  Hydrated  lime  added  to  concrete  has  some  undesirable  features,  but 
even  aside  from  these  it  is  an  expensive  diluent  of  inferior  strength,  and  inasmuch  as  practically 
the  same  effect  through  the  same  agency  may  be  realized  by  a  longer  mixing  of  materials,  the 
wisdom  of  its  use  is  not  yet  beyond  question. 

The  unfortunate  tendency,  as  before  pointed  out,  is  to  add  more  water  to  spouting  con- 
cretes to  make  them  flow  freely.  This,  however,  defeats  its  own  end,  inasmuch  as  segregation 
takes  place  very  readily  from  wet  mixtures,  so  that  there  is  initially  a  rapid  rush  of  semifluid 
materials  down  the  chute,  with  afterward  a  slow  dribbling  of  the  heavier  and  harsher  materials, 
oftentimes  requiring  men  in  the  rigging  with  hoes  to  keep  the  unwatered  sand  and  stone  from 
stopping.  With  sloppy  mixtures,  therefore,  not  only  is  the  quality  of  concrete  impaired  but 
also  the  cost  of  delivery  and  placing  is  very  largely  increased.  On  the  other  hand,  thoroughly 
mixed  concrete  without  excessive  water  may  be  successfully  delivered  through  spouts  disposed 
at  proper  pitch  without  segregation  or  the  loss  in  value  attendant  upon  the  use  of  excessively 
wet  mixtures. 

24/.  Sections  Used  in  Spouting. — It  is  desirable  that  concrete  spouting  be  arranged 
in  a  series  of  units  which  may  be  assembled  in  various  combinations.  Continuous-line  spouting 
should  be  changeable  to  swivel-head,  or  swivel-head  to  continuous-line,  as  the  conditions  of 
the  work  require,  it  being  necessary,  of  course,  to  have  in  stock  a  supply  of  the  necessary  units. 
This  interchangeability  is  of  great  value  in  service,  for  spouts  wear  at  the  head  and  foot  of  each 
unit  of  length.  By  reversing  a  trough  section,  end  for  end.  when  showing  heavy  wear  at  one 
point,  a  new,  unworn  surface  may  be  put  at  point  of  greatest  wear. 


Sec.  3-24/] 


CONSmVCTIOX  PLANT 


197 


A  standard  trough  section,  Fig.  34,  is  made  of  No.  14  gage  steel,  forming  a  trough  8^2  in. 
deep  by  10  in.  wide  on  top.  The  bottom  is  curved  to  practically  a  semicircle  of  4-in.  radius, 
the  upper  part  of  the  sides  being  straight  and  tangent  to  the  curve.  Each  section  is  punched 
with  standard  spacing,  arranged  for  connecting  all  of  the  various  attachments. 


Fig.  .34. 


The  hopper  head,  Fig.  35,  attached  at  one  end  for  receiving  the  concrete  from  the  bin,  or 
from  an  upper  trough  section,  forms  one  point  of  support  of  the  next  trough  section.  At 
the  other  end  is  the  splash  hood,  Fig.  36.  By  fastening  the  hopper  head  to  the  trough  section 
at  one  end,  and  the  splash  hood  at  the  other,  we  have  the  complete  trough  section,  Fig.  37. 


Fig.  35. 

These  24  by  24-in.  hopper  heads,  as  well  as  the  splash  hoods,  can  be  bolted  to  either  end  of  any 

standard  trough  section. 

Standard  trough  sections  are  joined  for  continuous-line  spouting  by  bolting  together  their 
,  angle-iron  yokes  or  flanges  and  bolting  on  the  compression  plate  part.  Thus,  several  sections 
j  are  joined  together,  with  a  hopper  head  at  one  end  of  the  entire  group,  and  a  splash  hood  at  the 

other  end. 


198 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  a-24/ 


Fig.  38  shows  the  swivel-hook  used  in  making  the  flexible  joint  between  successive  trough 
sections  for  swivel-head  spouting  and  shows  one  of  these  joints,  in  which  the  upper  line  of 
spouting  is  supported  by  a  fall  and  tackle  attached  to  the  bail  on  the  splash  hood;  while  the 
lower  line  is  supported  by  the  swivel-hook,  connecting  the  lower  hopper  head  with  the  splash 
hood  of  the  upper  line.    The  swivel-hook  is  kept  clear  of  the  path  of  the  concrete. 

In  some  cases  it  is  desirable  to  have  a  flexible  joint  in  continuous-line  spouting.  In  this 
case  the  two  sections  are  put  together  in  a  different  manner,  Fig.  39,  where  both  the  hopper 


Fig.  36. 


head  and  the  splash  hood  are  dispensed  with.  The  hanger  plate  is  here  used  in  conjunction 
with  a  special  yoke,  after  one  of  the  angle-iron  yokes  has  been  removed.  This  allows  a  slight 
movement  sideways,  without  requiring  the  attachments  for  the  swivel-head  operation. 

Various  types  of  spouting  have  been  tried,  ranging  from  round  pipe  to  rectangular  troughs. 
Best  results  have  been  secured  from  the  use  of  5-in.  pipes,  or  10-in.  open  troughs,  the  latter 


Fig.  37. 


having  the  preference  for  flat  slopes,  and  the  former  where  there  is  necessity  for  varying  pitch, 
with  a  Jikelihood  of  steeper  pitch  than  named  above. 

With  open  spouting  the  use  of  remixing  hoppers  (Fig.  40),  in  connection  with  flexible 
spouting  (Fig.  41),  accomplishes  satisfactorily  the  necessary  changes  in  pitch. 

The  greatest  items  of  expense  in  spouting  plants  are  first  cost,  installati.on,  and  mainte- 
nance. Maintenance  charges  are  particularly  heavy.  The  ordinary  stock  spouting  which  is 
made  of  No.  14  gage  metal  will  seldom  handle  more  than  2000  cu.  yd.  without  renewal.    This  is 


Sec.  3-24/J 


CONSTRUCTION  PLANT 


199 


due  to  the  abrasive  action  of  the  material,  especially  as  affecting  the  rivets  which  join  the  various 
sections. 

A  recent  development  is  a  spout  made  up  of  two  or  more  longitudinal  sections  of  the  shape 
indicated  in  Fig.  42.    The  various  sections  are  interchangeable,  and  there  are  no  bolts  or  rivets 


Fig.  38. 


extending  through  the  spout,  all  joint  bolts  or  rivets  passing  through  the  flanges,  and  the 
various  longitudinal  joints  made  secure  by  fish  plates.    This  type  of  spouting  has  the  further 


Fig.  39. 


advantage  of  making  possible  renewal  of  worn  sections  severally,  instead  of  renewing  the 
length  of  spout  as  a  whole.  This  type  furthermore  ensures  a  spout  which  is  stiff  in  all 
directions,  a  point  of  considerable  importance. 


200 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  3-24^ 


24gr.  Hoists.— Whether  the  distribution  is  by  spouts,  by  carts,  or  by  barrows, 
it  has  become  general  practice  on  all  work  extending  above  ground  to  hoist  the  concrete.  For 
this  purpose  a  tower  is  practically  indispensable. 


Pig.  40, 


It  will  ordinarily  be  found  advisable'  to  install  the  hoist  at  the  beginning  of  operations, 
since  by  so  doing  the  mixer  may  readily  be  set  so  that  the  operation  of  charging  may  be  facili- 
tated, principally  by  cutting  out  inclines,  with  resultant  saving  in  labor. 


Fio.  41. 


Towers  are  constructed  of  steel  or  wood.  The  hoist  bucket  should  be  constructed  on 
the  simplest  lines  without  catches  or  trips.  A  substantial  bail  made  of  two  3-in.  Z-bars 
back  to  back,  is  arranged  to  operate  between  two  5^^-in.  wooden  guides,  and  is  fitted  at  the 


Sec.  3-24^] 


CONSTRUCTION  PLANT 


201 


lower  end  with  journals  in  which  rests  the  bucket  trunnion.  In  setting  up  the  tower  and 
bucket,  it  is  advisable  in  all  cases  to  set  the  bucket  so  that  it  is  balanced,  and  to  this  end  the 
front  guide  should  be  so  set  as  to  be  almost  in  contact  with  the  nose  of  the  bucket  when  the 
latter  is  pushed  back  to  a  point  where  the  load  will  tend  slightly  to  press  the  stops  on  the  sides 
of  the  bucket  backward  against  the  bail.    Friction  of  the  nose  against  the  guides  is,  by  this 


Fig.  42. 


means,  cut  down.  By  removing  the  front  guide  at  any  point  in  the  height  of  the  tower,  and 
placing  a  block  on  the  back  of  the  latter,  the  bucket  is  canted  forward  so  that  it  will  drop  its 
contents  out  through  the  opening  made  by  the  removal  of  the  front  guide.  The  bucket  auto- 
matically rights  itself,  and  is  pulled  back  into  position  by  the  weight  of  the  bail  when  the 
operator  releases  the  brake. 


Fig.  43. 

A  typical  hoist  is  shown  in  Fig.  43,  operating  in  connection  with  a  mixer,  the  power  being 
taken  from  an  extension  of  the  mixer  shaft.  The  power  equipment  of  the  latter  should  be  of 
sufficient  capacity  to  operate  both  mixer  and  hoist  at  the  same  time.  A  variation  of  this  plant 
showing  a  direct-connected  hoist  is  shown  in  Fig.  44,  but  for  ordinary  conditions  the  first- 
described  arrangement  is  preferable. 

At  any  desired  height  a  bin  or  hopper  is  set,  into  which  the  material  is  discharged  by  the 


202 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  3-24:g 


Fig.  45. 


Sec.  3-25]  CONSTRUCTION  PLANT  203 

hoist  bucket.    From  this  point  distribution  may  be  effected  by  wheelbarrow,  cart,  car,  or 
spout,  either  separately  or  in  combination.    A  concrete  bin  such  as  shown  in  Fig.  45  forms  the 
upper  end  of  a  spouting  system,  the  gate  of  the  hopper  under  manual  control  regulating  the 
y  flow. 

25.  Spouting  Plants. — Spouting  plants  may  be  classed  as  hoom  jdanln,  guy-line  plants,  and 
tower  plants. 

f  25a.  Boom  Plants. — In  boom  plants,  the  first  and  second  sections  of  spouting 

are  mounted  on  a  bracket  attached  to  the  hoisting  tower,  the  free  end  being  moved  by  tag  lines 
to  the  position  desired.    This  rig  offers  advantages  of  flexibility  and  freedom  of  movement 

II  not  often  obtained  in  placing  concrete.    Oftentimes  open-throated  booms  (through  which  the 

[i  first  section  of  spouting  is  carried)  are  used,  these  having  the  advantage  of  lending  lateral 

I  stability  to  the  spout  itself  as  well  as  of  economizing  space. 

25b.  Guy-line  Plants. — In  guy4ine  plants,  the  spout  is  suspended  by  blocks  and 

I  falls  from  guy  lines,  or  special  cables  suspended  between  towers,  or  other  supports  especially 
set  up  for  the  purpose.  The  advantage  of  this  type  of  spouting  plant  lies  in  its  ready  adapta- 
bility. It  is  limited,  however,  in  lateral  movement  unless  its  deficiencies  are  supplemented 
by  take-offs  at  various  points  with  small  boom  plants  or  supplementary  guy-line  plants. 

25c.  Tower  Plants. — Tower  plants  are  of  like  general  feature,  but  the  spouting 
line  is  supported  at  ends  of  successive  sections  by  movable  towers  or  tripods.  A  plant  of  this 
kind  is  less  flexible  than  a  boom  plant,  but  is  more  flexible  than  a  guy-line  plant,  inasmuch  as 
the  various  supports  in  the  line  may  be  moved  successively,  rendering  possible  the  covering  of 
a  very  wide  area  from  a  single  hoisting  tower.  A  guy-line  plant,  on  the  contrary,  requires 
under  like  circumstances  that  the  whole  line  be  dismantled  and  set  up  again  in  the  new  location. 

I25d.  Combinations  of  Spouting  Systems. — Combinations  of  the  above  systems 
i  are  used  advantageously  in  one  way  and  another  in  order  to  surmount  special  obstacles.  Among 
I  such  combinations  may  be  mentioned  a  rehoisting  tower  which  permits  covering  a  wider  area. 
'  In  such  a  plant  the  concrete  is  distributed  from  mixer  and  first  tower  through  chutes  to  a  hopper 
at  the  base  of  the  second  tower,  when  it  is  again  elevated  and  distributed  throughout  the  work. 
A  careful  study  is  required  in  order  to  make  spouting  plants  thoroughly  effective;  and  this  study 
should  always  be  made  before  the  job  is  started  to  make  sure  that  the  proper  radius  of  delivery 
and  best  arrangement  is  secured. 

25e.  Regulating  Flow  of  Concrete  in  Spouting  Plants. — It  is  quite  essential  for 
the  proper  operation  of  the  spouting  plant  that  concrete  should  be  uniformly  and  continuously 
carried  down  the  chutes.  To  this  end  a  receiving  hopper  is  placed  at  the  head  of  the  elevating 
tower,  with  a  man  in  control  of  its  gate.  Upon  this  man  then  depends  to  a  large  extent  the 
success  of  the  operation.  If  he  permits  a  proper  amount  of  material  to  flow  into  the  chutes, 
they  can  usually  be  relied  upon  to  carry  it  freely  providing  they  are  disposed  at  proper  inclina- 
tion. If  he  sees  the  line  becoming  choked,  upon  his  slackening  or  shutting  off  the  delivery 
depends  either  a  speedy  clearing  of  the  line  with  relatively  continuous  operation,  or  shutting 
down  for  an  indefinite  period. 

No  matter  what  type  of  mixing  equipment,  or  what  system  of  distribution  is  adopted, 
there  should  be  kept  in  constatnt  view  the  object  to  be  attained,  namely,  the  economical  pro- 
duction and  placement,  not  merely  of  materials  which  will  fill  form  spaces  with  possible  accept- 
ance, but  rather  of  materials  which  in  forms  will  solidify  and  endure  under  stress,  whatever  the 
nature  of  such  stress  may  be.  Each  yard  of  poor  concrete  carelessly  placed  gives  concrete  a 
black  eye.  Each  yard  of  good  concrete  properly  placed  is  testimony  as  to  the  abilities  of  this 
inherently  wonderful  material. 


SECTION  4 


CONCRETE  FLOORS  AND  FLOOR  SURFACES,  SIDEWALKS, 

AND  ROADWAYS 

CONCRETE  FLOORS  AND  FLOOR  SURFACES 

1.  The  Concrete -floor  Problem. — Concrete  floors  in  modern  commercial  buildings  are  of 
peculiar  importance.  Not  only  is  the  floor  slab  an  integral  part  of  the  structure,  making  pos- 
sible its  usefulness  by  supporting  applied  loads^ — such  as  machinery,  or  stored  goods —  but  such 
floors  must  further  perform  unusual  service  in  withstanding  severe  concentrated  stresses — as, 
for  instance,  those  due  to  passing  trucks  heavily  loaded — and  particularly  must  they  withstand 
at  their  top  surfaces  not  only  the  crushing  above  referred  to,  but,  in  addition,  a  constant 
and  severe  abrasion  through  the  impact  of  shoes,  or  the  movement  of  loads,  with  oftentimes 
attack  from  chemicals  used  in  manufacturing  processes. 

No  part,  therefore,  either  of  aggregates  or  of  the  cement  matrix  in  which  they  are  embedded, 
may  give  way  without  ''dusting,"  or  progressive  destruction,  of  the  floor  to  greater  or  less 
degree,  causing  not  only  annoyance  and  inconvenience,  but  possibly  more  serious  consequences 
by  reason  of  the  released  particles  being  carried  into  machinery  and  manufactured  products. 
These  particles  are  abrasive,  gritty,  and  may  be  chemically  injurious.  The  problem  of  satis- 
factory concrete-floor  surfaces  becomes,  therefore,  essentially  the  problem  of  producing  a 
concrete  (1)  of  a  strength  requisite  to  resist  compression  and  shear  due  to  floor  loads;  and  (2)  of 
sufficient  top-surface  resistance  to  withstand  the  mechanical  attack  of  normal  service.  Chem- 
ical attack  must  be  provided  for  by  special  supplementary  treat- 
ment with  a  resisting  paint  or  varnish. 

The  requisite  first  named  is  met  with  relative  ease.  Den- 
sity and  strength  through  use  of  proper  aggregates  and  good 
cement,  thoroughly  mixed,  without  excess  water,  and  carefully 
placed  are  the  procedures  to  be  followed  (see  chapters  on  "Aggre- 
gates" and  "Water"  in  Sect.  1  and  on  "Mixing,  Transporting, 
and  Placing  Concrete"  in  Sect.  2).  Porous  floor  slabs,  such  as 
that  shown  in  Fig.  1  do  not  make  either  for  strength  or  for  any  of 
the  qualities  desired  in  good  concrete. 

The  requisite  second  named — that  of  producing  a  resisting 
top  surface  is  more  difficult  to  meet  with  full  satisfaction.    If  the       Fig.    i— Rough  ^  Jracture 
surface  of  concrete  floors  (or  of  concrete  roads  or  sidewalks)  could  n^fied^2  dilmsO^°°'^  ^  ^ 
be  natural  stone  of  proper  quality  molded  with  the  same  ease  as 

is  concrete  and  made  integral  both  as  a  monolith  and  by  tying  with  steel  to  the  rest  of  the 
structure,  there  would  be  little  cause  for  complaint  on  the  score  of  dusting,  wear,  or  struc- 
tual  functioning.  Yet  the  aggregate  employed  in  concrete  is  natural  stone  in  fragments. 
Since  reinforcing  steel  does  not  affect  wearing  qualities  at  the  surface,  the  difficulty  must, 
therefore,  lie  either  in  the  choice  of  the  natural  materials,  in  the  proportion  of  these  materials 
exposed  as  resistants  to  abrasion,  or  else  in  the  quality  or  quantity  of  the  cementing  material 
holding  them  vise-like  against  the  abrading  forces. 

The  ideal  in  artificial  stone  floors  is  the  terazzo  floor  in  which  an  even  surface  (95  7o  or 
more  of  which  is  natural  stone  with  5%  or  less  of  cementing  material)  is  presented  to  wear. 
Grinding  concrete  floors  is  necessarily  expensive,  but  removing  a  surface  layer  by  such  means 

205 


206 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  4-2 


produces  a  superior  result  that  is  found  to  justify  the  cost.  The  significance  of  these  facts, 
together  with  what  is  known  of  the  general  top-surface  character  of  concretes,  leads  to  the 
conclusion,  which  is  fully  borne  out,  that  in  the  extreme  top  layers  of  a  concrete  floor  is  to  be 
found  much  of  whatever  difficulty  is  experienced. 

2.  "Dusting"  of  Concrete  Floors. — Research  has  shown  that  ''dusting"  floors  are  concretes 
which  are  at  least  locally  poor,  such  local  weakness  (most  evident  in  the  top  coat)  being  shown 
typically  in  Fig.  2,  wherein  the  sand  grains  are  seen  to  be  uncertainly  held  in  a  loose  and  easily 
abraded  matrix  of  what  appears  to  be  of  the  nature  of  efflorescence.  All  dusting-floor  surfaces, 
however,  are  not  identical  with  the  one  shown,  nor  are  the  causes  of  dusting  necessarily  the 
same.  Nevertheless,  the  process  of  progress  of  progressive  destruction  or  ''dusting"  is  much 
the  same  in  most  cases  and  is  largely  due  to  a  loose  condition  of  the  cement  binder  which  permits 
the  resistant  sand  grains  to  fall  out,  exposing  fresh  surfaces  of  soft,  hydrated  cement  to  attrition, 
with  repetition  of  the  process  until  remedies  are  applied,  or  until  resistant  strata  at  irregular 

depths  below  the  surface  are  reached.  These  actions  are  aug- 
mented at  times  by  chemical  action,  either  from  moisture  or  from 
other  atmospheric  or  fluid  agencies. 

3.  Making  Good  Concrete  Floors  and  Floor  Surfaces. — A 
good  concrete  floor  is  essentially  a  good  concrete.  The  principles 
of  making  good  concrete— the  right  materials  and  the  right  propor- 
tions of  same,  including  water;  thorough  mixing;  careful  placing; 
careful  curing — epitomize  the  making  of  good  floors. 

To  these  axiomatic  and  self-evident  general  principles  should 
be  added  the  following: 
•.3^  1.  Whenever  possible,  run  top  coat  and  base  together.    If  this 

Fig.  2. — Dusting  surface  of  is  not  possible  or  advisable,  remove  top  surface  of  base  to  a  depth 
di^Sf  (Magnified   5  j^^^^      -^^^    r^^^^^  ^^^^^^  placing  top  coat,  roughen  the  base 

surface  well  and  wash  clean,  using  hose  or  brushes.    This  pro- 
cedure is  necessary  to  procure  a  proper  bond  between  top  coat  and  base. 
2.  Use  coarse,  rather  than  too  fine  material  in  the  top  coat.^ 
4.  Special  Surface  Finishes.  • 

4a.  Surface  Grinding. — "Granolithic"  is  a  term  applied  alike  to  concrete 
floors  having  cement  and  sand  finish,  and  to  those  having  a  surface  layer  of  crushed  granite, 
or  other  hard,  enduring  rock  bonded  with  cement.  As  above  noted,  a  desirable  finish  to 
such  floors,  a  finish  that  gives  a  pleasing  appearance  and  removes  much  of  any  tendency  there 
may  be  to  dusting  or  surface  disintegration  of  any  kind,  may  be  produced  by  surface  grinding 
when  the  concrete  is  from  4  to  7  days  old  by  means  of  a  machine  similar  to  that  employed  in 
grinding  terazzo  floors.  Such  grinding  removes  any  laitance  or  loose  material  from  the  surface, 
produces  a  smooth  though  not  polished  surface  and,  by  selection  of  aggregates  before  laying 
with  special  reference  to  color,  gives  an  unusually  pleasing  effect. 

46.  Integral  Pigments. — Pigments  of  one  coloration  or  another,  chemically 
inert  toward  concrete,  can  be  had  of  a  number  of  dealers.  Inasmuch  as  surface  color  only  is 
desired,  it  is  advantageous  to  apply  them  only  in  a  relatively-thin  mortar  layer  at  the  top 
surface.  This  layer  should  be  truly  integral  with  the  layers  below,  else  it  will  scale  off.  It 
should  further  be  borne  in  mind  that  the  coloring  value  in  concrete  of  any  integral  pigment 
will  be  affected  strongly  by  the  color  of  Portland  cement,  which  is  itself  a  pigment,  white  when 
hydrated,  gray-green  when  unhydrated.  According,  therefore,  to  the  color  added,  the  effect 
of  pigment  in  concrete  will  be  more  or  less  intense  according  to  its  percentage  presence  as 
related  to  the  percentage  of  cement  in  the  mixture  and  to  the  degree  of  hydration  of  the  latter. 
The  color  of  aggregates  may  also  affect  the  result.  Care  should,  therefore,  be  exercised  in  at- 
tempting to  secure  a  given  intensity  of  final  color,  not  to  use  pigments  in  such  quantity  as  to  be 
detrimental  to  the  concrete.    Small  trial  batches  will  aid  in  securing  the  effect  desired. 

J  See  L.  C.  Wason:  Tmns.  A.S.M.E.,  1914,  p.  400. 


Sec.  4-4c] 


CONCRETE  FLOORS  AND  FLOOR  SURFACES 


207 


4c.  Finish  Produced  by  Removal  of  Water  From  Surface. — A  process  of  finishing 
floors  said  to  give  excellent  results  is  the  abstraction  of  excess  surface  water  through  absorption 
by  dry  cement  laid  on  webbing  over  the  soft  floor.  ^  This  method  should  be  advantageous 
in  many  instances,  particularly  where  excess  water  is  used.    The  process  is  proprietary. 

4:d.  Integral  Hardeners  and  Surface  Compounds. — A  number  of  compounds 
are  on  the  market  designed  to  be  incorporated  with  the  surface  to  make  it  resistant.  One  of 
these  is  carbide  of  silicon  (carborundum)  under  one  name  or  another.  This  material  unques- 
tionably has  great  abrasive  resistance  and  if  properly  held  in  place  by  cement  should  produce 
a  surface  capable  of  withstanding  severe  traffic.  There  is,  however,  no  reason  to  expect  better 
conditions  of  manufacture  attending  its  use  than  would  obtain  where  it  is  omitted;  and  as 
good  quartz  sand  or  crushed  durable  rock  properly  bedded  in  cement  is  capable  of  supplying 
most  needs;  and  inasmuch  as  the  sparkling,  glistening  effect  incident  to  the  use  of  carborundum 
is  often  objectionable,  the  advantages  to  be  expected  from  it  should  be  carefully  looked  into 
before  it  is  employed. 

Common  iron,  powdered,  is  extensively  marketed  as  a  surface  hardener  for  concrete  floors. 
A  variety  of  claims,  many  of  them  conflicting,  are  advanced  by  its  advocates.  Some  assert 
that  the  iron  oxidizes  (rusts)  with  expansive  filling  of  pores  and  prevention  of  further  moisture 
penetration.  Soil-ammoniac  may  even  be  added  to  promote  this  rusting.  Others  claim  no 
rusting  with  the  virtue  residing  in  the  superior  hardness  of  such  iron  as  remains  at  the  surface. 

It  is  unquestionably  a  fact  that  the  average  iron  in  contact  with  moist  air  will  rust.  This 
produces  a  characteristic  red  stain  of  rust  in  the  concrete,  but  it  is  doubtful  if  as  an  incident  to 
mixing  or  placing,  this  iron  rust  can  be  so  directed,  distributed,  and  placed  as  to  constitute 
a  reliable  pore  filler;  and  it  is  further  more  likely  to  be  an  attractor  of  moisture  than  a  preventive 
of  moisture  penetration,  since  rust  (Fe203-X  H2O)  is  deliquescent.  Further,  iron  is  so  inferior 
in  hardness  to  common  quartz  sand  as  to  make  the  ratio  of  comparison  about  230  (for  quartz) 
to  18  (for  iron),'-^  so  that  with  equally  satisfactory  embedment  in  cement,  iron  should  prove 
inferior  to  ordinary  sand.  In  addition,  factory  grease  is  often  not  removed  from  the  iron,  so 
that  attachment  of  cement  is  hindered,  if  not  inhibited. 

There  is  no  top  coat  superior  in  all-around  qualities  to  good  quartz  sand  of  proper  size  and 
grading,  nor  is  there  any  additive  at  present  known  qualified  per  se  to  overcome  initial  deficien- 
cies resulting  from  faulty  manufacture  or  inferior  materials. 

5.  Causes  of  Common  Defects  in  Concrete  Floors. — A  statement  of  defects  commonly 
found  in  concrete  floors  and  the  causes  which  give  rise  to  them  is  conversely  an  aid  to  the  pro- 
duction of  floors  of  proper  endurance.  Avoidance  of  wrong  practices  is  the  surest  guaranty 
of  success.    Such  a  listing  of  the  causes  of  defects,  therefore,  follows : 

(a)  Poor  Cement. — This  cause  is  infrequent.  It  is  true  that  defective  Portland  cements 
are  occasionally  manufactured  and  that  they  are  marketed,  but  misuse  of  cement  is  more 
frequent  than  deficiencies  in  the  cement  itself.  Other  causes  should  be  sought  and  eliminated 
before  blame  is  attached  to  the  cement. 

(6)  Poor  Quality  of  Sand. — This  cause  is  relatively  frequent.  Sands,  as  before  noted, 
are  derived  from  the  breakdown  of  natural  rocks;  and  in  most  sand  deposits  the  grains  have 
existed  for  millions  of  years,  so  that  their  inherent  quality  and  endurance  is  vouched  for,  but 
decomposing  cementing  materials,  such  as  clay  (uniting  very  small  mineral  particles  to  form  the 
larger  grains),  or  organic  matter,  or  dirt,  or  other  impurities,  may  render  the  best  sand  unfit 
for  use  in  concrete.    Be  sure  of  the  quality  of  sand  before  laying  the  floor  (see  Art.  30,  Sect.  1). 

(c)  Poor  Grading  of  Sand.— This  cause  is  relatively  frequent.  It  needs  no  demonstration 
to  prove  that  the  greatest  quantity  of  sand  in  a  given  volume  will  be  obtained  when  the 
|)articles  are  so  graded  in  size  that  smaller  grains  will  he  between  the  spaces  of  larger  grains, 
progressively  down  the  scale  of  sizes.  Likewise,  the  least  quantity  of  sand  in  a  given  volume  will 
be  had  when  all  the  grains  are  of  one  uniform  size.    This  truth  is  sometimes  stated  by  saying 

1  See  P.  M.  Bruner:  Proc.  Am.  Con.  Inst.,  1915. 

2  Scleroscope  scale. 


208 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  4-5 


that  "minimum  voids"  of  "  maximum  density"  is  obtained  with  graded  sizes  of  grains;  and  that 
maximum  voids"  or  ''minimum  density"  is  obtained  when  the  grains  are  all  of  one  size. 
Sand  for  concrete  floors  and  particularly  for  the  top  coat  should,  therefore,  be  graded  in  size 
in  such  manner  as  to  give  ''maximum  density"  with  maximum  quantity  of  enduring  silicious 
material  of  proper  grain  size  at  the  surface.  Be  sure  of  the  grading  of  sand  before  laijing  the 
floor. 

(d)  Dirty  Water. — The  occurrence  of  defects  due  to  the  use  of  dirty  water  is  relatively 
infrequent.  Dirty  water  is  not  merely  water  that  carries  fine  silty  matter  in  suspension,  but 
more  particularly  contaminated  water,  carrying  organic  matter,  such  as  stable  or  barnyard 
drainage.  Organic  matter  of  this  kind  is  very  injurious  to  concrete  and  may  even  cause  failure 
to  set,  or  total  disintegration.    Use  only  water  of  unquestionable  cleanness. 

(e)  Too  Much  Water. — The  use  of  too  much  water  is  of  general  occurrence.  With  excess 
water  in  a  mix,  the  fine  particles  of  stone,  and  the  fine  particles  of  sand,  and  the  finest  particles 
of  floor  cement  separate  and  rise,  forming  a  thick  scum  at  the  top  of  the  slab.  This  is  where 
the  slab  should  be  most  enduring,  but  if  too  much  water  is  used,  a  material  having  about  the 
resistance  and  character  of  chalk  is  substituted  for  the  enduring  materials  desired.  Avoid 
excess  water.    Use  thorough  mixing  to  obtain  the  plasticity  desired. 

if)  Wrong  Proportions  of  Materials. — Arbitrary  proportions  in  concrete  making  have  little 
except  careless  convenience  to  recommend  them.  Through  lack  of  understanding  and  be- 
cause of  the  supposed  difficulty  of  proper  proportioning,  they  have  remained  in  practice.  It 
should  be  borne  in  mind  that  each  sand  and  each  gravel  has  properties  peculiar  to  itself;  and 
that  the  proportions  in  which  they  should  be  used  in  combination  with  cement  and  water 
apply  to  them  only,  so  that  such  proportions  cannot  be  taken  as  a  criterion  for  the  use  of  other 
sands  or  gravels.  Proportion  the  materials  so  as  to  obtain  maximum  density  (see  chapter  on  "Ag- 
gregates" in  Sect.  1  and  on  "Proportioning  Concrete"  in  Sect.  2). 

{g)  Insufficient  Mixing. — One  of  the  reasons  that  excess  water  is  so  commonly  used  in  con- 
crete is  that  it  renders  mixing  easy.  The  desire  for  ease  and  rapidity  of  working  tends  to  carry 
the  speeding-up  process  beyond  allowable  limits  so  that  insufficient  mixing  is  more  often  in- 
dulged in  than  is  realized.  Whether  the  mixture  is  sloppy,  plastic,  or  dry,  mix  it  not  less  than  1 
min.  in  a  batch  machine,  or  an  equivalent  amount  if  other  form  of  mixing  is  employed. 

(h)  Too  Much  Tamping. — Concrete  may  be  tamped  too  much.  With  a  medium  wet  con- 
crete or  concrete  of  plastic  consistency,  tamping  to  a  certain  degree  is  desirable  to  compact  the 
mass.  But  tamping  to  more  than  the  required  degree  brings  unfortunate  results.  It  should 
be  recognized  that  sand  and  stone  and  cement  in  a  fluid  or  semifluid  concrete  are  non-coherent 
and  that  by  the  agitation  of  tamping,  heavier  materials  sink  and  lighter  materials  rise.  This 
causes  separation  or  "segregation,"  of  necessity  putting  fine,  chalky  materials,  not  adapted 
to  resist  abrasion,  at  the  wearing  surface.    DonH  flood  the  surface  by  tamping. 

(0  Too  Little  Tamping. — It  is  frequently  the  case  that  a  concrete  floor  is  deposited  in  such 
haste  and  with  so  little  care  that  it  does  not  compact;  and  particularly,  it  is  not  sufficiently 
joggled  to  remove  air  from  the  mass.  In  all  mixing  operations,  air  is  stirred  into  the  plastic 
mass,  much  as  it  might  be  into  a  stiff  batter;  and  if  such  air  is  not  removed  in  placing,  a  honey- 
combed structure  will  result.  Further,  the  tendency  of  entrapped  air  is  to  concentrate  at  or 
near  the  upper,  or  wearing  surface,  so  that  when  the  cement  has  set,  it  will  be  molded  as  bubbles 
in  the  mass.  Needless  to  say,  such  bubbles  are  holes  in  the  concrete;  and  holes  offer  very  poor 
resistance  both  to  stress  and  to  abrasion.  Tamp  enough  to  compact  the  concrete,  but  not  enough 
to  flood  it. 

(j)  Too  Much  Troweling. — After  a  concrete  floor  form  is  filled  and  screeded,  the  surface 
is  rough  and  irregular.  When  the  slab  has  taken  its  initial  set,  the  finisher  rubs  or  floats  the 
surface  to  an  even  finish  with  a  steel  or  wooden  trowel.  This  process  brings  considerable  water 
to  the  surface,  acting  in  a  manner  analogous  to  the  tamping  operation  before  referred  to,  so 
that  the  very  fine  particles  of  cement  and  sand  will  rise  to  the  surface.  Don't  flood  the  surface 
by  loo  much  troweling. 


Sec.  4-6] 


CONCRETE  FLOORS  AND  FLOOR  SURFACES 


209 


{k)  Use  of  Cement  as  a  Surface  Dryer. — It  is  not  infrequently  the  case,  particularly  when 
very  wet  concrete  is  used  and  it  is  desired  to  hasten  finishing  operations,  that  dry  cement  is 
sprinkled  over  the  surface  of  the  partially  set  mass,  and  worked  smooth  with  a  trowel  or  float. 
In  this  case,  the  liquid  it  is  sought  to  absorb  is  a  strong  solution  brought  up  from  the  body  of  the 
slab;  and  to  this  solution  the  new  cement  further  contributes  like  substances.  This  results 
in  a  deposit  of  fine  silicious  material  from  the  sand  and  hydrolized  cement  a  little  below  the  finish 
with  a  skin  of  nearly  pure  cement  directly  at  the  surface.  Necessarily,  therefore,  the  body  of 
the  concrete  slab  and  this  thin  veneer  of  neat  cement  at  the  surface  are  separated  by  a  loose, 
non-adhering  laitance  film,  so  that  scaling  in  patches  of  greater  or  less  size  soon  results  and  will 
continue  indefinitely  until  loose  portions  are  entirely  removed.  Use  less  water  in  mixing  and 
avoid  adding  cement  as  a  dryer  either  neat  or  mixed  with  sand. 

(l)  Use  of  Retempered  Concrete. — The  setting  of  Portland  cement  takes  place  in  two  stages: 
(1)  a  gradual  stiffening,  known  as  initial  set;  and  (2)  an  attainment  of  rigidity,  with  later  slow 
hardening  with  passage  of  time.  If  the  concrete  for  a  floor  has  been  mixed  for  some  time,  it 
may  have  taken  its  initial  set.  Adding  more  water  and  reworking  renders  the  mass  again 
plastic,  so  that  it  can  be  deposited  much  as  might  freshly  mixed  concrete.  A  certain  valuable 
property,  however,  has  become  lost  by  this  retempering,  or  rewetting,  inasmuch  as  among 
other  actions  interlacing  crystallization  had  already  begun,  and  by  rewetting  and  remixing, 
these  crystals  have  been  damaged  and  their  reticulation  destroyed.  Such  a  floor,  therefore, 
.will  be  of  inferior  strength  and  density  and  possibly  crumbly.  Avoid  using  concrete  which  has 
taken  its  initial  set. 

(m)  Loosening  of  Top  Coat  from  Base. — Where  floors  are  deposited  in  two  layers  and  par- 
ticularly where  the  under  floor  as  deposited  is  overwet,  the  upper  layer  (top  coat)  will  be  sepa- 
rated from  the  base  by  a  scum  of  laitance  deposited  at  the  top  surface  of  the  under  portion 
previous  to  setting.  If  the  top  coat  in  such  floors  is  of  good  quality  and  sufficiently  thick,  it 
may  stand  ordinary  shocks  and  wear,  but  if  it  is  thin,  or  is  subjected  to  sufficiently  intense 
stress,  it  will  become  loosened  and  at  best  be  unpleasant  in  use,  giving  a  hollow  sound  when 
struck,  or  walked  over,  or  in  extreme  cases,  will  become  shattered  and  crumble  into  pieces  of 
greater  or  less  size.  Cast  top  coat  and  base  at  one  operation  wherever  possible;  and  in  other 
cases,  remove  surface  of  base  to  a  depth  of  3^  in.  or  more  and  wash  thoroughly,  bonding  to 
top  coat  with  layer  of  rich  cement  grout.  Do  not  permit  this  latter  to  dry  out  or  set  before 
top  coat  is  applied. 

(n)  Placing  Concrete  in  Freezing  Weather  without  Protection. — Contact  between  Portland 
cement  and  water  results  in  a  chemical  reaction.  As  is  well  known,  the  speed  of  a  chemical 
reaction  is  a  function  of  the  temperature.  Below  50°F.  this  reaction  is  very  slow,  and  so  long 
as  this  temperature  persists,  there  is  comparatively  slight  formation  of  the  binding  or  cement- 
ing substance,  though  it  may  be  formed  later,  after  the  temperature  has  risen.  Furthermore, 
when  water  freezes  it  expands  with  a  force  of  approximately  300  tons  per  sq.  in.  with  a  volume- 
tric increase  of  8%,  so  that  in  frozen  concrete  there  is  a  general  disruption  and  dispersion 
of  components,  possibly  during  the  setting  process,  and  to  such  an  extent  that  in  concrete 
floors,  due  to  lack  of  hydrostatic  head,  they  rarely,  if  ever,  become  again  fully  consolidated, 
regardless  of  how  fully  the  cement  may  later  react  with  water.  Concrete  floors  which  have  been 
frozen,  therefore,  are  weak  and  scaly.  Use  heated  aggregates,  heated  water,  and  proper  protection 
when  concreting  in  freezing  weather.  Avoid  the  use  of  salt.  Its  advantages  are  not  commensu- 
rate with  its  disadvantages. 

6.  Remedial  Measures. — Obviously,  the  best  remedial  measures,  so  far  as  the  generality 
of  concrete  floors  is  concerned,  are  the  avoidance  of  improper  procedures  and  the  unceasingly 
careful  institution  of  proper  ones.  The  foregoing  list  of  the  causes  of  defects  is,  therefore,  a  list 
of  remedial  measures,  so  far  as  floors  yet  to  be  laid  are  concerned.  Where,  however,  recognized 
defects  exist  in  floors  in  place,  it  is  a  matter  of  serious  moment  to  effect  their  repair. 

6a.  Retopping.— Where  head  room  and  goods  or  machinery  in  place  will  permit, 
removal  of  existing  top  down  to  sound  concrete,  with  thorough  chipping,  roughening  and 

14 


210 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  4-66 


cleansing  of  the  exposed  surface  and  the  careful  laying  of  a  new  top  of  proper  quality  is  some- 
times the  most  advisable  and  in  the  end,  the  cheapest  procedure.  Details  of  bonding  top  coat 
to  base  have  been  previously  given. 

66.  Chemical  Hardeners. — Sodium  or  magnesium  fluosilicate  is  marketed  under 
various  trade  names  as  a  liquid  hardener.  A  pronounced  change  is  to  be  noted  in  the  appear- 
ance of  concrete  so  treated  with  a  greater  or  less  hardening  of  the  surface  and  corresponding 
resistance  to  abrasion,  according  to  the  initial  condition  of  the  concrete.  The  use  of  fluosili- 
cates,  originally  marketed  as  "fluates"  has  been  known  for  many  years,  with  a  comparatively 
recent  revival  through  aggressive  selling  campaigns  since  the  extension  of  uses  for  concrete 
buildings,  with  corresponding  increase  in  the  number  of  defective  floors. 

6c.  Use  of  Oils. — ^Linseed  oil,  both  boiled  and  raw,  with  and  without  additions 
and  adulterants  has  been  tried  as  a  binder  for  dusting  concrete  floors,  but  has  not  proven  ade- 
quate for  all  uses.  Its  value  may  be  gaged  by  the  resistive  and  retentive  values  that  an  oxidized 
film  of  a  like  oil  might  be  expected  to  possess  when  subjected  to  the  same  traffic  or  other  condi- 
tions which  gave  rise  to  the  original  complaint. 

China-wood  oil,  sometimes  called  Chinese  wood-oil,  or  Tung  oil,  either  alone  or  in  com- 
bination with  linseed  or  other  oils  or  resins  has  proven  somewhat  more  effective  than  plain 

linseed.  It  is  today  in  extensive  use  as 
a  basis  for  various  concrete  floor,  wall, 
and  water-resisting  paints  and  in  proper 
combinations  is  very  effective.  But  ex- 
cellent as  are  the  properties  of  this  oil 
it  is  not  necessarily  an  effective  remedy 
for  all  dusting  floors.  The  conditions 
attendant  on  each  individual  case 
should  be  minutely  studied  and  the 
chances  of  success  estimated,  rather 
than  attempting  the  haphazard  appli- 
cation of  any  palliative,  proprietary  or 
public,  on  the  chance  that  the  result 
desired  will  be  secured. 

Fig.  3.— Paint  film  on  concrete  floor.    (Magnified  20  diams.)  Qd.  Floor   CoatingS  and 

Paints. — It  is  oftentimes  desirable  for 
reasons  of  sanitation  or  of  appearance,  on  good  as  well  as  on  dusting  floors,  to  use  a  surface 
coat  of  paint.  A  number  of  excellent  floor  paints  are  on  the  market  which  can  be  had  in  a 
variety  of  colors,  the  surface  obtained  being  hard  and  sufficiently  resistant  to  abrasion  for 
most  purposes  and  capable  of  withstanding  the  action  of  water  almost  perfectly.  The  man- 
ner in  which  such  a  ffoor  paint  penetrates  into  the  body  of  the  concrete,  leaving  a  hard  re- 
sistant film  at  the  top,  is  shown  in  the  micrograph  of  Fig.  3. 

CONCRETE  SIDEWALKS 

7.  Structural  Functions. — Concrete  floors  and  concrete  sidewalks  have  similarity  of  func- 
tioning as  abrasion  and  impact-resisting  surfaces  and  dissimilarity  of  functioning  in  that  side- 
walks have  solid  bedding  and  low  concentrated  load  and  are  rarely  called  upon  to  act  as  beams. 
There  is  further  dissimilarity  in  that  the  perfection  of  surface  of  a  concrete  floor  is  not  required 
of  the  concrete  sidewalk,  since  the  latter  is  in  the  open  where  slight  surface  disintegrations  do 
no  harm  and  are  not  noticeable. 

8.  Essential  Qualities. — The  same  general  conditions  governing  the  manufacture  of  concrete 
floors  apply  to  the  manufacture  of  concrete  sidewalks  since  their  requisites  are  held  in  common. 
A  concrete  sidewalk  is  also  subject  to  the  same  character  of  disintegrations  as  is  a  concrete 


Sec.  4-9] 


CONCRETE  SIDEWALKS 


211 


floor,  aggravated  by  year-round  exposure  to  weathering  and  like  influences.  Like  precautions, 
therefore,  should  be  observed  in  its  manufacture. 

9.  The  Making  of  Concrete  Sidewalks.— The  disintegrations  of  sidewalks  seen  on  every 
hand  point  strongly  to  the  need  of  either  more  careful  procedures  than  those  usually  indulged 
in  or  else  to  improved  procedures,  but  in  view  of  the  many  successful  concrete  sidewalks  made 
by  careful  following  of  accepted  procedures,  indications  are  that  more  care  is  a  particularly  in- 
sistent demand. 

9a.  Porous  Subbase. — One  thing  that  must  be  always  guarded  against  in  a  con- 
crete pavement  is  the  action  of  frost.  For  this  reason,  adequate  drainage  of  subsoil  must 
be  provided.  The  porous,  or  draining  foundation  for  outdoor  construction  should,  there- 
fore, be  from  6  to  12  in.  thick,  dependent  upon  the  climate  in  which  it  is  situated  and  upon 
the  character  of  soil.  On  an  •  extremely  porous  or  sandy  soil  without  frost,  the  foundation 
may  be  omitted  entirely,  biit  it  is  erring  on  the  side  of  safety  to  use  a  porous  subbase  in  all 
cases. 

Such  a  subbase  may  be  cinders,  coarse  sand,  or  preferably  broken  stone  or  gravel.  This 
material  should  be  thoroughly  rammed  to  present  a  firm  and  unjdelding  stratum  and,  at  inter- 
vals, drains  of  coarser  sand  or  of  gravel,  or  even  open-tile  drains  may  be  advantageously  in- 
serted to  carry  off  water  which  may  collect.  Cinders  or  sand  should  be  thoroughly  wetted  and 
compacted  by  ramming. 

96.  Concrete  Base. — On  top  of  this  draining  foundation  is  placed  a  slab  of  coarse 
concrete  rammed  into  place,  of  a  quality  at  least  equivalent  to  that  obtained  with  arbitrary 
proportions  of  1  : 3  : 6.  This  base  is  usually  3  to  3)^  in.  in  thickness  and  it  is  separated  into 
blocks  by  form  boards  so  that  unequal  settlement  through  freezing,  rising  through  the  penetra- 
tion of  tree  roots  or  other  vegetation,  or  buckling  through  temperature  changes  may  not  injure 
the  walk.    Such  divisions  are  quite  essential  and  should  not  be  omitted. 

9c.  Top  or  Wearing  Surface. — Cast  upon  the  concrete  base  and  preferably  made 
integral  with  it  is  the  top  coat,  the  upper  surface  of  which  is  the  wearing  surface.  As  in  concrete 
floors,  the  more  silica  or  like  rock  material  which  can  be  exposed  to  wear  in  this  surface,  consist- 
ent with  proper  gripping  by  cement,  the  more  enduring  will  be  this  surface.  The  principles 
stated  for  producing  a  surface  of  like  character  on  concrete  floors  apply  with  equal  or  with  even 
greater  force  to  concrete  sidewalks. 

M.  Surface  Finishing. — After  screeding  it  is  customary  to  finish  the  top  surface 
of  pavements  either  by  floating  with  a  flat  trowel,  either  of  steel  or  of  wood  (with  or  without 
later  brooming  to  roughen  the  surface)  or  to  groove  or  checker 
the  floated  surface,  both  with  the  object  of  securing  rough- 
ness and  of  improving  its  appearance.  All  working  of  the 
surface  has  an  effect  similar  to  that  of  floating,  and  as  pointed 
out  in  Art.  5  under  ^'Floors"  it  may  cause  an  excess  of 
water  at  the  wearing  surface. 

As  in  making  concrete  floors,  the  use  of  dry  cement,  or 
dry  cement  and  fine  sand  sprinkled  over  an  excessively  wet 
surface,  is  a  common  reliance  for  speeding-up  the  finishing 
process.  Destruction  of  top  coat  is  often  to  be  traced  directly 
to  this  practice. 

9e.  Surface  Protection  and  Curing. — ^Laying 
cement  sidewalks  in  freezing  weather  is  always  attended  with 
risk.  Even  with  heated  aggregates  and  heated  water  (cement 
is  rarely,  if  ever  heated)  it  is  diflScult  if  not  impossible  to  main- 
tain the  temperature  of  the  mass  at  a  point  sufficiently  high 

and  for  a  time  sufl5ciently  long  to  insure  reaction  between  the  water  and  cement  so  as  to 
prevent  disruption  either  before  final  set,  or  so  near  that  time  that  reconsolidation  at  elevated 
temperatures  will  later  take  place.    It  should  further  be  borne  in  mind,  that  lowered  tempera- 


Fig.  4. — Typical  sidewalk  disin- 
tegration. (Public  Square,  Cleveland, 
Ohio.) 


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[Sec.  4-9/ 


ture  greatly  prolongs  the  period  of  plasticity,  leaving  water  uncombined  and  free  to  form 
disrupting  ice. 

Even  with  heated  aggregates,  therefore,  and  later  surface  protection,  great  care  must  be 
exercised  to  be  sure  that  minute  local  disruptions  (Fig.  4)  due  to  frost  have  not  made  the  con- 
crete, particularly  at  the  top,  ready  for  further  disintegrations,  either  through  attrition  or  by 
other  actions.    The  best  and  safest  plan  is  not  to  lay  concrete  sidewalks  in  freezing  weather. 

9/.  Protecting  Sidewalks  in  Hot  Weather. — In  view  of  what  has  been  said  in 
Art.  5  under  "Floors"  with  regard  to  the  effects  of  floating  and  troweling  in  bringing  water  to 
the  surface  and  remembering  further  the  requirements  of  cement  in  regard  to  quantities  of 
water  necessary  for  slow  hydration  and  chemical  interactions,  it  is  readily  to  be  understood 
that  rapid  evaporation  in  hot,  dry  weather  will  cause  hair  cracks,  through  a  too  rapid  removal 
of  water,  leaving  behind  and  directly  at  the  surface  such  of  its  products  as  may  be  in  solution, 
with  further  weakening  of  the  concrete  through  deprivation  of  the  remaining  cement  of  its 
necessary  reacting  water. 

To  guard  against  such  happenings,  as  soon  as  possible  after  finishing,  the  pavement  should 
be  covered  with  a  moist  protecting  canvas  supported  above  the  surface  by  a  frame,  or  by  a 
layer  of  moist  sand,  either  canvas  or  sand  being  kept  moist  for  several  days.  Only  by  observing 
precautions  such  as  these  can  success  be  obtained. 

9g.  Special  Surface  Finishes. — The  same  special  finishes  such  as  carborundum, 
or  iron,  suggested  for  concrete  floors  (Art.  4)  are  advocated  for  concrete  pavements  by  their 
sponsors.  The  same  remarks  apply  equally  to  both  uses,  as  does  a  restatement  of  the  fact 
that  no  additive  so  far  brought  out  is  capable  per  se  of  overcoming  defects  in  manufacture  and 
that  none  is  superior  in  all-around  qualities  to  good  clean  quartz  of  proper  grading. 

10.  Vault-light  Pavements. — Basement  areas  under  sidewalks  in  cities  are  a  valuable  asset 
but  it  is  necessary  that  they  be  cheaply  lighted.  This  desirable  end  is  accomphshed  through 
the  use  of  a  combination  of  round  or  square  lenses  of  thick  glass  set  in  cement  mortar,  formed 
into  pavement  blocks  of  requisite  size,  reinforced  with  steel  rods  and  supported  on  steel  or 
concrete  girders.  A  template  is  used  in  spacing  the  lenses,  the  mortar  being  troweled  in  place 
as  in  usual  cement  mortar  work.  From  the  standpoint  of  considerations  previously  presented, 
this  type  of  sidewalk  should  and  does  prove  very  enduring,  by  reason  of  the  large  area  of  resist- 
ant glass  exposed  to  abrasion  and  the  lessened  area  of  cement  mortar,  but  care  should  be  taken 
to  have  the  cement  portion  as  carefully  proportioned,  mixed,  and  laid,  as  it  would  be  where  the 
entire  wearing  surface  is  of  cement  mortar.  Joints  between  adjacent  blocks  and  adjoining 
constructions  are  sealed  with  a  waterproofing  compound.  Shattered  vault  hght  sidewalks 
are  frequently  seen,  this  shattering  being  due  to  the  wheels  of  heavily  laden  hand  trucks,  or  to 
improper  working  or  use  of  the  cement  mortar,  with  later  disintegration  through  frost  or 
other  actions,  with  loosening  of  lenses  and  permitting  of  continued  spalling  of  their  edges 
until  the  light-transmitting  properties  of  the  glass  are  impaired,  or  the  lens  broken  com- 
pletely. These  difficulties,  however,  do  not  reflect  upon  the  value  of  this  construction 
properly  executed. 

11.  Concrete  Curbing. — Concrete  in  curb  and  gutter  construction  has  met  with  much 
favor.  It  proves  generally  excellent  provided  it  is  properly  underdrained.  Integral  curb  and 
gutter  blocks  are  made  in  lengths  having  definite  cross-joints  but  no  longitudinal  joints,  as  such, 
by  the  action  of  frost  or  vegetation,  would  invite  separation  by  frost  or  by  the  action  of  pene- 
trant vegetation. 

12.  Summary. — Concrete  sidewalks,  no  less  than  other  constructions,  are  structures  of 
concrete;  and  to  be  enduring,  they  must  be  good  concretes.  Furthermore,  they  must  be 
particularly  protected  against  natural  disintegrating  forces,  chief  among  which  is  frost.  This 
requires  good  subdrainage  as  a  prime  requisite;  and  of  almost  equal  importance,  a  dense  struc- 
ture resistant  to  the  penetration  of  water.  To  secure  this,  rigid  observance  of  the  principles 
of  mixing  good  concrete  must  be  insisted  upon.  The  man  with  "20  years'  experience"  may 
only  be  one  who  persists  in  the  least  advisable  procedures. 


Sec.  4-13] 


CONCRETE  ROADWAYS 


213 


CONCRETE  ROADWAYS 

13.  Structural  Functions. — Concrete  sidewalks  and  concrete  roadway  pavements  are 
similar  in  that  they  are  impact  and  abrasion-resisting  surfaces  bedded  on  a  continuous  sub- 
base;  and  they  are  dissimilar  in  the  perfection  of  the  surface  required  and  in  the  degree  of 
impact  and  abrasion  which  they  must  sustain. 

14.  Essential  Qualities. — Concrete  roads,  no  less  than  concrete  floors,  are,  first  of  all, 
concretes,  so  that  their  character  is  governed  by  the  laws  basically  controlling  the  making  of 
good  concrete.  Particularly  must  provision  be  made  against  disintegration  through  weather- 
ing, through  the  heavy  impact  of  shod  hoofs  and  tires  of  loaded  vehicles,  and  through  the 
raveling  action  of  fast  motor  traffic.  The  best  means  for  this  purpose  at  present  known  are: 
(1)  proper  subdrainage;  and  (2)  the  securing  of  high-density  concrete  having  adequate 
cementation  of  adequate  quantities  of  rock  products  in  the  wearing  surface,  through  care  in 
selection  and  proper  proportioning  of  materials;  through  adequate  mixing,  careful  placing,  and 
proper  curing, 

15.  One-course  and  Two-course  Pavements. — The  tendency  at  the  present  time  is  toward 
the  use  of  one-course,  rather  than  two-course  roadway  pavements.  A  certain  roughness  of 
surface  is  very  desirable  to  prevent'  slipping ;  and  in  a  pavement  with  the  concrete  properly 
proportioned  and  mixed  there  is  a  requisite  amount  of  rock  material  in  the  surface  to  withstand 
abrasion,  with  the  added  advantage  that  the  slab  is  monolithic,  without  separation  planes,  as 
is  so  often  the  case  where  one  course  is  laid  upon  another  which  has  already  set.  The  general 
method  of  finish  is,  however,  similar  screeding,  floating,  and  troweling  being  done  in  the  usual 
manner. 

16.  The  Making  of  Concrete  Roadways. 

16a.  Porous  Subbase. — Inasmuch  as  a  concrete  roadway  pavement  should  not 
be  called  upon  to  sustain  beam  stresses,  a  continuous  unyielding  bed  must  be  provided,  else 
cracking  and  unequal  settlements  will  occur.  Such  a  solid  bedment  of  the  concrete  slab  requires 
special  provision  against  upward  heaving  by  frost  action,  which  necessitates  either  a  porous 
subbase  of  a  depth  sufficient  (together  with  side  drains)  to  clear  the  ground  of  water  below 
frost  line,  or  else  one  having  a  sufficiently  yielding  nature  to  permit  local  ground  eruptions 
without  extension  of  the  disturbance  to  the  concrete  slab  above  it,  though  this  latter  is  almost 
impossible  to  secure. 

It  is  regretable  that  so  little  attention  is  paid  to  this  important  feature  of  subdrainage. 
The  majority  of  concrete  roadways  are  placed  directly  on  rolled  ground,  often  without  pretense 
of  drainage  and  in  some  cases,  with  even  a  pronounced  dish  toward  the  center.  To  counteract 
the  effect  of  settlement  or  frost  action  encouraged  by  this  initial  fault,  reinforcement  is  embed- 
ded in  the  slab,  ^-lo  of  1%  of  steel  being  the  Joint  Conference  recommendation,  but  twice  to 
three  times  that  amount  being  actually  necessary  to  secure  a  modicum  of  assurance.  Concrete 
roadways  should  be  capable  of  enduring  and  rendering  splendid  service  without  reinforcement. 
Actually,  even  the  reinforcement  too  often  proves  inadequate  to  the  unnecessary  task  imposed 
on  it. 

166.  Proportioning  and  Selecting  of  Materials. — Arbitrary  proportions  are 
generally  used  in  pavement  work,  regardless  of  possible  benefits  obtainable  by  better  grading. 
For  one-course  work,  average  specifications  call  for  1:2:3  concrete;  and  for  two-course  work, 
1 :  2yi :  5  concrete  in  the  base  with  a  topping  of  1 : 2  mortar,  although  a  concrete,  using  fine  stone 
instead  of  sand  requiring  even  less  cement,  would  be  preferable. 

The  principles  of  proportioning  and  selection  of  materials  for  concrete  roadways  as  laid 
down  by  the  Aggregate  Committee  of  the  1914  National  Conference  are  as  follows: 

1.  For  fine  aggregate,  use  only  sand  or  other  fine  aggregate  free  from  very  fine  particles,  and  which  has  been 
actually  tested  by  mechanical  analysis,  and  for  the  tensile  strength  of  standard  mortar. 

2.  Use  coarse-grained  sands  or  hard  stone  screenings  with  dust  removed. 


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CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  4-16C 


3.  Use  sand  or  other  fine  aggregate  that  is  absolutely  clean. 

4.  For  coarse  aggregate,  use  hard  stone,  such  as  granite,  trap,  gravel,  or  hard  limestone. 

5.  If  bank  gravel  or  crushed  stone  is  used,  always  remove  the  sand  or  screenings  and  remix  in  the  proper 
proportions. 

If  local  conditions  prevent  following  any  of  these  rules,  adopt  some  other  material  than  concrete  for  your 
pavement. 

More  detailed  requirements  for  fine  aggregate  are: 

The  size  of  the  fine  aggregate  shall  be  such  that  the  grains  will  pass  when  dry  a  screen  having  H-in.  openings. 
In  the  field  a  ys-in.  mesh  or  in  some  cases  a  }^-in.  mesh  screen  may  be  used  for  this  separation. 

Not  more  than  10%  of  the  grains  below  the  H-in.  size  shall  pass  a  sieve  having  50  meshes  to  the  linear  inch, 
and  not  more  than  2  %  shall  pass  a  screen  having  100  meshes  to  the  linear  inch.  This  is  an  exceptionally  coarse 
sand,  but  coarse  sand  is  a  necessity  for  a  durable  pavement. 

16c.  Joints. — Expansion  joints  must  be  provided  to  prevent  cracking  due  to 
temperature  changes.  These  should  be  provided  at  linear  intervals  of  from  30  to  50  ft.  depend- 
ing upon  the  climate  of  the  region  in  which  the  pavement  is  situated.  Joints  should  also  be 
placed  at  changes  in  grade,  and  longitudinally  between  curbs.  The  usual  joint  is  from  ^  to 
}'2  in.  wide  and  the  National  Conference  recommends  a  preformed  plastic  filler.  A  variety 
of  special  compounds  for  this  purpose  are  on  the  market  and  also  metal-and-plastic  inserts 
intended  to  reduce  the  surface  exposure  of  joints  to  a  minimum. 


 r  ■■■   r     ■  ! 

Proper  consistency  for 
concnete  road  work 

h 

be  obi 

\ 

I 

1 

1 

1 

'With  this  consistency  about 
one-hatf  the  strength  Js  lost 

-1 

-1 

Wifh  the  sloppy  concnefe  sometime 
used  in  road  worlc  and  m  building  cor 
strudion,  t^o- thirds  to  three  three- 
fourths  of  Hie  possible  strength  erf 
the  concrete  is  lost. 

■  y 

70     80     90     \00     110     120     130     140     150     160     170     180  130 
Percent  of  water  giving  maximum  strength 

Fig.  5. — Proper  consistency  of  concrete  for  road  work.^ 


IQd.  Curing. — Difficulties  that  have  arisen  in  the  use  of  concrete  pavements 
have  forced  recognition  of  some  usually  neglected  though  well-known  principles  of  concrete 
making.  Among  these  is  protection  of  the  pavement  for  a  period  of  time  against  drying  in 
warm  weather  and  frost  in  cold  weather.  For  the  purpose  first  named,  earth  dams  permitting 
flooding  the  pavement  with  water  have  been  used  with  success;  also  protecting  canvases,  or 
layers  of  sand,  or  earth,  or  sawdust  have  been  used  each  being  kept  moist.  In  the  winter  time 
protection  against  frost  has  been  obtained  by  the  use  of  hay  or  straw  and  sometimes  manure. 
The  use  of  the  latter,  however,  is  dangerous,  inasmuch  as  manure  not  only  discolors  the  concrete, 
but  may  bring  about  disintegration  through  penetration  and  decomposition  of  organic  acids. 

16e.  Consistency. — Observation  indicates  a  general  tendency  to  mix  pavement 
concretes  too  wet  (see  Fig.  5).  The  proper  consistency  is  plastic,  permitting  compacting  and 
molding,  with  surface  finishing,  but  without  runoff,  or  separation  of  ingredients.  Overwet 
concretes  in  roadway  pavements  cannot  be  expected  to  have  better  qualities  than  the  same 
character  of  mix  possesses  in  other  types  of  structures. 

1  D.  A.  Abrams:  Bulletin  Portland  Cement  Assoc.  » 


SECTION  5 


PROPERTIES  OF  CEMENT  MORTAR  AND  PLAIN  CONCRETE 

By  Adelbert  P.  Mills^ 

STRENGTH  OF  CEMENT  MORTAR  AND  PLAIN  CONCRETE 

1.  Strength  in  General. — The  strength  of  mortar  and  concrete  made  with  a  given  cement 
is  dependent  primarily  upon:  (1)  the  inherent  strength  of  its  aggregates,  particularly  the  large 
aggregates;  (2)  the  proportion  of  cement  per  unit  of  volume  of  mortar  or  concrete;  (3)  the 
degree  of  compactness  or  densit}^  of  the  mortar  or  concrete;  and  (4)  the  time  afforded  subsequent 
to  final  deposition  in  molds  or  forms. 

(1)  .  With  a  given  aggregate  (sand,  or  sand  and  broken  stone  or  gravel)  the  mortar  or  con- 
crete strength  will,  other  things  being  equal,  increase  with  increased  proportion  of  cement  in 
the  mixture. 

(2)  .  With  a  given  proportion  of  cement  in  the  mixture  the  mortar  or  concrete  strength  will, 
other  things  being  equal,  increase  with  increased  density  of  the  mixture. 

(3)  .  Strength  normally  increases  with  age  for  an  indefinite  period. 

The  first  of  these  rules  does  not  apply  in  comparing  mortars  or  concretes  which  have  been 
made  with  different  aggregates,  with  different  cements,  with  different  proportions  of  water 
used  in  gaging,  or  with  different  methods  of  mixing  or  placing  the  mixture,  nor  in  comparing 
mortars  or  concretes  which  have  cured  under  different  conditions. 

The  density  of  the  mixture  secured  will  depend  primarily  upon  the  gradation  in  sizes  of 
the  aggregate,  but  may  also  be  affected  by  the  manner  and  extent  of  manipulation  of  the  mate- 
rial in  mixing  and  placing,  and  by  varying  the  proportion  of  water  used  in  gaging. 

The  second  rule  fails  as  a  basis  of  comparison  when  different  cements  are  used,  when  the 
aggregates  possess  a  different  mineral  character  or  are  to  a  differing  degree  contaminated  with 
mineral  or  organic  impurities,  and  may  not  apply  when  methods  or  conditions  of  making, 
placing,  and  curing  of  the  mixture  vary. 

The  third  rule  is  independent  of  most  other  factors  except  that  certain  circumstances 
such  as  the  proportion  of  water  used  in  gaging  and  the  conditions  of  curing  may  affect  the  rate 
of  increase  of  strength  with  age.  An  apparent  falling  off  or  retrogression  in  tensile  strength 
after  from  3  to  6  months  is  commonlj^  noted  in  tests  of  neat  cement,  and  less  commonly  in 
tests  of  mortars.  A  less-marked  retrogression  in  compressive  strength  is  also  frequently  ob- 
served in  tests  of  neat  cement,  and  a  slight  retrogression  in  compressive  strength  of  mortars 
and  concretes  is  not  infrequently  observed  after  long  periods. 

A  number  of  empirical  formulas  have  been  derived  by  various  experimentors  which  attempt 
to  express  a  definite  mathematical  relation  between  strength  of  mortar  and  concrete  and  the 
absolute  volume  of  cement  and  sand,  or  cement,  sand,  and  coarse  aggregate,  in  the  mixture. 
Owing  to  the  fact  that  the  effect  of  many  factors,  some  of  which  are  mentioned  above,  cannot 
be  taken  into  account  by  such  formulas,  their  application  is  restricted  to  certain  classes  of 
laboratory  investigations  which  do  not  involve  many  of  the  variables  encountered  in  the  use  of 
similar  materials  on  construction  work. 

2.  Laboratory  Tests,  Their  Use  and  Significance.— The  value  of  cement  mortars  and 
concretes  as  structural  materials  depends  primarily  upon  their  ni('chani<-nl  strength  and  dura- 

1  Assistant  Professor  of  Materials,  Cornell  University.    Author,  "Materials  of  Construction." 

215 


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[Sec.  5-2 


bility  when  hardened.  The  conditions  encountered  in  practical  use,  however,  are  necessarily 
so  variable  as  to  exclude  the  possibility  of  the  establishment  of  standards  based  directly  upon 
practical  experience. 

The  only  established  American  standards  for  mortars  are  those  for  tensile  strength  (see 
Appendix  A).  These  standards  merely  fix  values  of  tensile  strength,  determined  under  labora- 
tory conditions,  which  experience  has  shown  may  be  expected  of  cements  and  sands  found 
satisfactory  in  practical  construction  work,  in  order  that  inferiority  in  any  particular  mortar 
materials  may  be  detected  by  deviation  from  such  standards.  In  other  words,  knowing  that 
good  concrete  or  mortar  sands  will  in  laboratory  tests  show  a  tensile  strength  not  inferior  to 
that  of  standard  sand  mortars,  it  is  assumed  that  any  sand  which  exhibits  like  tensile  properties 
in  the  laboratory  will  not  fail  to  satisfactorily  meet  the  conditions  of  structural  use. 

The  conditions  encountered  by  a  mortar  in  a  structure  are  not  duplicated  in  the  laboratory, 
but  the  laboratory  method  is  so  standardized  that  the  external  conditions  of  the  test  may  be 
duplicated  elsewhere  or  at  a  different  time. 

Two  factors  operate  to  lessen  the  importance  of  laboratory  tests  of  mortars  as  an  indication 
of  suitability  of  the  material  for  construction  uses:  (1)  the  closeness  of  the  relation  between  the 
results  of  tensile  tests  and  the  qualities  which  a  mortar  in  a  structure  will  be  called  upon  to 
show  may  properly  be  considered  open  to  question,  and  (2)  laboratory  tests  of  this  class  of 
material  cannot  be  made  with  any  great  degree  of  precision,  and  the  results  may  be  very 
much  in  error  if  the  work  is  not  performed  under  proper  conditions  by  a  skilled  operator. 

Mortars  are  never  used  structurally  in  such  a  way  that  they  will  be  depended  upon  to 
carry  tensile  stress,  while  they  are  commonly  used  to  carry  compressive  stress.  From  this 
circumstance  it  may  be  argued  that  a  compressive  test  in  the  laboratory  will  afford  a  more 
direct  indication  of  the  structural  qualities  of  the  material  than  does  the  tensile  test.  The 
compressive  test  is  less  easily  made  than  the  tensile  test,  however,  and  calls  for  more  elaborate, 
more  expensive,  and  less  portable  equipment.  It  is  not  easy  to  establish  the  relationship 
between  laboratory  test  results  and  structural  qualities  of  mortars,  but  the  tensile  test  has  been 
made  so  much  more  generally  than  the  compressive  test,  that  the  average  man  has  no  experience 
by  which  he  may  judge  the  value  of  the  latter,  while  he  has  observed  that  materials  which  pass 
the  tensile  test  infrequently  prove  unsatisfactory  in  a  structure.  Whether  the  compressive 
test  will  fail  any  less  frequently  as  an  indication  of  unsuitability  remains  to  be  conclusively 
shown,  but  the  somewhat  inadequate  data  available  seem  to  point  toward  this  conclusion. 
It  is  undoubtedly  a  fact  that  certain  natural  impurities  in  sands,  as  well  as  certain  classes  of 
material  sometimes  intentionally  added  to  mortars  for  special  purposes  such  as  decreasing 
permeability  or  altering  the  appearance,  reveal  their  injurious  character  to  a  much  more 
marked  extent  in  compressive  tests  than  they  do  in  tensile  tests. 

The  results  of  laboratory  tests  of  mortars  are  affected  by  a  number  of  factors,  not  all 
of  which  are  readily  subject  to  control.  It  is  never  possible  to  determine  precisely  the  relative 
qualities  of  mortar  materials  tested  in  different  laboratories  or  by  different  operators.  The 
atmospheric  condition  of  the  laboratory,  with  respect  to  both  temperature  and  humidity,  is 
one  important  factor  which  ought  not  to  be  subject  to  variation,  but  is  so  nevertheless.  The 
most  important  consideration,  however,  is  the  fact  that  very  slight  variations  in  the  detail 
methods  of  manipulation  of  the  materials  in  making  test  specimens  affect  the  test  results  to 
so  great  an  extent  that  a  very  close  check  between  the  results  of  two  different  operators  is 
impossible. 

An  experienced  operator  may  be  able  to  check  his  own  results  within  say  5%,  but  a  second 
equally-experienced  operator  who  can  also  check  his  own  results  thus  closely,  may  not  be  able 
to  check  the  first  man  within  less  than  15  or  20%.  Each  man  has  developed  invariable  methods 
of  manipulation,  but  the  methods  of  the  two  men  will  never  be  identical.  This  fact  need  not 
invalidate  comparative  tests,  however,  and  the  results  of  tests  of  standard  mortar  and  mortar 
made  by  the  same  experienced  operator  with  a  commercial  sand  substituted  for  the  standard  I 
sand  should  be  truly  comparable. 


Sec.  5-3] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


217 


Bearing  in  mind  the  considerations  above  discussed,  it  may  be  concluded:  (1)  that  labora- 
tory acceptance  tests  of  mortar  must  not  be  considered  to  show  the  absolute  strength  which 
may  be  developed  in  a  structure,  but  merely  to  indicate  the  approximate  relative  value  of  th(? 
proposed  materials  and  materials  whose  suitability  has  been  proved;  and  (2)  that  laboratory 
tests  must  never  be  entrusted  to  anyone  who  has  not  had  a  large  experience  in  making  this 
particular  kind  of  test  with  the  advantage  of  a  fully  equipped  laboratory.  The  testing  of 
concrete  materials  is  not  the  job  for  a  novice,  and  the  average  field  laboratory  is  not  a  fit  place 
to  do  the  work. 

3.  Neat,  Mortar,  and  Concrete  Strength  Compared. — A  comparison  of  the  strength  of 
cement,  cement  mortar,  and  concrete  can  only  be  made  when  the  many  variable  factors  which 
influence  the  results  of  tests  have  been  eliminated  so  far  as  is  practically  possible.  This  means 
that  only  tests  made  with  identical  materials  under  the  same  auspices  are  truly  comparable. 


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Age  of  specimens 

Fig.  1— Relation  between  tensile  strength  of  neat  cement  and  cement  mortars  (9  brands  of  cement). 


The  strengths  of  the  cement,  mortar,  and  concrete  mixtures  shown  graphically  by  the  diagrams 
of  Figs.  1  and  2  are  based  upon  one  series  of  tests  made  by  the  Technologic  Branch  of  the  U.  S. 
Geological  Survey  at  the  Structural  Materials  Testing  Laboratories  formerly  located  at  St. 
Louis,  Mo.  The  complete  report  of  these  tests  is  contained  in  Bulletin  344  of  the  U.  S.  Geolog- 
ical Survey  and  Technologic  Paper  2  of  the  U.  S.  Bureau  of  Standards. 

The  diagrams  for  neat  cement  and  1 : 3  standard  sand  mortar  are  averages  of  three  tests 
of  each  mixture  for  each  of  nine  separate  brands  of  cement.  For  the  commercial  sand  mortars 
and  all  of  the  concrete  mixtures,  a  blend  of  these  nine  cements  was  used.  The  diagrams  aver- 
age the  results  of  three  tests  of  each  mortar  and  18  to  21  tests  of  each  concrete.  (The  irregu- 
larities shown  by  the  diagrams  for  the  commercial  sand  mortars  would  doubtless  not  appear 
if  they  represented  the  average  of  a  larger  number  of  tests.)  The  same  commercial  sand  was 
used  in  the  mortars  and  all  of  the  concretes.  It  is  described  as  Merrimac  River  sand  and  is 
composed  of  flint  grains  having  comparatively  smooth  surfaces.  It  has  a  fairly  well-graded 
composition,  its  void  content  is  not  particularly  high,  but  it  is  finer  than  is  desirable.  The  four 
coarse  aggregates  are  typical  well-graded  aggregates  of  the  classes  indicated.  It  should  not 
be  concluded  from  these  tests  that  granite  or  gravel  aggregate  can  be  depended  upon  to  excel 
limestone  in  all  cases.  Very  slight  differences  in  two  apparently  similar  materials  of  the  same 
class  will  often  make  a  great  difference  in  their  value  as  concrete  aggregate. 


218 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-4 


It  is  not  intended  that  the  diagrams  of  Figs.  1  and  2  shall  form  a  basis  for  definite  con- 
clusions concerning  the  relative  strengths  of  various  cement  mixtures,  but  only  to  show  in  a 
general  way  the  results  of  tests  of  typical  materials  in  various  mixtures.  The  value  of  any 
given  material  can  be  determined  only  by  tests  of  its  qualities  regardless  of  the  qualities  other 
materials  of  the  same  type  may  show.  The  more  important  of  the  many  factors  which  affect 
mortar  and  concrete  strength  are  considered  below. 


7dci.  E8dx 


3  Mo. 


6  Mo 

Age  of  specimens 


Fig.  2. — Relation  between  compressive  strength  of  neat  cement,  cement  mortars,  and  concretes 

(9  brands  of  cement). 


4.  Aggregates  of  Mortar  and  Concrete. — Testing  of  the  cement  used  in  all  important 

concrete  structures  has  been  common  practice  for  many  years,  but  the  importance  of  the 
quality  of  the  aggregate,  in  its  relation  to  the  quality  of  mortar  and  concrete  of  which  it  forms 
a  constituent,  has  not  yet  come  to  be  adequately  appreciated  by  the  majority  of  engineers, 
architects,  and  contractors.  While  cement  of  good  quality  is  essential  to  the  making  of  good 
concrete,  its  manufacture  has  today  been  standardized  to  such  an  extent  by  exacting  speci- 
fications that  in  the  average  case  it  is  actually  safer  to  assume,  without  tests,  that  the  cement 
is  satisfactory  than  to  assume  that  the  aggregate  materials  most  readily  available  may  properly 
be  used  without  careful  experimental  determination  of  their  quality. 

The  principal  requisites  for  concrete  aggregates  are  structural  strength  and  durability, 
a  proper  gradation  of  sizes  of  particles,  and  cleanliness  or  freedom  from  deleterious  matter. 

The  unsuitability  of  a  weak,  soft,  or  porous  material  is  quite  obvious,  but  a  well-graded 
limestone  aggregate  may  make  better  concrete  than  a  harder  granite  aggregate  whose  void 
content  is  high,  and  a  coating  of  matter  partly  or  wholly  of  organic  origin  upon  the  particles 


Sec.  5-5] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


219 


of  the  best-graded  granite  aggregate  obtainable  may  cause  the  concrete  in  which  it  is  used  to 
have  exceptionally  poor  qualities. 

The  physical  testing  of  aggregates  is,  unfortunately,  not  controlled  by  any  generally- 
accepted  specifications,  but  methods  are  at  the  present  time  undergoing  standardization  by  the 
technical  committees  of  the  most  interested  National  engineering  societies.  Some  of  the 
largest  engineering  organizations,  as  well  as  State,  Federal,  and  municipal  public  service 
commissions,  employing  large  quantities  of  concrete,  make  a  regular  practice  of  subjecting 
all  aggregate  materials  used  to  a  systematic  physical  examination.  The  variability  of  aggregate 
materials  available  in  different  localities,  and  even  of  an  aggregate  from  a  single  source  of 
limited  extent,  magnifies  the  importance  of  tests  not  only  in  choosing  the  most  suitable  aggre- 
gates from  those  available  for  construction  work  in  any  given  locality,  but  also  in  certifying 
the  quality  of  all  shipments  of  that  aggregate  to  the  job.  This  entails  a  considerable  expense 
for  the  testing  of  materials  which  possess  a  very  low  intrinsic  value.  It  is  an  expense  which 
may  be  justified,  however,  by  the  direct  benefit  gained  by  a  thorough  knowledge  of  how  avail- 
able materials  may  best  be  utilized.  An  unsatisfactory  material  may  be  greatly  improved  by 
washing,  perhaps,  or  by  screening  and  readmixture  of  the  different  grades  in  different  propor- 
tions, or  the  judicious  mixture  of  two  available  materials  may  be  found  to  yield  a  material 
greatly  superior  to  either  one  alone. 

It  is  very  desirable,  also,  that  the  proportions  of  the  mixture  of  cement  and  fine  and 
coarse  aggregate  be  not  rigidly  specified,  but  only  that  the  physical  properties  of  the  result- 
ing concrete  shall  be  up  to  a  fixed  standard  of  strength  or,  in  some  cases,  density  or  im- 
permeability. This  will  often  mean  that  when  the  local  materials  are  inferior,  a  concrete  of 
the  required  quality  may  be  attained  either  by  using  the  local  materials  in  a  rather  rich 
mixture,  or  by  importing  better  aggregate  from  a  distance,  using  a  leaner  mixture.  Thus 
the  relative  costs  of  the  additional  cement  used  with  the  local  materials,  or  the  freight  charges 
on  imported  aggregate  will  be  the  factor  which  determines  the  choice. 

For  tests,  specifications,  and  properties  of  aggregates,  see  chapter  on  "Aggregates"  in 
Sect.  1. 

5.  Effect  of  Mineral  Character  of  Aggregates. — The  structural  strength  and  durabihty 
of  concrete  aggregates  is  dependent  upon  the  mineral  character  of  the  rock  from  which  it  is 
derived.  In  the  case  of  coarse  aggregate  of  artificially  crushed  stone,  the  original  qualities  of 
the  rock  have  obviously  not  been  altered.  When  the  rock  has  been  broken  down  into  gravel 
or  sand  through  the  operation  of  natural  agencies,  the  structural  qualities  of  the  individual 
particles  of  the  material  will  still  be  identical  with  those  of  the  parent  rock  except  for  possible 
changes  effected  by  chemical  agencies. 

The  principal  classes  of  rocks  from  which  concrete  aggregates  are  derived  are  granites, 
trap-rocks,  limestones,  and  sandstones.  Granite  is  an  igneous  rock  of  variable  structure 
and  texture,  whose  principal  mineral  constituents  are  quartz  and  feldspar  with  varying 
amounts  of  mica,  hornblende,  etc.  The  structural  qualities  of  granites  vary  greatly  but 
granites  as  a  class  rank  among  the  hardest,  strongest  and  most  durable  stones.  The  term 
trap-rock  is  commonly  used  to  include  basalt,  diabase,  and  a  number  of  other  igneous  rocks 
possessing  similar  chemical  and  physical  properties.  The  principal  mineral  constituents 
of  most  of  these  rocks  are  pyroxene  and  feldspar.  They  are  commonly  rather  fine-grained, 
hard,  tough,  and  durable.  Limestones  contain  carbonate  of  lime,  calcite,  or  carbonate  of 
lime  together  with  the  double  carbonate  of  lime  and  magnesia,  dolomite,  as  the  essential 
constituent.  Sand  and  clay  are  common  impurities  and  some  varieties  contain  large 
amounts  of  shells  and  other  fossils.  Limestones  vary  greatly  in  structure,  strength,  hard- 
ness, and  durability.  Some  of  the  limestones  are  superior  in  structural  qualities  to  some 
of  the  granites,  but  the  average  limestone  is  inferior  to  the  average  granite  or  the  average 
trap-rock  as  concrete  aggregate.  Sandstones  consist  of  grains  of  varying  sizes,  chiefly 
quartz,  bound  together  by  silica  or  iron  oxide  or,  less  frequently,  by  lime  carbonate  or 
clay.    The  structural  qualities,  strength,  hardness,  and  durability  of  sandstones  vary 


220 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-5 


greatly  according  to  the  texture,  and  the  class  of  the  binder.  A  silicious  binder  excels 
any  other  in  all  respects;  an  iron  oxide  binder  is  usually,  though  not  always,  superior  to 
one  of  lime  carbonate ;  and  sandstones  having  a  clay  binder  are  in  all  respects  least  valuable 
as  concrete  aggregate. 

Fig.  3,  which  is  based  upon  tests  made  at  the  U.  S.  Bureau  of  Standards  {Tech.  Paper  58), 
shows  the  great  variability  in  strength  exhibited  by  concretes  made  with  different  classes  of 
coarse  aggregate  and  with  different  aggregates  of  the  same  general  class.  The  proportions 
were  1  : 2  : 4  in  all  cases,  and  the  same  cement,  a  blend  of  nine  standard  brands  of  Portland 
cement,  was  used  throughout.  Two  river  sands  of  similar  character  and  somewhat  similar 
granular  analysis  were  used  in  making  the  specimens  of  each  coarse  aggregate.  It  will  be  noted 
that,  except  in  the  case  of  the  granite  concretes  which  included  only  four  different  aggregates, 
the  range  in  strength  of  concretes  with  different  aggregates  of  the  same  class  is  often  more  than 
100%  of  the  average  strength. 

All  sands  are  derived  from  rocks  which  have  been  broken  down  or  disintegrated 
through  the  operation  of  purely-physical  agencies,  without  change  of  mineral  identity, 
or  which,  in  addition  to  disintegration,  have  been  more  or  less  decomposed  by  chemical 


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Age  in  weeks  Age  in  weeks  Age  in  weeks 

Fig.  3. — Comparative  strengths  of  concrete  with  various  types  of  aggregate. 


agencies  involving  the  formation  of  new  compounds.  The  principal  disintegrating  agen- 
cies are  temperature  changes,  which  are  operative  because  of  the  unequal  expansion  and 
contraction  of  the  component  minerals  and  because  of  frost  action,  and  abrasion  caused 
by  the  flow  of  water,  glacial  action,  or  by  winds.  Chemical  decomposition  is  accom- 
plished through  the  solvent  power  of  water,  facilitated  often  by  the  presence  of  various 
chemically-active  substances,  acids,  etc.,  carried  by  the  water. 

Quartz  is  the  mineral  which  makes  up  the  bulk  of  the  particles  of  most  sands.  This 
is  due  to  the  fact  that  only  the  harder  constituents  of  rocks  survive*  as  sand,  and  quartz  is 
not  only  a  very  common  constituent  of  rocks,  but  is  also  very  hard  and  resists  chemical 
decomposition.  The  fact  that  quartz  is  the  principal  constituent  of  a  sand  does  not 
insure  its  suitability  for  concrete,  however.  Comparatively  small  amounts  of  certain 
minerals  like  mica  or  even  feldspar  or  hornblende,  or  very  small  amounts  of  organic  impuri- 
ties will  render  a  quartz  sand  altogether  unfit  for  use.  Sandstone  is  a  common  source  of 
quartz  sand,  and  the  quality  of  the  sand  will  depend  upon  the  character  of  the  binder  of 
the  original  rock,  since  the  individual  particles  of  sand  are  made  up  of  still  smaller  parti- 
cles of  quartz  bound  together  by  silica,  iron  oxide,  lime  carbonate,  or  clay  according  to 
the  class  of  the  rock.    Sands  are  seldom  derived  from  trap-rock  or  granite  directly, 


Sec.  5-6] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


221 


though  sand  beds  may  often  be  largely  made  up  of  the  constituent  minerals  of  these 
rocks.  Pyroxene  and  hornblende  are  complex  silicates  possessing  a  degree  of  hardness, 
strength,  and  durability  slightly  inferior  to  that  of  quartz.  Hornblende  particularly  has 
inferior  weathering  qualities.  Feldspars  are  essentially  silicates  of  alumina  with  potash, 
soda,  or  lime.  They  are  considerably  less  strong  and  durable  than  quartz.  Mica  is  a 
very  objectionable  constituent  of  sands  for  concrete.  It  is  soft,  has  low  strength,  particu- 
larly in  shear,  and  its  laminated  structure  promotes  the  percolation  of  water.  Its  surface 
is  also  of  such  a  character  that  the  bond  secured  by  cement  is  very  poor.  Limestones  do 
not  serve  as  a  source  of  concrete  sands  although  calcite  and  dolomite  may  occur  in  sands 
derived  from  sandstones  having  a  calcium  carbonate  binder.  Limestone  screenings  or 
crusher  dust  are  also  sometimes  used  as  fine  aggregate  though  the  concrete  made  there- 
with is  usually  inferior  in  strength  to  that  made  with  an  average  sand,  and  it  is  also  apt 
to  be,  or  will  in  time  become,  more  permeable,  owing  to  the  solubility  of  calcite  and  dolomite. 

Sand  deposits  being  rarely  of  a  residual  character,  but  usually  deposited  by  stream  or 
glacial  action,  and  being  also  of  such  a  character  that  the  percolation  of  surface  waters 
through  the  beds  is  very  easy, 
the  material  is  often  contami-  ^ 
nated  by  matter,  much  of  it 
of  organic  origin,   carried  in 
suspension    by  water.  Thus 
the  coating  of  the  grains  by  ^  650 
such  substances  as  tannic  acid  c 
is  frequently  encountered.  j_  ^'^^ 
The  effect  of  such  impurities  "0^550 
is  extremely  detrimental  and  £ 
the  difficulty  with  which  their  500 
presence  may  be  detected  in- 
creases the  importance  of  care- 
ful  tests  of  concrete  sands. 

6.  Effect  of  Shape  and  Size 
of  Aggregates. — Specifications 
frequently  call  for  a  sharp  sand, 
i.e.,  one  composed  of  rough 
angular  particles,  in  spite  of 
the  fact  that  in  many  localities 


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90 


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Age  in  days 

Fig.  4a. — Effect  of  size  of  sand  upon  tensile  strength  1 :  1  mortar. 
(Tests  of  R.  P.  Davis.) 


river  or  beach  sands  having  somewhat  rounded  particles  are  the  only  ones  obtainable,  and 
have  been  used  with  perfect  satisfaction.  The  shape  of  the  particles  is  chiefly  important  in 
so  far  as  it  affects  the  void  percentage  of  the  material,  and  rough,  irregular  particles  do  not 
compact  better  than  rounded  particles.  On  the  contrary,  rounded  particles  which  afford 
no  opportunity  for  bridging  will  compact  into  the  densest  mass.  In  some  instances  the 
surface  facets  of  angular  particles  may  afford  a  better  adherence  for  cement  than  the 
rounded  surfaces  of  water  worn  particles,  but  this  factor  is  less  influential  than  is 
the  density  of  the  mass,  and  mortars  and  concretes  made  with  aggregates  composed  of 
worn,  rounded  particles  are  not  inferior  in  strength  to  those  made  with  "sharp"  aggregates, 
and  very  often  excel  the  latter  in  strength.  The  same  considerations  apply  in  the  case  of  crushed 
stone  vs.  gravel  as  coarse  aggregate.  Concrete  of  excellent  quality  or  very  inferior  quality 
may  be  made  with  either  class  of  material,  the  mineral  character  of  the  particles  and  the 
gradation  of  sizes  being  much  more  influential  factors  than  the  shape  of  the  particles  of 
aggregate.  The  requirement  of  sharpness  is  based  upon  an  erroneous  idea  of  the  positive 
advantage  gained;  it  often  works  hardship,  or  injury,  or  is  unenforcible,  and  should  be 
omitted  from  specifications. 

The  prevailing  size  of  the  particles  of  aggregates  is  more  important  than  the  shape,  but 


222 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-7 


far  less  important  than  the  gradation  of  sizes  because  of  the  direct  relation  of  the  latter  to 
density  and  strength.  A  comparatively  coarse  sand  is  always  preferable  to  fine  sand.  It 
has  a  smaller  surface  to  be  coated  with  cement  per  unit  of  volume  and  therefore  requi-res 
less  cement  to  produce  a  mortar  of  a  given  strength.  It  is  less  difficult  to  fill  its  interstices 
with  cement  than  in  the  case  of  fine  sand,  and  a  denser  mass  is  usually  secured  with  the 

same  proportion  of  cement. 
1  I  I  n  I  n  A  composition  of  coarse  sand 
and  finer  material  which  will 
serve  to  fill  the  voids  in  the 
coarse  material  will  usually 
excel  either  a  very  coarse  or 
a  very  fine  sand  alone  and 
will  lead  to  economy  of  ce- 
ment. This  is  particularly 
true  when  permeability  is  im- 
portant, a  mortar  made  with 
a  combination  of  coarse  and 


7  28 


90 


Age  in  days 

Fig.  Ah. — Effect  of  size  of  sand  upon  tensile  strength  1:  2  mortar, 
(Tests  of  R.  P.  Davis.) 


360 


sizes  of  particles  are  well 
graded  from  coarse  to  fine, 
being  less  permeable  than  one 
made  with  either  exclusively 

coarse  or  exclusively  fine  material. 

The  relation  between  size  of  sand  and  tensile  strength  of  mortar  is  shown  by  Figs.  4a, 
46,  and  4c  for  1  : 1,  1  : 2,  and  1  : 3  mortars,  respectively.  These  diagrams  are  based  upon 
tests  made  in  the  laboratories  of  the  College  of  Civil  Engineering,  Cornell  University,  by  R.  P. 
Davis  {"  Materials  of  Construc- 
tion," by  A.  P.  Mills,  pp.  152- 
153).  The  various  sands  used 
were  prepared  artificially  by 
separating  a  natural  beach  sand 
of  nearly  pure  quartz  into  eight 
sizes  or  combinations  of  sizes. 
It  is  shown  that  the  sand  which 
passes  the  20-mesh  sieve  and  is 
retained  on  the  30-mesh  sieve 
produces  the  strongest  mortar 
for  all  mixtures  and  at  all  ex- 
cept the  early  ages.  The  sand 
of  all  sizes  finer  than  that  pass- 
ing the  10-mesh  sieye  ranks 
second  for  all  mixtures,  the 
blend  of  equal  amounts  of  10- 
20  and  30-40  sand  ranks  third, 
10-20  sand  ranks  fourth,  and 


180 

Age  in  days 


Fig.  4c. 


•Effect  of  size  of  sand  upon  tensile  strength  1:  3  mortar. 
(Tests  of  R.  P.  Davis.) 


all  finer  sizes  of  sand  rank 
lower  in  the  order  of  their  fine- 
ness. 

7.  Relation  Between  Density  and  Strength. — The  term  density  is  employed  referring  to 
mortars  and  concretes,  meaning  the  ratio  of  the  sum  of  the  absolute  volumes  or  absolutely 
solid  substance  of  the  individual  constituents  contained  in  a  measured  unit  volume  of  mortar 
or  concrete  to  the  measured  unit  volume  of  the  materials  combined  in  the  form  of  mortar  or 


Sec.  6-7] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


223 


concrete,  water  being  neglected  as  an  individual  constituent.  In  other  words  the  density  is  the 
solidity  ratio,  the  ratio  of  the  volume  of  solids  to  the  volume  of  the  mass  of  mortar  or  concrete. 

Many  experimental  studies  have  shown  that  the  strength  of  mortars  and  concretes  is 
directly  proportional  to  the  density  of  the  mixture.  The  density  of  the  mixture  is  dependent 
partly  upon  the  thoroughness  of  mixing,  the  amount  of  water  used  in  gaging,  etc.,  but  is  pri- 
marily dependent  upon  the  gradation  of  sizes  of  the  aggregates.  Aggregates  in  which  the 
relative  amount  of  particles  of  different  sizes  is  such  that  the  particles  of  one  size  just  suffice 


sr 

C300 

s. 


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16  .rf 

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.600     £10      £20     .630      .640      .650      £60     .670      .680      .690      .700      .710      .720      730     .740     .750      760      .770      .780  .790 

Density  of  mortar 

Fig.  5a. — Relation  of  "density"  or  solidity  ratio  of  1:3  mortar  to  tensile  strength.    Age,  13  weeks. 

to  fill  the  voids  of  the  next  larger  size  will  have  a  minimum  void  space,  and  will  therefore  re- 
quire a  minimum  proportion  of  cement  to  secure  a  product  of  given  strength.  The  ideal  con- 
^  Crete  of  maximum  density  would  be  made  with  aggregates  of  this  character,  and,  in  addition, 
would  be  so  proportioned  that  the  mortar  just  suffices  to  coat  the  particles  and  fill  the  voids  of 
the  coarse  aggregate,  and  the  cement  just  suffices  to  coat  the  particles  of  sand  and  fill  its  voids. 
This  ideal  can  of  course  only  be  approximated  in  practice  because  the  larger  particles  of  each 


-  6000 
+- 

^  sooo 

n,  4000 


19° 

^  37 

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^^ 

36  0 

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oll4 

102 

99 

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sr « 

30 

9? 

>Z9 

10 

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139 
Cbl52 

.  109; 
113  "' 

'""'^ 

^o'°o 

120 

O|07 

n  2« 
0  84 
78 

'J 

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 151 

144 

0 

149 

"110 

.590   .600     .610     .620     .630     .640     .650      .660     .670    .680     j690     .700     .710      .7£0     .730      740.     ,750    .760  J70 

Densi+y 

Fig.  56. — Relation  of  "density"  or  solidity  ratio  to  compressive  strength  of  1:3  mortars.    Age,  13  weeks 


aggregate  will  not  closely  approach  each  other.  Owing  to  the  wedging  action  of  the  smaller 
particles  the  larger  stones  and  grains  of  sand  are  forced  apart  so  that  the  density  of  the  mixture 
is  certain  to  be  less  than  that  theoretically  possible.  A  slight  excess  of  mortar  over  that  theo- 
retically required  is  usually  beneficial  to  density  and  strength. 

The  relation  of  density  of  1  :  3  mortars  to  tensile  strength  is  shown  by  Fig.  5a  which  com- 
I  prises  tests  of  157  different  natural  sands  made  by  the  U.  S.  Bureau  of  Standards  {Tech.  Paper 


224 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-8 


58).  The  numbers  on  the  diagram  indicate  the  order  of  fineness  of  the  sands,  No.  1  being  the 
coarsest,  and  No.  157  the  finest.  The  corresponding  relation  of  density  and  compressive 
strength  for  the  same  mortars  is  shown  by  Fig.  55.  Note  that  Figs.  5a  and  56  show  that 
the  densitv  of  mortars  is  in  general  inversely  proportional  to  the  fineness  of  the  sand  used,  the 
finer  the  sand,  the  lower  the  density. 


4200f 
4000 
3800 


3000 
.E  2800 


I 

E,400 

^  leoo 

1000 
600 


 5 

-5 — ' 

y 

5  

y 

Density 

Fig.  G. — Relation  between  density  and  compressive  strength  of  concrete.    (Mix  1:2:4.    Age,  4  weeks.) 

The  relation  of  density  to  compressive  strength  of  1:2:4  concretes  made  with  various 
aggregates  is  shown  by  Fig.  6.  The  diagram  is  based  upon  tests  made  by  the  U.  S.  Bureau  of 
Standards  {Tech.  Paper  58,  Tables  23-26).  The  data  are  not  extensive  enough  to  definitely 
fix  the  relation  sought  because  of  the  inevitable  wide  variation  in  test  results  due  to  variable 


7da  IMo.  3  Mo. 


9  Ma  >£Ma 
Fig.  7. — Effect  of  mica  upon  tensile  strength  of  1  :  3  standard  sand  mortar. 


6  Mo. 

Age 


factors  other  than  density.    That  the  relation  is  a  direct  one,  approximately  that  shown  by 
the  straight  line  upon  the  diagram,  is,  however,  a  justifiable  conclusion.  i 
8.  Effect  of  Mica,  Clay,  and  Loam  in  Aggregates.— The  occurrence  of  mica,  clay,  and^ 
loam  in  aggregates  has  been  explained  in  connection  with  the  consideration  of  mineral 


,Sec.  6-9] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


225 


_  '5  ZO 

Percen+age  of  clay  in  sand 

Fig.  8. — Effect  of  clay  upon  strength  of  1  :  3 
commercial  sand  mortar.  (All  mixtures  artifici- 
ally made  in  the  laboratory.) 


composition  in  Art.  5.  The  very  detrimental  effect  of  mica  upon  the  strength  of  1  :  3 
standard  sand  mortar  is  shown  by  Fig.  7.  The  diagrams  are  based  upon  tests  made  by  W. 
N.  WilHs  {Eng.  News,  vol.  54,  p.  145).  The  loss  in  strength  amounts  to  15  to  25%  vvith 
2H%  of  mica  in  the  sand,  25  to  45%  with  5%,  of  mica,  and  becomes  still  more  marked  as 
the  proportion  of  mica  is  increased.  Mr.  Willis  also  observed  that  increasing  the  proportion 
of  mica  increased  the  voids  in  the  sand  from  37%  with  no  mica,  to  67%  with  20%  of  mica. 
The  weight  was  at  the  same  time  lowered  20%o,  and  the  amount  of  water  required  in  gaging 
the  mortar  was  3  times  that  required  in  gaging  ^ 
mortars  free  from  mica. 

The  effect  of  clay  in  sands  is  dependent  upon 
its  state  of  subdivision  and  the  uniformity  with 
which  it  is  distributed  through  the  sand.  In  most 
laboratory  tests  the  addition  of  clay  in  moderate 
amounts  has  been  found  to  be  beneficial.  Typical 
results  of  laboratory  tests  are  exhibited  by  Fig.  8 
which  is  derived  from  tests  made  by  F.  L.  Koman 
(Eng.  &  Cont.,  vol.  43,  p.  403).  With  the  materials 
here  used  the  maximum  increase  in  strength  due 
to  clay  additions  was  observed  to  be  about  20%,  and  was  secured  with  additions  of  10  to  15% 
of  clay.  Similar  tests  made  by  L,  T.  B.  Southwick  and  G.  A.  Wellman  {Eng.  Rec,  vol.  63, 
p.  332)  show  that  maximum  strengths  of  1  :  13-2,  1:3,  1  :  4)^,  and  1  :  6  mortar  mixtures  are 
secured  with  3%,  10%,  15%,,  and  20%  of  clay,  respectively.  These  laboratory  results  do  not 
prove  that  similar  percentages  of  clay  will  be  beneficial  or  harmless  in  natiual  clayey  sands. 
The  manner  of  distribution  and  degree  of  fineness  of  the  clay  in  concrete  sands  will  be  the  de- 
termining factors,  and  the  amount  permissible  will  not  usually  approach  the  above  limits. 
Lumps  of  clay  do  not  become  broken  up  in  concrete  mixing,  and  should  be  carefully  excluded 
from  aggregates. 

Loam,  in  the  usual  acceptance  of  the  term,  is  earth  which  is  made  up  of  vegetable  mold 
together  with  clay  or  sand  or  both.    It  is  extremely  injurious  to  mortars  and  concretes  because 

of  its  content  of  organic  matter.  Fig.  9,  derived 
from  the  series  of  tests  of  F.  L.  Roman  above  re- 
ferred to,  shows  the  effect  of  loam  and  organic 
matter  in  sand  upon  strength.  From  those  tests 
it  appears  that  5%  of  this  loam  (about  1.5% 
organic  matter  in  the  sand)  reduces  the  strength 
of  the  mortar  about  20%,  and  other  amounts  are 
nearly  proportionally  detrimental.  Organic 
matter  naturally  occurring  in  sands  is  frequently 
Percentage  of  loam  in  sand  found  detrimental  to  an  even  greater  extent  than 

Percentage  of  organic  matter  in  sand  Caoprox.)  is  indicated  by  these  tests,  wherein  the  organic 
Fk;.  O.-Effect  of  organic^loam  upon  strength  of  1:3  j.^^^^  -^^  ^j^^  ^j^^^p^  powdor  was  mixed  with 

the  sand.  Organic  matter  not  infre(iuently  covers 
sand  particles  with  a  film  which  is  not  easily  perceptible,  but  which  tremendously  retards  the 
normal  rate  of  hardening  and  gaining  strength.  An  investigation  made  by  Sanford  E.  Thomp- 
son {Trans.  Am.  Soc.C.E.,  vol.  65)  led  to  the  conclusion  that  organic  matter  constituting  over 
10%  of  the  silt  and  at  the  same  time  over  0.1%  of  the  sand  is  distinctly. injurious. 

9.  Effect  of  Consistency. — The  important  relation  of  consistency  to  the  strength  of  mortar 
and  concrete  is  shown  by  Figs.  10  and  11.  The  amount  of  water  is  expressed  as  a  percentage 
of  the  total  dry  weight  of  aggregates  and  includes  any  moisture  carried  by  the  sand  or  coarse 
aggregate  in  its  natural  condition.  These  diagrams  are  based  upon  tests  made  in  the  labora- 
tories of  the  Sheffield  Scientific  School  under  the  direction  of  Prof.  Barney  {Eng.  and  Cont., 
vol.  42,  p.  244). 
15 


226 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-9 


These  tests  show  that  a  quite  definite  percentage  of  water  is  required  to  produce  a  mortar 
or  concrete  of  maximum  strength  with  given  materials.  For  the  particular  materials  used  in 
this  case  the  maximum  1  :  2  mortar  strength  was  attained  with  about  15.6%  of  water,  and  the 
maximum  strength  of  1:2:4  concrete  with  about  8.4%  of  water.  For  other  materials  or 
other  mixes  these  consistencies  for  maximum  strength  will  not  remain  the  same,  but  for  any 


\ 

N 

V 

< 

y 

14         15  lb  17  18  19  20  21 

Percentage  of  wafer  based  on  fotal  dry  weight  of 
cement  and  sand 
Fig.  10. — Effect  of  consistency  upon  strength  of  1  :  2  mortar. 


mixture  of  given  materials  there  is  a  critical  consistency  which  will  be  productive  of  higher 
strength  than  any  drier  or  wetter  consistency.  This  fact  is  particularly  important  in  view  of 
the  common  practice  of  using  extremely  wet  concrete  mixes  in  order  to  be  able  to  deliver  the 
concrete  on  the  work  cheaply  and  expeditiously  by  the  use  of  chuting  devices  between  mixer 
and  forms.    The  fact  should  be  understood  that  such  wet  mixtures  may  be  used  only  with  a 


considerable  sacrifice  in  strength  of  the  concrete  placed.  On  the  other  hand,  these  tests  indicate 
that  nothing  is  gained  by  making  a  concrete  so  dry  that  it  must  be  rammed  or  tamped  in  place 
instead  of  being  puddled.  Concretes  containing  8  to  9%  of  water  are  of  a  sufficiently  mushy 
consistency  to  be  readily  puddled,  but  from  12  to  15%  of  water,  or  even  more,  is  commonly 
used  to  produce  the  fluid  consistency  desirable  for  chute  or  spout  delivery. 


Sec.  5-10] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


227 


For  harmful  effects  from  the  use  of  excess  water  and  for  suggested  procedures,  see  chapter 
on  ''Water"  in  Sect.  1. 

10.  Compressive  and  Tensile  Strengths  Compared. — The  compressive  and  tensile  strengths 
of  the  same  mortar  mixture  may  be  contrasted  by  a  comparison  of  the  diagrams  of  Figs.  1 
and  2,  pages  217  and  218.  A  direct  comparison  for  1:3  standard  sand  mortar  is  afforded 
by  Fig.  12  which  is  based  upon  tests  of  seven  brands  of  cement  made  in  the  Structural  Materials 
Laboratory  formerly  maintainedat  St.  Louis,  Mo.,  by  the  U.  S.  Geological  Survey  (U.  S.  Geol.  Surv. 


360 


Age  in  days 


Fig.  12. 


■Ratio  of  compressive  to  tensile  strength  of  1 
of  30  tests  of  one  brand. 


3  standard  Portland  cement  mortar. 
Curve  is  average  of  7  brands.) 


(Each  result  is  average 


Bull.  331).  The  specimens  used  were  standard  tension  briquettes  and  2-in.  compression  cubes. 
It  is  shown  by  the  diagram  that  the  average  value  of  the  ratio  of  compressive  strength  to  tensile 
strength  is  far  from  being  constant  as  the  age  increases  because  of  the  relatively  more  rapid 
rate  of  gain  in  tensile  strength  during  the  first  few  weeks  and  the  very  slight  gain  or  actual 
retrogression  which  characterizes  the  tensile  strength  after  the  first  6  months.    The  average 


160      200  240 

Age  in  days 

Fig.  13. — Ratio  of  compressive  to  tensile  strength  of  1  :  3  mortar  using  blend  of  7  Portland  cements  and  22  com- 
mercial sands. 


value  of  the  ratio  for  all  cements  is  about  6  between  the  1-month  and  the  6-month  periods, 
but  the  individual  brands  of  cement  show  variations  of  from  15  to  40%  from  this  average. 

A  similar  series  of  tests,  made  under  the  same  auspices,  with  a  blend  of  the  above  7  brands 
of  cement  and  22  commercial  sands  in  1  : 3  mortars  has  been  made  the  basis  of  the  diagrams  of 
Fig.  13.  Because  of  the  very  wide  variations  shown  by  the  22  different  mortars,  only  the 
average  for  all  the  mortars,  the  average  for  the  5  mortars  showing  the  highest  value  of  the 


228 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec,  5-10 


ratio  and  the  average  for  the  5  mortars  showing  the  lowest  value  of  the  ratio  are  plotted.  The 
same  variation  in  the  ratio  of  compressive  to  tensile  strength  with  age  shown  by  standard  sand 
mortars  is  exhibited  by  the  commercial  sand  mortars. 

An  inspection  of  Figs.  12  and  13  will  show  that  the  tensile  strength  of  mortars  is  not  more 
than  a  very  approximate  indication  of  the  probable  compressive  strength  of  similar  mortars 
with  the  same  cement,  and  even  then  the  age,  the  mixture,  and  the  sand  used  are  sources  of 
variation  which  must  be  taken  account  of. 

The  tensile  strength  of  concrete  is  a  property  of  little  importance  because,  being  low  in 
comparison  with  the  compressive  strength,  concrete  is  practically  never  designed  to  carry 
tensile  stress.    When  concrete  is  used  in  situations  involving  tensile  stress  it  is  more  economical 


Tensile  and  Compressive  Strengths  of  Concrete 


Character  of  coarse 
aggregate  and  mix 


Age,  months  (approx.) 


Tensile 
tests 


Compression 
tests 


Compressive 
strength 
(lb.  per  sq.  in.) 


Tensile 
strength 
(lb.  per  sq.  in.) 


Ratio 
tensile  strength 


compressive  strength 


Limestone  1  :2:4.. 


Sandstone  1  : 2  : 4 


Sandstone  1  :2}4  -5. 


Average . 


Average . 


Average . 


2,206 
2,708 
2,500 


2,505 


1,069 
1,375 
1,417 
1,722 
2,000 
2,139 


1,620 


1,028 
1,639 
972 
889 
1,042 
2,083 
1,472 
1,889 
1,639 

1,406 


278 
308 
253 
306 
264 
257 

278 


149 
142 
133 
178 
158 
128 
153 
150 
161 


150 


121 
114 
106 
158 
114 
97 
179 
129 
139 

129 


11.1% 


9.3% 


9.1% 


Sec.  6-11] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


229 


to  use  steel  reinforcement  than  to  use  the  very  large  sections  which  would  be  required  if  the 
concrete  were  depended  upon  to  carry  tension. 

An  indication  of  the  comparative  strength  of  concrete  in  tension  and  compression  is  afforded 
by  the  table  shown  on  page  228.  These  data  were  derived  in  tests  made  by  the  writer  in  the 
laboratories  of  the  College  of  Civil  Engineering,  Cornell  University.  The  concrete  was 
mixed  and  the  specimens  molded  in  the  field. 

Note  that  the  values  of  the  ratio  of  tensile  to  compressive  strength  in  this  table  would 
have  been  somewhat  lower  had  the  specimens  been  tested  in  compression  at  the  same  age  they 
were  in  tension. 

11.  Strength  of  Plain  Concrete  Columns. — The  strength  of  plain  concrete  columns,  as 
determined  by  tests  of  laboratory  specimens  whose  dimensions  are  comparable  with  those  of 
columns  used  in  structures,  is  usually  not  less  than  75  nor  more  than  90%  of  the  strength  of 
cubes  of  the  same  concrete,  the  column  length  not  exceeding  10  to  12  diameters. 

A  number  of  series  of  tests  of  plain  concrete  columns  are  tabulated  below  and  on  page 
230.  The  strength  of  cubes  of  similar  concrete  is  indicated  where  data  from  comparable  tests 
are  available. 

Strength  of  Plain  Concrete  Columns 


Watertown  Arsenal  Tests  ^ 


Mixture  and 
character  of 
coarse  aggregate 

Age, 
months 

Com- 
pressive 
strength 
(lb  per 
sq.  in.) 

Cross- 
section, 

inches 
(approx.) 

Length, 
feet 

1 

1 

Mortar 

6 

5,011  + 

12 

5  X  12 

5 

8 

1 

2 

Mortar 

6 

3,652 

12 

5  X  12 

5 

8 

1 

2 

Mortar 

6 

2,488 

12 

5  X  12 

5 

8 

1 

3 

•  Mortar 

6 

2,062 

12 

5  X  12 

5 

8 

1 

3 

Mortar 

6 

2,692 

12 

5  X  12 

5 

8 

1 

4 

Mortar 

6 

1,564 

12 

5  X12 

5 

8 

1 

4 

Mortar 

6 

1,471 

12 

5  X  12 

5 

8 

1 

5 

Mortar 

6 

1,038 

12 

5  X  12 

5 

8 

1 

5 

Mortar 

6 

1,082 

12 

5  X12 

5 

8 

1 

1 

:  2  (Pebbles) 

5 

1,525 

12 

5  X  12 

5 

8 

1 

1 

:2  (Pebbles) 

8 

1,720 

12 

5  X  12 

5 

8 

1 

1 

:2  (Trap  rock) 

5 

3,900 

12 

5  X12 

5 

8 

1 

2 

:3  (Pebbles) 

8 

1,769 

12 

5  X  12 

5 

8 

1 

2 

:4  (Pebbles) 

3)^ 

1,710 

12 

5  X12 

5 

8 

1 

2 

:4  (Pebbles) 

5 

1,506 

12 

5  X  12 

5 

8 

1 

2 

:  4  (Trap  rock) 

5 

1,750 

12 

5  X12 

5 

8 

1 

2 

:4  (Trap  rock) 

6 

1,990 

12 

5  X  12 

5 

8 

1 

2 

:5  (Pebbles) 

3 

1,100 

12 

5  X  12 

5 

8 

1 

3 

:6  (Pebbles) 

5 

700 

12 

5  X  12 

5 

8 

1 

3 

:6  (Pebbles) 

8 

462 

12 

5  X  12 

5 

8 

1 

3 

:  6  (Trap  rock) 

4 

1,350 

12 

5  X  12 

5 

8 

1 

2 

:4  (Cinders) 

871 

12 

5  X  12 

5 

8 

1 

3 

:6  (Cinders) 

5 

1,060 

12 

5  X12 

5 

8 

»  "Tests  of  Metals,"  1904,  1905. 


230  ^  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  5-12 


University  of  Illinois  Tests^ 


Ratio 
col.  strength 

Mixture 
(coarse 

aggregate, 
crushed 

limestone) 

Compressive 
strength  of 
columns 
(lb.  per  sq.  in.) 

Age 
columns, 
months 
(approx.) 

Compressive 
strength  of 
cubes 
(lb.  per  sq.  in.) 

Age 
cubes, 
months 
(approx.) 

Cross- 
section, 

inches 
(approx.) 

Length, 
feet 

cube  strength 

(approx.) 

1:1>^:3 
1:1M:3 

2,120 
2,480 

2 

2 

12  in.  cyl. 
12  in.  cyl. 

10 

95.3 

2 

2,600 

2 

10 

69.9 

1:2:3% 

1,710 

2 

2,443 

2 

12  X  12 

12 

1:2:3% 
1:2:3% 

2,004 
1,610 
1,709 
1,189 

2 

9X9 

12 

2 

12  X  12 
12  X  12 

12 

1:2:3% 

2 

12 

6 

60.5 

1:2:3% 

2 

1,962 

.2 

12  X  12 

1:2:3% 
1:2:3% 
1:2:3% 
1:2:4 

1,079 
2,650 
2,770 
1,165 
2,000 
2,210 
1,590 

2 

9X9 
12  X  12 

6 

12 

12 

16 

12  X  12 

12 

2 

12  in.  cyl. 
12  in.  cyl. 
12  in.  cyl. 
12  in.  cyl. 

10 

1:2:4 

2 

10 

1:2:4 

2 

10 

78.1 

1:2:4 

2 

2,035 

2 

10 

1:2:4 

1,945 
1,460 

2 

12  in.  cyl. 
12  in.  cyl. 

10 

78.3 

1:2:4 

2 

1,865 

2 

10 

1:2:4 

1,810 
1,925 

2 

12  in.  cyl. 
12  in.  cyl. 

10 

80.4 

1:2:4 

6 

2,390 

6 

10 

99.7 

1:2:4 

1,845 

6 

1,850 

6 

12  in.  cyl. 

10 

99.7 

1:2:4 

1,770 

6 

1,775 

6 

12  in.  cyl. 

10 

99.8 

1:2:4 

2,680 

6 

2,685 

6 

12  in.  cyl. 

10 

85.3 

1:2:4 

2,160 

6 

2,530 

6 

12  in.  cyl. 

10 

74.6 

1:2:4 

1,770 

6 

2,370 

6 

12  in.  cyl. 

10 

1:3:6 

955 

2 

12  in.  cyl. 
12  in.  cyl. 
12  in.  cyl. 
12  in.  cyl. 

10 

1:3:6 

1,110 
575 

2 

10 

1:4:8 

2 

10 

1:4:8 

575 

2 

10 



TJniversi  ty 

OF  Wisconsin  Tests^ 

84.0 

1:2:4 

2,040 

2 

2,427 

2 

12  X  12 

10 

88.0 

1:2:4 

2,110 

2 

2,395 

2 

12  X  12 

10 

91.7 

1:2:4 

2,055 

2 

2,240 

2 

12  X  12 

10 

88.1 

1:2:4 

2,080 

2 

2,360 

2 

12  X  12 

10 

1  Bulls.  10  and  20  of  the  Univ.  of  111.  Eng.  Exper.  Station. 

2  Data  from  tests  of  cubes  made  at  ages  which  do  not  correspond  even  approximately  to  the  age  of  the  column 
made  from  the  same  concrete  have  been  omitted. 

3  Bull.  300. 


12.  Effect  of  Method  of  Mixing. — The  method  of  mixing  mortars  and  concretes  may- 
vary  with  respect  to:  (1)  amount  of  water  used;  (2)  duration  of  mixing  operation;  and  (3) 
detail  method  of  manipulation.  The  effect  of  variation  in  the  amount  of  water  used  is  con- 
sidered in  Art.  9.  The  effect  of  the  duration  of  the  mixing  operation  is  shown  by  Fig.  14 
which  is  based  upon  tests  by  Prof.  Scofield  of  Purdue  University  {Eng.  and  Cont.,  Jan.  17,  1915). 
All  of  the  concrete  was  mixed  in  a  Chicago  Cube  Mixer  of  23'^-cu.  ft.  capacity,  run  at  the  rate 
of  26  revolutions  per  min.  These  concretes  are  all  much  stronger  than  the  average  com- 
mercial concrete  but  this  fact  does  not  affect  the  significance  of  the  test  results.  It  appears 
that  with  the  particular  materials  used  a  very  decided  advantage  is  gained  by  operating  this 
mixer  much  longer  than  the  usual  period  of  mixing.  The  actual  time  of  mixing  most  advan- 
tageous to  the  quality  of  concrete  produced  under  given  conditions  will  probably  vary  greatly 


Sec.  6-13] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


231 


with  different  materials  and  with  different  mixers.  It  is  very  probable,  however,  that  the 
average  concrete  used  in  every  day  practice  would  be  considerably  improved  in  quality,  if  it 
were  mixed  for  a  longer  period.  This  is  certainly  true  of  concretes  which  are  turned  out  at  a 
rate  of  a  batch  per  minute  as  is  sometimes  the  case.  A  distinct  advantage  is  gained  by  mixing 
beyond  the  point  which  produces  a  batch  of  even  color.  The  mass  becomes  more  viscous; 
there  is  less  danger  of  separation  of  fine  and  coarse  material;  for  a  given  water  content  it  appears 
to  possess  a  wetter  consistency  and  flows  better  in  transporting  by  chute  and  in  depositing  in 
the  forms;  and  it  forms  a  concrete  of  greater  density,  less  permeability,  and  greater  strength. 

It  cannot  be  said  that  machine-mixing  will  invariably  produce  better  concrete  than  hand- 
mixing,  but  for  all  except  the  smallest  work  it  is  less  expensive  and  is,  therefore,  generally  pre- 
ferred. Hand-mixing  is  more  apt  to  be  severely  slighted  than  machine-mixing  because  of  the 
heavy  labor  involved  and  the  comparatively  long  time  required. 


'cubes^  r 


Fig.  14. 


20  22   24  £6  28  30 

Total  time  of  mixing  in  minutes 

-Effect  of  time  of  mixing  upon  strength  of  concrete. 


In  comparative  tests  of  concretes  made  with  the  same  materials,  weighed  and  molded  by 
employees  of  the  laboratory  of  the  U.  S.  Bureau  of  Standards,  but  mixed  in  the  field  by  three 
different  contractors,  each  being  permitted  to  use  his  own  methods  of  mixing,  both  hand  and 
machine,  all  conditions  being  the  same  except  the  actual  mixing  of  the  materials,  variations 
of  as  much  as  70%  in  compressive  strength  were  obtained  {Tech.  Paper  58,  U.  S.  Bureau  of 
Standards). 

13.  Effect  of  Method  of  Placing.— The  importance  of  the  effect  of  the  methods  of  manipula- 
ting and  molding  laboratory  specimens  of  mortar  upon  the  qualities  of  the  specimens  shown 
by  tests  has  been  discussed  in  Art.  2.  The  same  factors  are  operative  in  the  case  of  molding 
laboratory  specimens  of  concrete,  and  their  disturbing  effect  becomes  even  more  pronounced 
when  the  work  is  done  in  the  field.  Experimental  data  are  lacking  which  might  show  the  extent 
of  the  effect  of  variations  in  molding  methods,  but  an  indication  of  the  importance  of  this  fac- 
tor is  afforded  by  any  series  of  tests  of  mortar  or  concrete  specimens  made  from  the  same  batch 
of  material  and  stored  and  tested  in  an  identical  manner.  A  number  of  such  apparently  iden- 
tical specimens  may  perhaps  vary  in  strength  less  than  5%  if  made  by  an  experienced  operator, 
but  a  second  equally-experienced  operator  using  the  same  materials  and  the  same  general 


232 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5^14 


methods  will  often  obtain  results  which  are  not  within  20%  of  those  of  the  first  man.  This 
deviation  must  be  attributed  primarily  to  slight  differences  in  detail  methods  of  molding  the 
specimens. 

When  special  methods  of  handling  the  materials  are  considered,  only  very  scanty  compara- 
tive data  are  available.  The  following  tests  reported  by  R.  E.  Goodwin  of  the  Materials 
Testing  Division  of  the  New  York  Public  Service  Commission  indicate  that  concrete  placed  in 
mass  may  possess  greater  strength  than  when  it  is  cast  in  molds  of  the  size  ordinarily  use<l  • 
{Eng.  News,  Feb.  18,  1915).  Several  pieces  of  concrete  were  cut  from  existing  subway  struc- 
tures at  places  designated  before  the  concrete  was  placed  in  the  forms.  While  the  concrete 
was  being  poured  in  the  forms,  samples  from  the  same  batches  were  cast  in  molds.  A  portion 
of  the  specimens  thus  molded  were  stored  in  moist  sand  on  the  work,  while  others  were  stored 
in  the  laboratory  moist  room.  In  addition  similar  specimens  were  made  from  the  same  mate- 
rials brought  from  the  work  and  mixed  and  molded  in  the  laboratory.  The  pieces  of  concrete 
taken  from  the  work  were  cut  from  various  portions  of  12-in.  walls  at  the  age  of  2  months 
and  after  being  rough-dressed  were  polished  smooth  to  exact  dimensions.  All  tests  were  made 
at  the  age  of  90  days ;  the  concrete  was  a  1 : 2 :  4  mixture ;  and  all  specimens  were  6  by  6  by  12  in. 


Compressive  Strength  of  Field  and  Test-sample  Concrete 


Conorote  made  on  the  work 
(All  in  one  line  are  from  the  same  batch) 

Concrete  made  in  the  laboratory 
(Samples  of  same  materials  from  the  work  used) 

Specimens 
cut  from 
12-in.  wall 

Specimens 
poured  in 
molds  and 
stored  on 
the  work 

Specimens 
poured  in 

molds  aiul 
stored  in 

moist  room 

Consistency 
of  batch 

Specimens 

made  in 
laboratory 
and  stored 
on  the  work 

Specimens 

made  in 
laboratory 
and  stored 
in  moist  room 

Consistency 
of  batch 

(4)  3,095 

(4)  2,410 
(4)  2,415 
(4)  2,760 

(4)  2,880 



(2)  2,585 
(4)  2,020 

(4)  2,870 
(4)  1,720 

(3)  2,060 

(4)  1,775 

wet 
very  wet 

wet 
very  wet 

(4)  2,135 
(4)  2,225 
(4)  1,980 
(4)  1,900 

(4)  2,080 
(4)  1,930 
(4)  1,705 
(4)  1,910 

wet 
wet 
wet 
wet 

Average 
(16)  2,670 

Average 
(10)  2,480 

Average 
(15)  2,110 

Average 
(16)  2,060 

Average 
(16)  1,910 

(Figures  in  parentheses  indicate  number  of  specimens  averaged  for  each  result.) 


The  quality  of  concrete  deposited  under  water  is  usually  considered  to  be  decidedly  in- 
ferior to  that  of  concrete  placed  under  normal  conditions  where  water  is  not  encountered. 
This  is  doubtless  true  if  the  material  is  permitted  to  fall  freely  through  the  water,  or  if  the  cir- 
cumstances are  such  that  the  formation  of  laitance  is  facilitated.  That  first  quality  concrete 
can  be  made  in  subaqueous  construction  was  shown,  however,  during  the  construction  of  the 
Detroit  River  Tunnel.  In  this  case  concrete  of  1:3:6  mix  was  deposited  at  a  depth  of  60 
to  80  ft.  below  the  water  surface  through  12-in.  tremies.  Test  cores  cut  from  the  tremie- 
deposited  concrete  by  a  6-in.  shot  drill  showed  a  compressive  strength  of  from  2740  to  4000  lb. 
per  sq.  in.  1  year  after  deposition.  Other  specimens  in  the  shape  of  roughly-cut  6-in.  cubes  of 
1:2:4  tremie-deposited  concrete  developed  a  strength  of  from  1800  to  3040  lb.  per  sq.  in., 
and  it  was  believed  that  their  strength  was  impaired  by  the  operation  of  cutting  {Trans.  Am. 
Soc.  C.  E.,  vol.  74,  p.  338).  The  matter  of  the  pressure  under  which  this  concrete  was  deposited 
probably  has  some  bearing  upon  the  quality,  for  in  this  case  the  hydrostatic  pressure  at  the 
bottom  of  a  tremie  tube  was  about  30  lb.  per  sq.  in. 

14.  Effect  of  Regaging. — The  Joint  Committee  on  Concrete  and  Reinforced  Concrete 
recommends  that  "the  remixing  of  mortar  or  concrete  that  has  partly  set  should  not  be  per- 
mitted" (Proc.  Am.  Soc.  C.  E..  Dec,  1916,  p.  1673),  and  most  engineers  specify  that  mortar  or 


Sec.  5-14] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


233 


concrete  shall  be  used  within  1  hr.  or  even  ^  hr.  after  it  is  gaged.  It  is  undoubtedly  gonerallv 
advisable  on  construction  work  to  adhere  to  the  practice  of  not  permitting  regaging  and  it  is 
particularly  important  that  concrete  which  has  stood  undisturbed  for  some  time  be  not  per- 
mitted to  get  into  the  form  in     ^   _ 

GAGING  UPON    STRENGTH   OF  MoRTARS  Ag 

4  Months 
Office  of  Public  Roads  Tests  ^ 


Effect  of  Regaging 


its  non-plastic  condition,  but 
the  harmful  effect  of  regaging 
is  often  less  pronounced  than 
is  commonly  believed,  and 
exceptions  to  the  general  rule 
may  under  certain  circum- 
stances properly  be  made. 

The  data  on  this  page 
show  that  the  strengthof  Port- 
land-cement mortars  is  not  in- 
juriously affected  by  allowing 
them  to  stand  for  periods  of 
from  1  to  3  hr.,  and  then  re- 
gaging and  molding.  In  fact 
the  delayed  treatment  ap- 
pears slightly  beneficial  owing 
probably  to  the  increased 
amount  of  working  given  the 
material.  This  effect  is  one 
that  has  been  shown  with  singular  unanimity  by  a  considerable  number  of  experimenters  using 
all  classes  of  cement.  One  fact  brought  out  particularly  by  the  tests  of  Mr.  Sabin  is  that  the 
material  regaged  should  not  merely  be  remixed,  but  should  have  sufficient  water  added  so 
that  the  original  consistency  will  be  restored  after  regaging. 


Mix 

Mortar 
made  up 
into  briquettes 
immediately 
after  mixing 

Mortar   broken  up 
after  initial  set  and 
made  into  bricjuettes. 
W^ater  added  to 
restore  normal 
consistency 

^lortar  l)roken  up 
after  final  set  and 
made  into  briciuettes. 

restore  normal 
consistency 

Tensile  strength 

in  lb.  per  sq.  in. 

Neat 

657 

653 

540 

1:1 

628 

678 

563 

1:2 

504 

554 

499 

1:3 

407 

326 

353 

Initial  set 

1  hr.  42  min. 

Final  set 

7  hr.  15  min. 

Effect  of  Regaging  upon  Tensile  Strength  of  1 : 2  Mortar — Age  1  Year 

Tests  of  L.  C.  Sabin2 


Molded 
imme- 
diately 

Stood 
1  hr., 

regaged 
and 

molded 

Stood  3  hr., 
regaged 

each  hour 
and  then 
molded 

stood  3  hr., 
regaged  each  hour 
with  water  added 
to  restore  original 
consistency  and 
then  molded 

Stood  5  hr., 
regaged 
each  hour 
and  then 
molded 

Stood  5  hr., 
reiaged  each  hour 
with  water  added 
to  restore  original 
consistency  and 
then  molded 

Stood 
5  hr., 
regaged 
and  then 
molded 

Stood 

5  hr. 
regaged 
and  then 
molded 

No  water 

579 
Water  a 
554 

added 

565 
dded  to 
579 

in  regaging 

569 
restore  ori 

ginal  consistency 
627 

570 

624 

568 

560 

Natural  cements  and  quick-setting  Portland  cements  appear  to  be  less  capable  of  showing 
an  undiminished  strength  after  regaging  than  do  normal  or  slow-setting  Portlands. 

The  most  pronounced  effect  of  regaging  of  mortars  and  concretes  is  in  the  direction  of 
retarding  the  set  and  delaying  the  hardening,  thus  reducing  the  strength  at  early  periods. 
Candlot  (''Ciments  et  Chaux  Hydrauliques, "  1898,  p.  358)  found  that  mortars  regaged  after 
attaining  their  final  set  all  required  8  to  10  hr.  to  set  regardless  of  the  rapidity  or  slowness  with 
which  the  mortar  originally  set.    This  effect  of  regaging  alone  will  often  be  a  sufficient  cause 

1  U.  S.  Department  of  Agriculture,  Bull.  235. 
-  "Cement  and  Concrete,"  p.  253. 


234 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-15 


for  prohibiting  regaged  mortar  or  concrete  on  construction  work  requiring  an  early  assumption 
of  load. 

Candlot  also  found  that  regaging  had  a  very  detrimental  effect  upon  adhesive  strength  of 
mortars  to  stone,  the  loss  being  often  50%.  Sabin  ("Cement  and  Concrete,"  p.  290)  also 
found  that  regaging  was  detrimental  to  adhesive  strength  of  mortar  to  stone,  the  effect  being 
more  pronounced  with  rich  mortars.  Earnest  McCullough  {Eng.  News,  Jan.  11,  1906)  found 
that  regaged  mortars  showed  a  loss  in  power  to  adhere  to  old  mortar  or  concrete,  but  found  that 
the  addition  of  10  to  12%  of  lime  to  the  regaged  mortar  produced  a  material  whose  adhesive 
strength  considerably  excelled  that  of  mortar  placed  when  freshly  mixed. 

15.  Effect  of  Curing  Conditions. — The  principal  variations  in  curing  conditions  which 
affect  the  process  of  hardening  and  gaining  strength  of  mortars  and  concretes  are:  (1)  varia- 
tions of  moisture  conditions,  and  (2)  variations  of  temperature. 

The  effect  of  different  conditions  of  exposure  to  moisture  is  shown  by  the  following  data 
based  upon  tests  made  at  the  U.  S.  Bureau  of  Standards  {Tech.  Paper  58).  The  test  specimens 
were  8  by  16-in.  cylinders.. 


Effect  of  Variation  of  Moisture  Condition  in  Curing  Period 
Tests  of  Bureau  of  Standards^ 


Alix,  class  of  concrete,  and  curing  conclitions 

Compressive  strength  (lb.  per  sq.  in.) 

1  week 

4  weeks 

13  weeks 

26  weeks 

52  weeks 

1 : 6  gravel  (quaking) :   In  damp  closet  entire  period. 

1,898 

1,968 

2,172 

2,400 

1:6  gravel  (quaking):    4  weeks  in  damp  closet, 
then  removed. 

1,648 

1,825 

2,063 

2,220 

1:2:4  trap  rock   (quaking) :    Immersed  immedi- 
ately after  molding. 

2,851 

.3,570  + 

4,094  + 

3,956 
4,247  + 

3,978  + 

3,978  + 

4,100 

8  weeks  in  damp  closet,  then  immersed  

3,190 

3,457 

3,389 

1:2:4  gravel  (mushy) :    Sprinkled  daily  for  1  week, 
then  stored  indoors  in  dry  room. 

481 

1,104 

1,469 

4  weeks  in  damp  room,  then  placed  in  open,  exposed 
to  weather. 

1,834 

2,500 

1:2:4  gravel  (quaking) :  In  damp  closet  entire  period 

2,612 
2,085 

These  tests  indicate:  (1)  that  concrete  specimens  cured  in  the  moist  air  of  the  damp  closet 
until  tested  become  somewhat  stronger  than  ones  immersed  in  water  after  a  longer  or  shorter 
period  in  the  damp  closet,  or  ones  immersed  immediately  after  molding.  (This  may  be  due  in 
part  at  least  to  the  fact  that  the  immersed  specimens  were  tested  while  still  holding  much  more 
water  than  the  damp  closet  specimens.)  (2)  Specimens  cured  in  the  damp  closet  are  con- 
siderably stronger  than  ones  cured  in  the  comparatively  dry  air  of  the  laboratory,  even  though 


1  Tech.  Paper  58. 


Sec.  5^15] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


235 


the  latter  were  sprinkled  daily  for  the  first  week.  (3)  Specimens  gained  strength  in  the  open 
air  exposed  to  the  weather  to  a  considerably  greater  extent  than  did  others  cured  indoors  in  a 
comparatively  dry  room,  but  not  to  as  great  an  extent  as  ones  stored  in  the  damp  closet. 

The  relation  between  the  mean  temperature  encountered  during  the  curing  period  and  the 
strength  of  1:2:4  concrete  is  shown  by  the  diagram  of  Fig.  15.  This  diagram  was  con- 
structed by  A.  B.  Mc Daniel  as  a  summary  of 
the  results  of  tests  made  at  the  Engineering  Ex- 
periment Station  of  the  University  of  Illinois  {Bull. 
81).  The  concrete  used  was  a  1:2:4  mixture  by 
weight  (1:2.2:3.6  by  volume),  the  coarse  aggre- 
gate being  crushed  limestone.  A  portion  of  the 
specimens  were  6  by  6-in.  cylinders,  some  were 
6-in.  cubes  and  the  balance  were  8  by  16-in. 
cylinders.  All  values  were  reduced  to  an  equiva- 
lent value  for  8  by  16-in.  cylinders,  however. 
Ten  sets  of  specimens  were  made,  and  each  set  was 
subjected  to  a  different  mean  temperature  through- 
out the  period  of  curing.  The  mean  temperatures 
employed  were  26.5°,  27.1°,  30°,  34.7°,  35.5°, 
48.5°,  68°,  71.8°,  72.8°,  and  95.6°  respectively. 
The  marked  effect  of  low  temperatures  in  at  least 
delaying,  if  not  permanently  preventing,  the 
hardening  process  is  excellently  shown  by  the 

diagram  of  Fig.  15.    The  diagram  represents  the  results  obtained  with  only  one  mixture  of 
one  class  of  materials,  but  the  relative  effect  of  various  temperatures  on  other  concretes 
may  be  expected  to  at  least  approximate  the  relation  found  for  this  concrete,  and  the  dia- 
gram should  furnish  sugges- 

Effect  of  Curing  1  : 4  Mortar  under  Steam  Pressure     tive  information  useful  in  es- 
(8  X  16-in.  cylinders) 
Tests  of  Bureau  of  Standards^ 


20  ZZ  24  26  28 


Fia.  15. — Effect  of  temperature  of  curing  upon 
compressive  strength  of  1:2:4  concrete.  (The 
temperatures  given  are  the  mean  temperatures 
encountered  during  the  period  of  curing.) 


timating  the  strength  of  con- 
crete cured  at  abnormal  tem- 
peratures. 

Certain  classes  of  con- 
crete products  such  as  tiles 
and  blocks  are  subjected  to 
an  accelerated  hardening 
treatment  by  the  use  of  steam. 
The  effect  of  such  treatment 
upon  strength  is  shown  by 
data  given  on  this  page  from 
tests  of  the  U.  S.  Bureau  of 
Standards  {Tech.  Paper  58). 

The  results  show  that  up 
to  80  lb.  per  sq.  in.  gage  pres- 
sure, steam  has  an  accelerat- 
ing action  upon  the  harden- 
ing of  cement  mortar,  and 

that  the  compressive  strength  increases  with  the  pressure  as  well  as  with  the  time  of  exposure 
to  steam.  A  compressive  strength  considerably  (in  some  cases  over  100%)  in  excess  of  that 
obtained  normally  after  aging  for  6  weeks  may  be  obtained  in  2  days  by  using  steam  under 
pressure  for  curing.    Furthermore,  the  steam  permanently  accelerates  the  hardening  of  the 


Gage 
pressure 
(lb.  per 
sq.  in.) 

Tempera- 
ture 
(Fahr.) 

Duration 
of  exposure 
to  steam 
(hours) 

Compressive  strength 

2  days 

7  days 

14  days 

28  days 

Not 

613 

1,296 

1,528 

1,727 

steamed. 

0 

212 

48 

1,267 

2 

218 

24 

1,808 

1,792 

1,805 

10 

239 

24 

1,786 

1,555 

1,701 

1,902 

20 

258 

24 

2,139 

2,284 

2,740 

40 

286 

24 

3,292 

3,381 

3,984 

80 

323 

24 

3,964 

3,966 

4,433 

80 

323 

24 

4,487 

4,187 

4,840 

1  Tech.  Paper  58. 


236 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  6-16 


concrete  which  subsequently  increases  in  compressive  strength  with  age  upon  exposure  to  the 
atmosphere. 

It  was  noted  that  the  steam-cured  concrete  was  more  uniform  in  appearance  and  lighter 
in  color  than  normally-aged  mortar  from  the  same  materials.  These  tests  were  made  upon 
Portland-cement  mortars,  but  the  same  conclusions  were  found  to  apply  to  concretes.  The 
mortar  or  concrete  should  obtain  an  initial  set  before  exposure  to  the  steam  treatment. 

16.  Effect  of  Freezing. — The  effect  of  low  temperatures  in  delaying  or  permanently  pre- 
venting the  hardening  of  mortar  and  concrete  has  been  shown  by  Fig.  15.  In  the  event  of  the 
temperature  being  close  to  the  freezing  point  of  water  from  4  to  8  times  as  long  a  period 
is  required  to  obtain  a  final  set  as  is  required  at  normal  room  temperatures.  If  water  in  mortar 
or  concrete  freezes  before  the  cement  has  set,  it  is  not  available  for  the  chemical  action  of  setting 
and  hardening  and  hence  the  concrete  or  mortar  will  not  set  at  all  until  the  ice  melts.  These 
facts  must  be  borne  in  mind  when  removing  forms  from  concrete  placed  during  cold  weather. 
If  the  temperature  hovers  above  the  freezing  point  for  some  time  after  concrete  is  deposited, 
there  is  a  possibility  of  the  water  drying  out  before  the  greatly  delayed  setting  has  taken  place. 
If,  however,  the  concrete  has  begun  to  set  before  the  temperature  drops  considerably  below  the 
freezing  point,  the  expansion  of  the  water  in  solidifying  produces  an  expansive  force  in  excess 
of  the  cohesive  strength  of  the  green  concrete.  This  action  results  in  a  destruction  of  the  bond 
and  crumbling  of  the  concrete  when  the  ice  melts.  If  the  temperature  does  not  fall  more  than 
a  very  few  degrees  below  freezing,  the  result  may  simply  be  the  further  delaying  of  the  set 
without  appreciable  injury. 

Two  factors  operate  to  lessen  the  injurious  effect  of  freezing  upon  mortar  and  concrete: 
(1)  concrete  is  a  rather  poor  heat  conductor,  the  outer  portion  therefore  serving  as  an  insulation 
for  the  bulk  of  the  material  and  preventing  an  injurious  lowering  of  the  temperature  in  the 
interior  of  th^  mass;  and  (2)  the  chemical  action  of  setting  and  hardening  of  cement  being  an 
endothermic  reaction,  the  heat  evolved  serves  to  raise  the  temperature  of  the  material  and 
so  offsets  to  a  degree  the  loss  of  heat  by  radiation  and  conduction.  Experimental  data  secured 
during  the  construction  of  the  Arrow  Rock  Dam  and  the  Kensico  Dam  (see  Art.  42)  indicate 
that  mass  concrete  shows  a  rise  in  internal  temperature  of  from  20  to  40°F.  above  the  initial 
temperature  within  a  period  of  from  15  to  30  days. 

Serious  injury  is  oftenr  suffered  by  concrete  which  encounters  temperatures  considerably 
below  the  freezing  point  within  the  first  few  hours  after  placing,  but  this  injury  is  usually  con- 
fined to  the  outermost  portion  of  the  work  and  seldom  penetrates  more  than  an  inch  or  two  of 
depth.  A  very  frequent  form  of  injury  is  a  scaling  off  of  a  very  thin  crust  of  rich  material 
which  has  been  flushed  to  the  surface  in  finishing  the  work. 

Numerous  experimental  studies  of  the  effect  of  frost  action  on  mortars  have  been  made  and 
have  led  to  somewhat  conflicting  conclusions,  but  practically  all  of  these  have  involved  the  uSe 
of  such  small  specimens,  briquettes,  2-in.  cubes,  etc.,  that  the  condition  of  exposure  is  compar- 
able only  to  that  of  the  outermost  surface  layer  of  concrete. 

Authorities  are  quite  in  accord  in  prescribing  that  "concrete  should  not  be  mixed  or  de- 
posited at  a  freezing  temperature,  unless  special  precautions  are  taken  to  avoid  the  use  of 
materials  containing  frost  or  covered  with  ice  crystals,  and  to  provide  means  to  prevent  the 
concrete  from  freezing  after  being  placed  in  position  and  until  it  has  thoroughly  hardened." 

17.  Effect  of  Salts. — Common  salt  (NaCl)  is  frequently  used  as  an  ingredient  of  the  mixes 
of  concrete  or  mortar  which  must  be  placed  in  cold  weather.  Its  primary  effect  is  the  lowering 
of  the  temperature  at  which  water  will  freeze.  Approximately  1  %  of  salt  in  the  mixing  water 
lowers  the  freezing  point  1°F.  Calcium  chloride  (CaCla)  is  also  used  to  a  lesser  extent  to  serve 
the  same  purpose. 

The  effect  of  common  salt  and  calcium  chloride  upon  the  strength  of  a  1  : 2  : 4  limestone 
concrete  is  shown  by  the  diagrams  of  Fig.  16  which  are  derived  from  tests  made  by  H.  E. 
Pulver  and  S.  E.  Johnson  of  the  University  of  Wisconsin  {The  Wisconsin  Engineer,  October, 
1913).    The  specimens  were  4-in.  cubes,  and  the  tests  were  made  in  duplicate,  one  series  of 


Sec.  6-17] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


237 


specimens  being  cured  indoors  at  normal  temperatures  (60°-75°F.),  the  other  cured  out  of 
doors  or  in  a  refrigerator  at  temperatures  below  32°F.  The  amounts  of  the  salts  used  are 
expressed  as  percentages  by  weight  of  the  mixing  water. 

The  tests  show  that  common  salt  used  alone  is  quite  injurious  to  the  strength  of  concrete 
cured  at  normal  temperatures,  the  loss  being  roughly  proportional  to  the  amount  of  salt  used. 
With  concrete  cured  at  temperatures  below  freezing,  however,  it  facilitates  the  hardening 
process.  The  tests  show  an  increase  of  strength  for  the  addition  of  NaCl  up  to  12%,  after 
which  there  is  a  decrease.    Common  salt  retards  the  setting  of  concrete  to  a  considerable  degree. 

Calcium  chloride  used  alone  is  beneficial  to  the  strength  of  concrete,  whether  cured  at 
normal  temperatures  or  below  freezing,  up  to  about  4  %  CaClj,  at  which  point  the  maximum 


u 
c 

t 
5,1 

m 
in 

I 


K 

- 

CD 


1000 


3  0  y  \c 
Perceni-age  NaCl 


o 


li: 

Pr 

12  Wk 

6<7oCaClE  1 

cr 
in 
v. 


3000 


r 

s 

'1 

— < 

h 

'2  1 

1  6«7oCaC 

0  3 


^     ^     9  12 
Percentage  NaCI 


0  3 


Fig.  16. — Effect  of  salts  upon  strength  of  1  :  2  :  4  concrete. 

  specimens  cured  at  normal  temperatures  (60  to  75°  F. 

 specimens  cured  at  low  temperatures  (below  32°  F.). 


.     6     9  12 

Percentage  NaCf 


15 


strength  is  obtained.  This  maximum  strength,  however,  in  the  case  of  the  cold-cured  specimens 
is  only  about  one-half  the  maximum  strength  of  the  cold-cured  specimens  having  12%  of  com- 
mon salt.    Calcium  chloride  accelerates  the  setting  of  concrete. 

With  concretes  cured  at  low  temperatures  the  best  effect  was  obtained  with  a  mixture  of 
2%  of  CaClz  and  9%  of  NaCl.  This  mixture  gave  about  the  same  strength  as  the  cold-cured 
concrete  having  12%,  of  NaCl  alone,  and  was  not  as  detrimental  to  the  strength  of  normally 
cured  concrete  as  the  NaCl  alone  seemed  to  be. 


238 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-18 


18.  Effect  of  Hydrated  Lime  and  Waterproofing  Compounds. — The  addition  of  hydrated 
lime  in  small  percentages  has  not  a  very  marked  effect  upon  the  strength  of  laboratory  specimens 
of  mortar  and  concrete.  Fig.  17,  which  is  based  upon  tests  made  by  Prof.  Harry  Gardner 
of  the  University  of  Kansas  (Eng.  Rec,  vol.  64,  p.  309),  shows  the  effect  of  varying  percentages 
by  weight  Of  hydrated  lime  upon  the  tensile  strength  of  1  :3  standard  sand  mortars.  The 
replacement  of  the  cement  by  hydrated  lime  appears  to  be  slightly  beneficial  to  strength  up  to 
about  15%,  except  in  the  case  of  tests  made  at  the  ages  of  3  and  7  days  wherein  the  effect  was 
generally  detrimental  in  proportion  to  the  amount  of  lime  used.  Other  tests,  notably  those  of 
H.  S.  Spackman  {Concrete-Cement  Age,  vol.  4,  p.  112  and  Eng.  Rec,  vol.  69,  p.  25)  have  shown 
that  small  amounts  of  hydrated  lime  sometimes  appear  to  affect  the  strength  favorably,  some- 
times unfavorably.  The  most  pronounced  effect  of  hydrated  lime  added  to  mortars  and  con- 
cretes is  its  producing  a  more  plastic,  better-working  material.  The  fat,  viscous  mortar 
produced  spreads  better  under  the  trowel,  and  in  the  case  of  concrete  the  presence  of  a  small 
amount  of  lime  hydrate  tends  toward  the  production  of  a  mixture  of  greater  uniformity  by 

prevention  of  the  separation  of  fine  and  coarse 
materials.  This  fact  may  constitute  a  distinct  ad- 
vantage in  the  case  of  the  average  construction 
job  which  would  not  be  noted  under  the  ideal 
conditions  of  mixing  and  molding  in  the  laboratory. 

The  effect  of  a  large  number  of  commercial 
waterproofing  compounds  upon  the  tensile  and 
compressive  strengths  of  mortars  in  1  :  4,  1  :  6,  and 
1  :  8  mixtures  has  been  investigated  b^'-  the  U.  S. 
Bureau  of  Standards  {Tech.  Paper  3).  Figs.  18o 
and  186  show  the  results  of  tests  of  the  effect  of  15. 
such  compounds  upon  the  compressive  strength  of 
1  :  4  mortar.  These  results  are  typical  of  the  re- 
sults obtained  with  all  mortar  mixtures,  and  the 
results  obtained  in  tensile  tests  do  not  differ 
greatly  from  those  obtained  in  compression.  The 
proprietary  compounds  are,  of  course,  not  identi- 
fied by  name,  but  they  are  classified  as  follows: 
No.  27  is  dolomitic  hydrated  lime;  No.  28  is  a 
solid  chemically  active  filler  designed  to  form  an 
insoluble  lime  resinate  void  filler;  Nos.  29  to  36 
inclusive  are  water-repelling  solid  substances  con- 
sisting essentially  of  stearic  acid  with  soda  and  potash  or  lime,  designed  to  form  an  insoluble 
lime  soap;  No.  37  is  cement  containing  a  water-repelling  substance;  Nos.  38  to  40  inclusive 
are  chemically  active  liquid  fillers  designed  to  fill  the  voids  with  either  tar,  insoluble  lime  sili- 
cate, etc. 

19.  Effect  of  Sea  Water  Used  in  Gaging. — The  use  of  sea  water  to  gage  cement  mortars 
and  concretes  is  almost  invariably  forbidden  by  specifications  for  work  done  in  localities  where 
the  use  of  sea  water  might  be  convenient.  It  has  not  been  conclusively  shown,  however,  that 
the  use  of  sea  water  instead  of  fresh  water  has  a  particularly  harmful  effect.  Messrs.  Taylor 
and  Thompson  (''Concrete,  Plain  and  Reinforced,"  1916,  p.  166)  found  by  a  very  Hmited  number 
of  tests  of  1  :2  : 4  concrete  cubes  that  there  was  no  appreciable  difference  in  strength  of  specimens 
gaged  with  sea  water  and  other  specimens  gaged  with  fresh  water. 

Results  obtained  in  comparative  tensile  tests  of  mortar  briquettes  made  by  Cloyd  M. 
Chapman  are  shown  by  Figs.  19,a,  19,&  and  19,c  {Eng.  News,  vol.  63,  p.  291).  These  tests 
were  made  upon  three  sets  of  specimens :  series  (A)  specimens  were  gaged  with  fresh  water  and 
cured  in  fresh  water;  series  (B)  specimens  were  gaged  with  fresh  water  and  cured  in  sea  water; 
and  series  (C)  specimens  were  gaged  with  sea  water  and  cured  in  sea  water.    The  specimens 


Fig. 


Percen+age  hydra+ed  lime 
00        95  90  85  60  75  10 

Percentage  cement 

17. — Effect  of  hydrated  lime  upon  tensile 
strength  of  1  :  3  standard  mortar. 


Sec.  5-19] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


239 


were  tensile  briquettes  and  the  sea-water  curing  was  done  in  tanks  in  the  laboratory  using  a 
frequently  changed  bath  of  sea  water.    These  tests  indicate  that  the  use  of  sea  water  for  gaging 


g-3500 
S.3000 
S  2500 


S  1000 

I 

€  500 

s 


/,' 

iy^y.^  ■  

--^rr-^  

)3  26  ^  52. 

Age  of  test  pieces  in  weeks 


350Q 
3000 
2500 
2000 
1500 
1000 
500 




1  Z  4 


52 


13  26 

Age  of  test  pieces  in  weeks 
& 

Fig.  18. — Compressive  strength  of  waterproofed  mortars.    (One  part  Portland  cement  to  4  parts  No.  1  sand.) 


Age  in  mon-t-hs 


Age  in  months 


Age  in  months 

o  6  c  . 

Fig.  19.— Effect  upon  tensile  strength  of  gaging  cement  mortars  with  sea  water,  a,  Specimens  gaged  with 
fresh  water — cured  in  fresh  water:  6,  specimens  gaged  with  fresh  water— cured  in  sea  water;  c,  specimens  gageu 
with  sea  water — cured  in  sea  water. 

is  not  particularly  detrimental  to  the  tensile  strength  of  mortars  except  in  very  lean  mixtures. 
The  condition  of  curing  of  these  specimens  was  probably  not  as  severe  a  test  as  actual  immer- 


240 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  6-20 


sion  in  moving  sea  water  would  have  been.  On  the  other  hand,  the  section  of  the  specimens 
was  so  small  that  any  superficial  or  surface  effect  of  the  sea  water  would  appear  to  have  an 
injurious  effect  much  greater  than  that  suffered  by  concrete  of  large  bulk  exposed  in  sea  water. 

20.  Effect  of  Oils  Used  in  Gaging.— The  use  of  certain  classes  of  mineral  residual  oils  in 
gaging  mortars  and  concretes  with  the  object  of  dampproofing  them  or  reducing  their  permea- 


0  5  10  15  20         E5  0  5  10  15  20  Z5 

Perc,en+age  of  oil  based  on  weigh+  Percentage  of  oil  based  on  weight 

of  cement  of  cement 


Fio.  20. — Effect  of  mineral  residual  oils  upon  compressive  strength  of  1  :  3  mortar. 
•    (Tests  of  Logan  Waller  Page.) 


bility  lends  importance  to  the  consideration  of  the  effect  of  such  oils  upon  the  strength  of  the 
mortars  or  concretes  in  which  they  are  used.  Figs.  20  and  21  present  the  results  of  tests 
made  by  Logan  Waller  Page,  Director  of  the  Office  of  Public  Roads  (U.  S.  Dept.  of  Agriculture, 
Bull.  230).    It  appears  from  these  tests  that  the  use  of  mineral  oils  up  to  from  5  to  10%  of 


3000 
^2500 
i.  EOOO, 

C  2000 
SI  1500 

-t=  500 


r 

1 ■ 2  4  concrete 

/ 

1.3.5  concrete 
^  — 1 

r  lY 

lYr- 

1  ;  3  .'6  concrete 

1 

8 

3  5  10  15         20  25 

f^rcentage  of  oil  based  on  weight 
of  cement 


-?000 
1500 
1000 
500 

2000 
1500 
1000 
■  500 


M'.3;5  concreto 

L 

 lYr"!] 

ia. 

L  3  :6  con 
water  c 

Crete 
jred  _ 

Yr 

0  5  10  \5  20  25 

Percentage  of  oil  based  on  weight 
of  cemenf 


Fig.  21. — Effect  of  mineral  residual  oils  upon 


compressive  strength  of  concrete.     (Tests  of  Logan  Waller  Page.) 


the  cement  lowers  the  compressive  strength  to  a  moderate  degree  only  but  that  larger  amounts 
may  be  very  injurious. 

Other  tests  made  by  Arthur  Taylor  and  Thomas  Sanborn  {Trans.  Am.  Soc.  C.  E.,  vol. 
76,  p.  1094)  using  Western  asphaltic  oils  showed  a  more  marked  falling  off  in  strength  of  mortars 


-Sec.  &-21] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


241 


than  was  observed  in  Page's  tests.    At  28  and  50  days  the  compressive  strengths  of  3-in.  cubes 
of  1  : 3  mortar  made  by  the  incorporation  of  Western  oils  were  as  follows : 
Many   oils  used  for  various 

Effect  of  Asphaltic  Oils  upon  Strength  of  1  : 3 
Mortar 
Compressive  Strength 


Character  and  percentage 
of  oil  used 

28  days 

50  days 

(lb.  per 
sq.  in.) 

Relative 
value 

(lb.  per 
sq.  in.) 

Relative 
value 

No  oil 

3,950 

100.0 

4,400 

100.0 

Boiler  fuel 

5 

2,435 

61.6 

3,620 

82.4 

Boiler  fuel 

10 

1,780 

45.1 

2,460 

56.0 

Boiler  fuel 

15 

1,460 

37.0 

2,000 

45.5 

Boiler  fuel 

25 

712 

18.2 

1,000 

22.8 

Richmond  fuel 

10 

1,640 

41.5 

Road  oil  No.  6 

10 

1,235 

31.2 

Liquid  asphalt 

10 

1,080 

27.4 

commercial  purposes  contain  animal 
oils,  vegetable  oils  or  admixtures 
of  these.  Such  oils  have  been  found 
to  be  capable  of  not  only  weaken- 
ing cement  mortars  and  concretes, 
but  actually  to  disintegrate  con- 
crete in  some  cases,  the  effect  being 
most  pronounced  in  the  early  stages 
of  setting  and  hardening  (see  tests 
of  James  C.  Hain,  Eng.  News, 
March  16,  1905). 

21.  Effect  of  Laitance. — Lai- 
tance  is  a  whitish  substance  which 
is  washed  out  of  concrete  and  sub- 
sequently deposited  as  a  scum  when 
there  is  an  excess  of  water  used  in 
mixing  (see  chapter  on  "Water"  in 
Sect.  1),  or  when  concrete  is  depos- 
ited in  water,  or  when  water  collects 

in  pools  on  the  surface  of  freshly  laid  concrete.  The  laitance  consists  of  the  finest  flocculent 
matter  in  the  cement  together  with  some  silt  and  clay  from  the  aggregates.  Its  occurrence 
is  explained  by  the  formation  of  amorphous  hydrates  in  the  early  stages  of  the  setting  of  cement. 
The  composition  of  laitance  is  practically  identical  with  that  of  cement,  but  it  hardens  only 
very  slowly  and  never  acquires  much  strength.    As  a  consequence,  if  not  removed  by  water 

and  brushes  or  by  a  steam  jet,  it  forms  a  distinct 
plane  of  weakness  between  successive  layers  of 
concrete.  The  washing  out  of  a  portion  of  the 
finest  part  of  the  cement  means  the  loss  by  the 
concrete  of  just  so  much  of  its  most  valuable 
constituent,  because  it  is  the  impalpably  fine 
portion  of  the  cement  which  is  most  active  in 
binding  together  the  inert  particles  of  the  aggre- 
gate. This  same  material  alone  does  not  develop 
great  cohesiveness,  however.  A  familiar  example 
of  this  fact  is  afforded  by  the  relative  behavior 
of  very  finely  ground  cements  and  cements  of 
only  average  fineness  in  neat  and  mortar  mixtures. 
The  cement  of  average  fineness  will  greatly  excel 
7-28     7-90  7-180  7^60  in  neat  strength,  but  the  cement  which  is  ground 

Age  interval  in  days  so  finely  that  the  proportion  of  impalpably  fine 

Fig.  22. — Rate  of  increase  in  tensile  strength  of  material  is  very  large  will  form  mortars  of  greatly 

standard  1  :  3  mortar.    (Each  result  the  average  of  9  .        ,         ,  i 

to  70  tests.)  superior  strength. 

22.  Rate  of  Increase  in  Mortar  Strength 
—Retrogression.— The  relation  between  the  early  test  strength  and  the  subsequent  gain  in 
strength  is  shown  by  Figs.  22  and  23  which  are  based  upon  the  tests  of  the  former  Structural 
Materials  Laboratory  of  the  U.  S.  Geological  Survey  in  St.  Louis  (U.  S.  Geol.  Surv.  Bull. 
331).  The  rate  of  gain  in  both  tensile  and  compressive  strength  for  these  1  : 3  mortars  (made 
with  seven  typical  Portland  cements)  is  shown  to  be  approximately  inversely  proportional  at 


16 


242 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  6-23 


all  ages  to  the  strength  at  7  days,  those  mortars  which  show  the  lowest  tensile  or  compressive 
strength  at  7  days  maintaining  the  best  rate  of  gain  in  strength  at  all  ages. 


500 


0  i  1  I  I  i  I  I  I  I  I  >  I  '  I  I  I  I  I  I  I 
7-Za     7-90  7-180  7-3&0 

Age  jn+erval  in  days 


Fig.  23. — Rate  of  increase  in  compressive  strength  of  standard  1  :  3  mortar. 
(Each  result  the  average  of  20  to  70  tests.) 

The  following  table  indicates  the  relation  between  the  early  strength  of  mortar  and  sub- 
sequent retrogression  in  strength  as  determined  by  the  Structural  Materials  Laboratory  Tests 
above  quoted : 

Retrogression  in  Strength  of  1:3  Standard  Mortars 


Tests  of  Structural  Materials  Laboratory 


Strength  at  7  days 
(lb.  per  sq.  in.) 

%  showing  retrogression  between 
ages  of 

7  and  28 

days 

28  and 

90  days 

90  and 
180  days 

180  and 

360  days 

Tension 

Below  200 

0 

0 

86 

86 

200-  250 

0 

0  * 

62 

71 

250-  300 

0 

0 

48 

100 

300-  350 

0 

0 

57 

100 

Compression 

Below  800 

0 

0 

0 

20 

800-  900 

0 

0 

0 

14 

900-1,000 

0 

0 

8 

25 

1,000-1,100 

0 

0 

0 

12 

1,100-1,200 

0 

0 

0 

20 

1,200-1,500 

0 

0 

22 

0 

Above  1,500 

0 

40 

40 

20 

23.  Transverse  Strength. — The  transverse  strength  of  granular  brittle  materials  Hke 
mortars  and  concretes  is  best  expressed  by  the  Modulus  of  Rupture.    The  modulus  of  rupture 


Sec.  5-24] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


243 


is  the  apparent  stress  in  the  extreme  fiber  of  a  transverse  test  specimen  under  the  load  which 
produces  rupture.  For  specimens  of  rectangular  section  of  breadth  b  and  height  h,  loaded 
centrally  on  a  span  I,  the  breaking  load  being  W,  the  modulus  of  rupture  is  computed  by  the 
formula 

Modulus  of  rupture  =   r 


The  extreme  fiber  stress  thus  computed  is  not  the  actual  fiber  stress  because  the  formula 
involves  the  inaccurate  assumption  that  the  material  deforms  elastically  for  all  stresses  up  to 
rupture.  The  comparative  relations  between  results  are  not  affected  by  this  inaccuracy  of 
•the  formula,  however,  when  the  tests  compared  are  made  upon  specimens  of  similar  material, 
because  the  computed  values  of  the  modulus  of  rupture  are  very  nearly  proportional  to  the 
actual  stresses. 

Since  the  extreme  fiber  stresses  on  the  tension  side  and  on  the  compression  side  of  a  beam 
of  homogeneous  material  are  equal,  and  the  tensile  strength  of  mortar  or  concrete  is  only  a  small 
fraction  of  the  compressive  strength,  the  transverse  strength  of  mortar  or  concrete  is  almost 
wholly  dependent  upon  the  tensile  strength.  The  modulus  of  rupture  found  in  transverse 
tests  will  invariably  be  considerably  in  excess  of  the  tensile  strength,  however,  because  the 
computed  stress  in  the  extreme  fiber  considerably  exceeds  the  actual  stress. 

The  data  on  this  page  constitute  a  summary  of  a  portion  of  an  extensive  series  of  tests  of 
transverse  strength  of  mortars  and  concretes  made  by  Wm.  B.  Fuller.  ("  Concrete,  Plain  and 
Reinforced"  by  Taylor  and  Thompson,  p.  334.)    The  tests  were  made  upon  specimens  6  by  6  in. 


in  section,  supported  on  spans  of  30  and  60  in. 
crushed  trap-rock  aggregate  were  used 
throughout  the  series  of  tests.    The  speci- 
mens were  broken  at  the  age  of  1  month. 

24.  Shearing  Strength.— The  shear- 
ing strength  of  mortars  and  concretes 
possesses  great  significance  because  com- 
pressive failure  of  short  compressive  speci- 
mens or  structural  members  is  usually 
failure  by  shearing  on  a  diagonal  plane, 
and  because  shearing  stresses  are  impor- 
tant considerations  in  all  cases  of  concrete 
beams.  It  is  very  difficult,  however,  to 
make  experimental  determinations  of 
pure  shearing  strength  because  most 
methods  and  devices  which  may  be  used 
to  make  shearing  tests  involve  either  a 
cutting  action,  bearing  pressures,  or  beam 
stresses.  The  data  on  the  shearing  strength 
of  mortars  given  on  page  244  are  derived 
from  tests  made  by  Feret.  The  speci- 
mens used  were  prisms,  2  by  2  cm.  in  sec- 
tion, subjected  to  single  shear,  the  condi- 
tions being  such  that  beam  stresses  prob- 
ably affected  the  results  considerably. 
Specimens  were  tested  after  5  months 
curing. 


One  brand  of  cement  and  the  same  sand  and 

Transverse  Strength  of  Mortars  and 
Concretes 
Tests  of  William  B.  Fuller 


Proportions 
by  weight, 

Proportions 
bv  volume. 

Modulus  of  rupture 
(lb.  per  sq.  in.) 

cement:  sand: 
stone 

cement:  sand: 
stone 

Maxi- 
mum 

Mini- 
mum 

Aver- 
age of  G 

1 

0:0 

1 

0:0 

968 

850 

906 

1 

1:0 

1 

1.17:0 

866 

628 

734 

1 

2:0 

1 

2.34:0 

640 

592 

616 

1 

3:0 

1 

3.51:0 

432 

392 

418 

1 

4:0 

1 

4.68:0 

294 

262 

279 

1 

5:0 

1 

5.85:0 

180 

170 

173 

1 

6:0 

1 

7.02:0 

94 

92 

93 

1 

1:2 

1 

1.17:  2.06 

798 

646 

710 

1 

1:3 

1 

1.17:  3.09 

732 

573 

655 

1 

2:4 

1 

2.34:  4.12 

480 

399 

439 

1 

2:5 

1 

2.34:  5.17 

413 

349 

380 

1 

3:5 

1 

3.51:  5.17 

308 

262 

285 

1 

3:6 

1 

3.51:  6.21 

246 

213 

228 

1 

4:8 

1 

4.68:  8.25 

158 

156 

157 

1 

6:10 

1 

7.02:10.34 

91 

87 

89 

244 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-24 


Shearing  Strength  of  Cement  Mortars 
Tests  of  R.  Fereti 


C  haracter  of  sand 

Approximate  pro- 
portions by  weight 

Ultimate  strength  (lb.  per  sq.  in.) 

Ratio  of 
shear  to 
compres- 

Cement 

Sand 

Shear 

Tension 

Compres- 

Very  coarse  granite  sand  

1 

18.6 

170 

69 

240 

0.71 

1 

9.9 

570 

146 

870 

0.66 

6.9 

1,070 

212 

1,540 

0.70 

5.2 

1,440 

258 

2,350 

0.61 

4.1 

2,000 

314 

3,320 

0.60 

3.2 

2,560 

367 

4,170 

0.61 

1 

2.5 

2,790 

421 

5,210 

0.54 

1.8 

3,580 

480 

5,970 

0.60 

1 

1.2 

3,930 

537 

6,670 

0.59 

0.7 

3,640 

563 

6,810 

0.65 

Medium-sized  very  shelly  sand. . 

1 

12.9 

256 

81 

310 

0.83 

1 

7.0 

.  669 

182 

950 

0.70 

1 

5.0 

1,040 

240 

1,510 

0.69 

4.1 

1,350 

278 

1,990 

0.68 

3.1 

1,810 

320 

2,720 

0.67 

2.5 

2,250 

368 

3,430 

0.66 

2.0 

2,650 

415 

4,380 

0.61 

1.4 

2,750 

521 

5,440 

0.50 

0.9 

3,580 

541 

6,100 

0.59 

1 

0.5 

3,540 

602 

6,720 

0.53 

Very  fine  silicious  sand  

1 

12.3 

156 

67 

160 

0.97 

1 

5.8 

370 

126 

540 

0.69 

3.5 

768 

214 

1,230 

0.62 

2.4 

1,410 

302 

1,940 

0.73 

1  8 

9  1 

oD'± 

0.75 

I 

1.3 

2,570 

436 

3,710 

0.69 

1.0 

2,750 

510 

5,000 

0.55 

\ 

0.7 

3,070 

574 

5,760 

0.53 

0.5 

3,570 

647 

6,500 

0.55 

0.3 

4,120 

691 

7,110 

0.58 

Equal  parts  of  coarse  medium  and 

5.0 

1,720 

328 

2,350 

0.73 

fine  ground  quartzite  

3.0 

3,100 

450 

4,010 

0.77 

2.0 

3,070 

518 

4,810 

0.64 

20-31-mesh  ground  quartzite.  .  . 

3.0 

456 

3,640 

Neat  Portland  cement  

0.0 

3,680 

698 

8,040 

0.46 

The  data  at  the  top  of  page  245,  showing  the  results  of  shearing  tests,  are  derived  from  tests 
made  at  the  Massachusetts  Institute  of  Technology  under  the  direction  of  Prof.  C.  M.  Spofford. 
The  specimens  were  cylinders  5  in.  in  diameter  and  153^^  in.  long.    The  ends  were  securely 


1  Data  taken  from  "Concrete,  Plain  and  Reinforced"  by  Taylor  and  Thompson,  p.  136,  1909  Edition. 


I  Sec.  6-24]  CEMENT  MORTAR  AND  PLAIN  CONCRETE  245 

clamped  in  cylindrical  bearings  and  the  load  was  applied  along  the  middle  third  of  the  length 
by  a  semi-cylindrical  block.    The  final  failure  appeared  to  be  by  true  shear. 

The  following  data  are 
taken  from  tests  made  at  Shearing  Strength  of  Concrete 

the    University  of   Illinois    Summary  of  Massachusetts  Institute  of  Technology  Tests i 


Engineering  Experiment 
Station  under  the  direction 
of  Prof.  A.  N.  Talbot  {Bull 
8).  Two  methods  of  testing 
were  used.  In  the  first  a 
6-in.  hole  was  punched  in  a 
concrete  plate  or  block;  in 
the  second,  a  short  beam  4 
by  4  in.  in  cross-section  was 
securely  clamped  at  the  ends 
and  the  middle  third  of  the 
d  length  loaded.  Three  forms 
jj  of  specimens  were  used  in 
the  punching  tests:  (1)  plain 
concrete  plate;   (2)  recessed 


Proportions 

Method 
of 

Shearing  strength 
(lb.  per  sq.  in.) 

Compressive 
strength 
(lb.  per  sq.  in.) 

Ratio  of 
shear  to 

storing 

Max. 

Min. 

Ave. 

5  by  15^^2-in. 
cylinders 

compres- 
sion 

1:2:4 

air 

1,630 

960 

1,310 

2,070 

0.63 

1:2:4 

water 

2,090 

1,180 

1,650 

2,620 

0.63 

1:3:5 

air 

1,590 

890 

1,240 

1,310 

0.94 

1:3:5 

water 

1,380 

840 

1,120 

1,360 

0.32 

1:3:6 

air 

1,450 

950 

1,180 

950 

1.25 

1:3:6 

water 

1,200 

1,030 

1,120 

1,270 

0.88 

Shearing  Strength  of  Concrete 


Summary  of  University  of  Illinois  Tests 


Propor- 
tions 

Form  of  specimens 

Method  of 
storing 

Shearing 
strength 
(lb.  per 
sq.  in.) 

Compressive  strength 
(lb.  per  sq.  in.) 

Ratio  of  shear 
to  compression 

Cube 

Cylinder 

Cube 

Cylin- 
der 

1:3:6 

air 

679 

1,230 

0.55 

1:3:6 

water 

729 

1,230 

0.59 

1:3:6 

damp  sand 

905 

2,428 

1,322 

0.37 

0.68 

1:3:6 

damp  sand 

968 

1,721 

1,160 

0.56 

0.83 

1:2:4 

damp  sand 

1,193 

3,210 

2,430 

0.37 

0.49 

1:3:6 

air 

796 

1,230 

0.65 

1:3:6 

water 

692 

1,230 

0.56 

1:3:6 

water 

879 

1,230 

0.71 

1:3:6 

damp  sand 

1,141 

2,428 

1,322 

0.47 

0.86 

1:3:6 

damp  sand 

910 

1,721 

1,160 

0.53 

0.78 

1:2:4 

Recessed  block  

damp  sand 

1,257 

3,210 

2,430 

0.39 

0.52 

1:3:6 

Reinforced  recessed  block 

air 

1,051 

1,230 

0.86 

1:3:6 

damp  sand 

1,821 

2,428 

1,322 

0.75 

1.38 

1:3:6 

damp  sand 

1,555 

1,721 

1,160 

0.90 

1.39 

1:2:4 

Reinforced  recessed  block 

damp  sand 

2,145 

3,210 

2,430 

0.67 

0.88 

1:3:6 

Restrained  beam  

damp  sand 

1,313 

2,428 

1,322 

0.54 

1.00 

1:3:6 

damp  sand 

1,020 

1,721 

1,160 

0.59 

0.88 

1:2:4 

Restrained  beam  

damp  sand 

1,418 

3,210 

2,430 

0.44 

0.58 

1  Taken  from  Bull.  8,  Uni.  of  111.  Eng.  Exp.  Sta. 


246 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  &-25 


Adhesion  of  New  to  Old  Concrete 
Transverse  Strength  of  Joints — Tests  of  Hector  St. 
George  Robinson 


Method  employed  to  secure 
a  bond 

Computed  ten- 
sile stress 
in  extreme 
fiber 
(lb.  per 
sq.  in.) 

Efficiency  of 
bond,  % 

Sohd  specimens  with  no 
joint 

302 
362 
289 
340 
352 

Average. 

329 

100.0 

Surface  (molded  against 
rough    board)  merely 
wetted 

140 
78 
130 
110 
172 

Average. 

126 

38.3 

Surface  roughened  with  a 
chisel,      cleaned  and 
wetted 

194 
170 
205 
142 
165 
234 

Average. 

185 

56.2 

Surface  roughened, 
cleaned,  and  thoroughly 
coated  with  neat  cement 
grout 

325 
272 
280 
248 

Average. 

281 

85.5 

Surface  treated  with  hy- 
drochloric acid,  washed, 
brushed,  and  wetted 

oUU 
248 
260 
201 
340 
271 

Average 

270 

82.0 

filled  with  additional  fresh  concrete.    All  specimens 


concrete  block;  (3)  recessed  concrete 
block  reinforced  outside  of  the  area 
subjected  to  the  direct  action  of  the 
punch. 

25.  Adhesive  Strength. — The  ad- 
hesion of  mortars  to  various  building 
materials  is  a  matter  of  much  impor- 
tance which  has,  however,  been  insuffi- 
ciently investigated.  Fig.  24  presents 
the  results  of  tests  made  by  General 
E.  S.  Wheeler  (Report  Chief  of  Engi- 
neers, U.  S.  A.,  1895,  p.  3019,  and  1896 
pp.  2799,  2834).  Discs  of  the  material 
concerned,  1  by  1  in.  square  and  in. 
thick,  were  prepared  and  inserted  in 
the  center  of  briquette  molds.  The 
molds  were  subsequently  filled  with 
mortar  and  the  specimens  were  tested 
in  the  usual  manner  in  tension.  Mr. 
Wheeler  found  that  a  consistency  wet- 
ter than  that  which  gives  a  maximum 
tensile  strength  is  required  to  give  a 
maximum  adhesive  strength  of  mortar 
to  stone,  even  though  the  surface  of 
the  stone  be  saturated  with  moisture. 
Irregularities  of  the  surface  of  stone  or 
brick  appeared  not  to  affect  adhesive 
strength,  but  a  dirty  surface,  or  in- 
sufficient moistening  of  the  surface 
greatly  reduced  adhesion. 

25a.  Adhesion  to  Con- 
crete Previously  Placed. — The  adhe- 
sion of  concrete  to  old  work  of  the 
same  character  constitutes  an  impor- 
tant problem  in  many  classes  of  con- 
struction work,  but  few  experimental 
determinations  of  the  bond  between 
new  and  old  work  have  been  made. 
The  data  on  this  page  have  been  derived 
from  a  series  of  tests  made  by  Hector 
St.  George  Robinson  in  1912  {Proc.  In- 
stitute of  Civil  Engineers,  vol.  189,  p. 
310).  The  specimens  used  were  prisms 
of  1:2:4  concrete  30  in.  long  and  4 
by  4  in.  in  section.  One  set  were  solid 
prisms.  The  remainder  were  made  by 
placing  a  stop-board  in  the  mold  8  in. 
from  one  end  and  allowing  the  con- 
crete molded  in  this  end  to  harden  for 
7  days  before  the  stop-board  was  re- 
moved and  the  balance  of  the  mold 
were  tested  after  further  hardening  for 


Sec.  5-256] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


247 


28  days.  Four  different  treatments  accorded  the  face  of  the  old  concrete  to  improve  the 
bond  are  enumerated.  The  tests  were  made  by  rigidly  clamping  the  8-in.  portion  of 
I  each  beam  in  a  fixed  support  and  loading  the  cantilever  beam  at  a  point  20  in.  from  the  sup- 
port. The  relative  strengths  of  the  various  joints  thus  tested  was  determined  by  computing 
the  extreme  fiber  stress  on  the  tension  side  of  the  joint  (modulus  of  rupture).  The  ap- 
parent tensile  strength  thus  computed  is  much  higher  than  the  actual  tensile  stress,  but  the 
relative  efficiencies  of  the  various  methods  of  securing  a  bond  are  nevertheless  shown. 


Fig   24  — Adhesive  strength  of  Portland  cement  mortar.     1  part  cement;  1  part  crushed  quartz  (Nos.  20-30). 

(Wheeler,  Report  of  Chief  of  Eng'r's,  1895.) 

256.  Adhesion  or  Bond  to  Steel. — See  Art.  2,  Sect.  6. 
26.  Strength  of  Natural  Cement  Mortar  and  Concrete. — The  production  and  use  of  natural 
cement  in  the  United  States  has  declined  so  rapidly  since  1899,  when  the  amount  produced 
reached  its  maximum  of  nearly  10,000,000  bbl.  per  year,  and  greatly  exceeded  the  output  of 
Portland  cement,  that  the  present  importance  of  natural  cement  as  a  material  of  engineering 
construction  is  almost  negligible  in  comparison  with  that  of  Portland  cement.  The  reasons 
for  the  great  decline  in  importance  of  natural  cement  are  briefly:  (1)  the  great  improvement  in 
quality  and  lowering  of  cost  of  Portland  cement;  (2)  the  inferiority  of  the  average  natural  ce- 


FlG. 


„         _        10       T2       14        16        la       20  22 
Age  .  in  months 

25a. — Tensile  strength  of  natural  cement— average  of  10  brands.  (Sabin.) 


ment  to  the  average  Portland  cement  in  structural  qualities;  (3)  the  great  variability  in  quality 
shown  by  natural  cements  owing  to  the  lack  of  close  control  of  the  manufacturing  process; 
and  (4)  a  general  distrust  of  natural  cement  among  engineers  and  others  which  is  often  alone 
responsible  for  its  use  being  forbidden  by  specifications. 

Natural  cement,  mortars,  and  concretes  vary  greatly  in  strength  owing  to  a  great  varia- 
bility in  both  composition  and  constitution  of  the  cement.  "  This  variation  is  found  not  only 
in  comparing  cements  from  different  locaUties,  but  even  in  comparing  samples  taken  at  ditterent 
times  from  the  output  of  any  one  locality.    The  only  general  statements  that  may  be  made 


248 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-27 


concerning  their  strength  is  that  natural  cements  rarely  show  more  than  half  the  tensile  strength 
of  Portland  cements  of  the  same  age,  and  their  compressive  strength  rarely  exceeds  one- 
third  that  of  Portland  cement  in  similar  mixtures"  ("  Materials  of  Construction,"  by  A.  P. 
Mills).  The  diagrams  of  Figs.  25a  and  256  average  the  results  obtained  from  tensile 
tests  of  mortars  of  ten  representative  brands  of  natural  cement  made  by  L.  C.  Sabin  ("Report 
Chief  of  Engineers,"  1895,  p.  2937),  and  compressive  tests  of  eight  to  nine  brands  of  natural 
cement  made  by  Clifford  Richardson  {Brickhuilder,  vol.  6,  p.  253). 

Very  few  data  are  available  showing  the  strength  of  natural  cement  concretes.  Tests 
made  at  the  Watertown  Arsenal  in  1899  show  the  following  strengths  of  12-in.  cubes  of  1  :  2  :  4 


3000 


Is 

>  X 

w  0-1500 
E  500 


28 


Age  in  days 


90 


Fig.  256. — Compressive  strength  of  natural  cement — average  of  8  to  9  brands  (1  brand  only  at  90  days). 

{Richardson.) 


trap-rock  concrete  made  with  one  brand  of  typical  natural  cement  ("Tests  of  Metals,"  1899 
and  1901): 


Max. 
(lb.  per  sq.  in.) 

Min. 
(lb.  per  sq.  in.) 

Average  of  5 
(lb.  per  sq.  in.) 

Compressive  strength  at   3  months  

Compressive  strength  at  14  months  

460 
914 

263 
585 

332 
715 

Sabin  ("Cement  and  Concrete,"  p.  314)  quotes  the  following  tests  made  by  A.  W.  Dow  for 
the  Engineer  Commissioner  of  the  District  of  Columbia  in  1897.  The  specimens  were  12-in. 
cubes  of  1:2:6  concrete,  made  with  six  different  coarse  aggregates  and  tested  at  the  age  of 
12  months.  Comparative  tests  of  a  Portland-cement  concrete  made  with  the  same  aggregates 
with  the  same  proportions  are  also  reported. 


Max. 

Min. 

Average 

(lb.  per  sq.  in.) 

(lb.  per  sq.  in.) 

(lb.  per  sq.  in.) 

Compressive  strength  of  1  :  2  :  6 

Natural-cement  concrete  

915 

763 

844 

Compressive  strength  of  1  :  2  :  6 

Portland-cement  concrete  

3,060 

1,850 

2,670 

The  standard  specifications  of  the  American  Society  for  Testing  Materials  (A.  S.  T.  M. 
Standards,  1916)  require  that  the  minimum  tensile  strength  of  1:3  natural  cement  mortar 
made  with  standard  Ottawa  sand  shall  be: 

7  days  (1  day  in  moist  air,    6  days  in  water) — 50  lb.  per  sq.  in. 
28  days  (1  day  in  moist  air,  27  days  in  water) — 125  lb.  per  sq.  in. 

27.  Strength  of  Cinder  Concrete. — The  compressive  strength  of  a  number  of  mixes  of 
concrete  made  with  anthracite  coal  cinders  and  six  different  Portland  cements  is  shown  by 


I  Sec.  5-27]  CEMENT  MORTAR  AND  PLAIN  CONCRETE  240 

the  following  summaries  of  two  series  of  tests  made  at  the  Watertown  Arsenal  ("Tests  of 
Metals,"  1898,  1903,  and  1904).    The  specimens  of  each  test  series  were  12-in.  cubes,  and  the 
I  average  values  given  are  means  of  from  two  to  four  tests. 

Strength  of  Cinder  Concrete 


Watertown  Arsenal  Tests — Tests  Made  in  1898 


Brand  of 
cement 

Proportions 
of  mixture 

Average  compressive 
strength 
(lb.  per  sq.  in.) 

1  month 

3  months 

A 

1 

1:3 

1,466 

2,001 

B 

1 

1:3 

1,032 

1  393 

C 

1 

1:3 

2,329 

2'834 

D 

1 

1:3 

1,602 

2,414 

E 

1 

1:3 

1,438 

1,890 

F 

1 

1:3 

1,379 

1,788 

A 

1 

2:3 

1,098 

1,634 

A 

1 

2:4 

904 

1,325 

A 

1 

2:5 

769 

1,084 

B 

1 

2:5 

471 

685 

C 

1 

2:5 

940 

1,600 

D 

1 

2:5 

696 

1,223 

E 

1 

2:5 

744 

880 

A 

1 

:3:6 

529 

788 

Tests  Made  in  1903  and  1904  (One  Brand  of  Cement) 


Proportions  of 
mixture 

Compressive  strength  (lb.  per  sq.  in.) 

5  weeks 

32  weeks 

1  year,  15  weeks 

Max. 

Min. 

Ave.  of  3 

Max. 

Min. 

Ave.  of  2 

Max. 

Min. 

Ave.  of  4 

1:2  :4 
1:2M:5 
1:3  :6 

2,430 
1,400 
1,200 

1,950 
1,570 
1,350 

2,143 
1,457 
1,293 

2,600 
2,020 
1,730 

2,500 
1,980 
1,560 

2,550 
2,000 
1,645 

2,610 
1,950 
1,400 

2,410 
1,480 
1,290 

2,488 
1,700 
1,363 

f  More  recent  tests  of  cinder  concrete,  the  results  of  which  should  be  indicative  of  the 
range  of  quality  of  the  cinder  concrete  used  in  building  construction,  are  summarized  in  the 
table  on  page  250.  These  tests  constitute  a  portion  of  a  study  of  "  Cinder  Concrete  Floor  Con- 
struction" by  Harold  Perrine  and  by  George  E.  Strehan  {Trans.  Am.  Soc.  C.  E.,  vol.  79, 
p.  523).  The  specimens  were  8  by  16-in.  cylinders  made  by  competent  men  with  laboratory 
training,  but  the  material  was  taken  from  that  going  into  the  floors  of  various  structures 
then  in  process  of  construction  in  New  York  City.    The  samples  were  taken  without  advance 


250 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-28 


Strength  of  Cinder  Concrete 
Perrine  and  Strehan  Tests 


Class  of  concrete 

Compressive  strength  (lb.  per  sq.  in.) 

1  month 

2  months 

6  months 

1  year 

1 

2:5  continuous-mixer  concrete,  low-grade  cinders. . 

407 

701 

933 

913 

1 

2 : 5  batch-mixer  concrete,  good  cinders  

818 

1,254 

1,744 

1,465 

1 

980 

1,035 

1,478 

1,475 

1 

2 : 5  hand-mixed  concrete,  good  cinders  

507 

662 

754 

813 

Strength  of  Cinder  Concrete 
Structural  Materials  Laboratories'  Tests 


notice  been  given  the  contractor,  and  the  specimens,  after  being  molded  on  the  job,  were 
tested  in  the  Columbia  University  Laboratory. 

Tests  of  1:2:4  cinder  concrete 
made  at  the  Structural  Materials 
Testing  Laboratories  at  St.  Louis  in 
1909  are  summarized  on  this  page 
{Tech.  Paper  2,  U.  S.  Bureau  of 
Standards).  Tests  of  21  cylinders  8 
by  16  in.  are  averaged. 

28.  Working  Stresses. — For  work- 
ing stresses  recommended  by  the  Joint 
Committee,  see  Appendix  B. 


Compressive  strength 
(lb.  per  sq.  in.) 

At  age  of 
52  weeks 

4  weeks 

13. weeks 

26  weeks 

Max  

1,964 

2,445 

2,792 

2,958 

Min  

1,499 

1,981 

2,187 

2,493 

Ave  

1,647 

2,217 

2,525 

2,761 

ELASTIC  PROPERTIES  OF  CEMENT  MORTAR  AND  CONCRETE 

29.  Stress-strain  Curves  for  Mortars  and  Concretes. — Typical  stress-strain  curves  for 
a  number  of  classes  of  1:2:4  concrete  at  the  age  of  1  year  are  presented  by  Fig.  26.  These 
curves  average  the  results  of  tests  of  21  specimens  (8  by  16-in.  cylinders)  for  each  class  of  con- 


.E  3200 

■<n  eeoo 

15  2400 
o)  2000 
5n  1600 

0) 

^(200 
O  600 

u 

400 
0 


C 

J 

7 

/ 

f 

/ 

- 

/ 

i 

v 

-Yield  Doint 

t 

I 

--Yield  point 

f 

t 

i 

i 

■Y 

eld  r)oin+ 

t 

r 

\  i  .A  Granl+e 
concrete 

V.Z  A  Limestone 
concrete 

V 

2  '4  Grovel 

/ 

\:e:4  Cinder 
concrete 

concrete 

0  .0005        O0\0  .0005         /DO  10  0005        .0010  .0005         0010  .0015 

Strain  in  inches  per  inch 
Fig.  26. — Stress-strain  curves  for  concretes.    (Curves  are  averages  for  21  tests.    Age  12  mo.) 


Crete,  made  at  the  Structural  Materials  Laboratories  at  St.  Louis  (U.  S.  Bureau  of  Standards 
Tech.  Paper  2).  At  earlier  ages  tests  of  these  same  concretes  resulted  in  stress-strain  curves 
closely  resembling  these  1-year-test  curves  except  that  the  slope  of  the  curves  is  less,  and  the 
curvature  greater,  at  the  earlier  test  periods. 


i|  Sec.  6-30] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


251 


Stress-strain  curves  for  mortars  exhibit  the  same  characteristics  as  do  these  curves  fv)r 
concretes. 

30.  Yield  Point. — Mortars  and  concretes  are  not  perfectly  elastic  materials  for  any  range 
of  loading,  there  being  a  slight  decrease  in  the  proportion  of  stress  to  strain  as  the  stress  in- 
creases, and  a  slight  permanent  set  for  very  low  stresses.  Even  the  first  portion  of  the  stress- 
strain  curve  is,  therefore,  not  a  perfectly  straight  line,  but  for  purposes  of  curve  plotting  it  is 
sensibly  so  up  to  a  certain  point.  This  point  where  deviation  from  a  practically  straight-line 
relation  between  stress  and  strain  is  first  perceived  is  designated  the  yield  point.  Beyond  the 
yield  point  the  slope  of  the  curve  decreases  at  an  increasingly  rapid  rate,  and  the  permanent 
set  increases  correspondingly. 

The  following  table  gives  values  of  the  yield  point  in  tests  of  mortars  of  three  proportions 
made  by  the  Bureau  of  Standards  {Tech.  Paper  58). 

Yield  Point  of  Mortars 


Age  4  weeks 

Age  13  weeks 

Proportions 
by  volume 

Yield  point 
(lb.  per  sq.  in.) 

Modulus  of 
elasticity 
(lb.  per  sq.  in.) 

Ultimate 
strength 
(lb.  per  sq.  in.) 

Yield  point 
(lb.  per  sq.  in.) 

Modulus  of 
elasticity 
(lb.  per  sq.  in.) 

Ultimate 
strength 
(lb.  per  sq.  in.) 

1:1 
1:2 

1,834 

4,243,000 

5,613 
3,070 
1,432 

2,600 
1,833 
700 

4,153,000 
4,673,000 
2,200,000 

6,739 
4,560 
1,663 

1:4 

400 

2,120,000 

The  yield  points  of  various  classes  of  1:2:4  and  1:3:6  concretes  at  ages  up  to  1  year 
are  shown  by  Fig,  27  which  is  based  upon  tests  of  the  Bureau  of  Standards  {Tech.  Paper  58). 


— 



Ultimate  sfrenoth' 

( 

—  1 

3-6  concretes 

Fig 


13  26 
Age  in  weeks 

27.— Yield  point  of  1 


2  : 4  and  1 


13  26 

Age  in  weeks 

3  :  6  concretes. 


52 


Values  of  ultimate  compressive  strength  for  the  same  concretes  are  shown  for  purposes  of  com- 
parison. These  tests  indicate  that  the  yield  point  of  the  average  concrete  is  in  the  neighborhood 
of  three-tenths  of  the  compressive  strength  at  1  month  and  about  four-tenths  of  the  compressive 
strength  at  1  year. 

31.  Modulus  of  Elasticity.— The  modulus  of  elasticity  of  an  elastic  material  is  the  quotient 
obtained  by  dividing  unit  stress  by  the  corresponding  unit  deformation  or  strain,  the  limit 
of  elastic  behavior  not  being  exceeded.  In  American  practice  the  unit  of  measurement  is 
pounds  per  square  inch.  Since  mortars  and  concretes  are  not  perfectly  elastic  materials,  the 
deformation  not  bearing  a  constant  relation  to  the  stress  for  any  range  of  loading,  the  quotient 


252 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-32 


of  stress  divided  by  strain  will  vary,  decreasing  as  the  stress  increases.  Properly  speaking  an 
inelastic  material  has  no  modulus  of  elasticity,  but  practice  has  sanctioned  the  use  of  the  term 
in  connection  with  mortars  and  concretes,  meaning  the  quotient  of  any  small  stress  increment  by 
the  corresponding  strain  increment.  The  value  of  E  thus  computed  is,  therefore,  the  slope  of  a 
short  chord  of  the  stress-strain  curve,  or  if  the  stress  increment  be  very  small,  E  at  any  point  on 
the  stress-strain  curve  is  represented  by  the  tangent  to  that  curve.  Within  the  limits  of  work- 
ing stresses  for  mortars  or  con- 

8 


o 

c 


4000 


3000 


.E6 

(J)  ' 

^  5000 
j3 


2000 


1000 


4000 


3000 


20OO 


cretes  the  value  of  E  changes 
only  very  slightly,  and  its  initial 
value  may,  therefore,  properly  be 
used  for  purposes  of  design.  This 
initial  value  of  E  may  most  con- 
veniently be  determined  by  not- 
ing the  slope  of  the  tangent  to 
the  first  portion  of  the  stress-strain 
curve. 

The  values  of  the  initial  mod- 
ulus of  elasticity  for  the  three 
mortar  mixtures  mentioned  in  the 
last  preceding  chapter  are  given 
in  the  above  table.  Values  of  E 
found  for  the  various  concretes 
also  mentioned  above  are  given  in 
Fig.  28.  Little  may  be  said  by  way  of  generalization  concerning  E  for  concretes.  It  increases 
with  age  and  with  the  richness  of  the  mix,  but  varies  greatly  with  different  classes  of  aggre- 
gate materials  and  with  different  aggregates  of  the  same  general  class.  E  for  cinder  concrete 
appears  to  be  something  less  than  one-half  the  average  value  found  with  rock  concretes. 

The  design  values  of  E  recommended  by  the  Joint  Committee  are  given  in  Appendix  B. 


Y 

—  1: 

2:4c 

sncre+es  — 

1000 


-t:3 

:6  con 

cre+«s  

26 


52 


Fig. 


Age  in  weeks 

28. — Modulus  of  elasticity  of  1 


4    \^       26  S( 

Age  in  weeks 

4  and  1:3:6  concretes. 


CONTRACTION  AND  EXPANSION  OF  CEMENT  MORTAR  AND 

CONCRETE 

32.  Coefficient  of  Expansion. — Mortars  and  concretes  expand  as  the  temperature  is  raised 
and  contract  as  the  temperature  is  lowered.  The  coefficients  of  linear  expansion  per  degree 
Fahrenheit  for  a  series  of  mortars 
and  crushed  stone  concretes  tested 
under  the  writer's  direction  in  the 
laboratories  of  the  College  of  Civil 
Engineering,  Cornell  University,  in 
1916  are  listed  in  the  table  on  this 
page.  All  of  the  specimens  were 
molded  in  the  shape  of  bricks  8  in. 
long,  4  in.  wide,  and  2  in.  thick. 
Heating  was  done  in  a  specially-con- 
structed resistance  type  of  electric 
furnace,  and  distortion  was  meas- 
ured by  a  special  extensometer 
actuated  by  fused  quartz  contact 
bars  extending  through  the  furnace  walls.  Measurements  were  made  to  the  nearest 
0.000,000,9  in.  per  in.  of  length  of  the  specimen.  The  test  results  listed  are  averages  of  from 
two  to  ten  tests  of  each  class  of  material,  the  ages  varying  from  1  to  8  months.  The  range  of 
temperatures  employed  was  from  about  70°  to  212°F. 


Mortars 

Concretes 

Mixture 

Coefficient  of 
expansion  per 
degree  Fahrenheit 

Mixture 

Coefficient  of 
expansion  per 
degree  Fahrenheit 

Neat 

0.000,007,83 

1:13^:3 

0.000,006,77 

1:1 

0.000,007,43 

1:2  :4 

0.000,006,60 

1:2 

0.000,006,00 

1:23^:5 

0.000,005,58 

1:3 

0.000,006,05 

1:3  :6 

0.000,005,37 

1:4 

0.000,005,94 

1:5 

0.000,005,77 

Sec.  5-33] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


253 


•-  c: 
«o  o 

It  ° 


O 


05 

0.00 

-0.05 
-0.10 


Specimen  No.I46-Cl 


These  tests  show  that  the  coefficient  of  expansion  of  mortars  and  concretes  increases  with  in- 
crease of  richness  of  the  mix,  but  that  the  range  of  values  between  a  very  lean  concrete  and  neat 
cement  is  comparatively  short.  An  average  concrete  will  have  a  temperature  coefficient  almost 
exactly  equal  to  that  of  the  average  steel.  This  fact  is  one  of  great  importance  in  all  cases  of 
I  reinforced  concrete. 

33.  Moisture  Changes. — Mortars  and  concretes  expand  in  volume  if  kept  wet  or  immersed 
in  water,  and  contract  if  exposed  in  air.  Experiments  made  by  Prof.  A.  H.  White  at  the 
University  of  Michigan  {Proc.  Am. 
Soc.  Test.  Mat.,  vols.  11  and  14)  +0.10 
indicate  that  this  property  is  not 
confined  to  the  early  hardening 
period  but  is  characteristic  of  mor- 
tars and  concretes  even  after  20 
years  in  service.  Fig.  29a  shows 
the  variations  in  length  observed 
in  two  1-in.  by  1-in.  by  4-in.  bars 
of  1:3  mortar  tested  by  Prof. 
White.  These  bars  appear  to 
have  suffered  no  impairment  of  the 
ability  to  expand  immersed  and 
contract  when  exposed  to  air  even 
after  a  period  of  nearly  5  years. 
These  particular  specimens,  when 
about  4  years  old,  show  increases  in  length  of  about  0.05%  in  a  3  to  4-month  period  when 
placed  in  water  after  thorough  drying  out,  and  their  contraction  in  air  is  scarcely  less  rapid. 
Specimens  of  the  same  mixes  made  with  other  cements  showed  in  a  number  of  cases  more  ex- 
tensive volume  changes  than  do  the  ones  shown  in  Fig.  29a.  One  mortar  stored  in  air  con- 
tracted about  1.10%  in  the  first  3  months.  A  specimen  cut  from  the  rich  mortar  top  coat 
of  a  sidewalk  which  had  been  in  service  for  20  years  expanded  about  0.16%  when  stored  in 


o  Immersed  in  water 
@  In  air  of  room 
^  in  olessicator 

In  water- sat ura+ed  air 


Specirnen  No.  I46-Q2 


Time  in  years 


Fig.  29a. 


-Expansion  and  contraction  of  1  :  3  mortars  when  alter- 
nately wet  and  dried. 


50       60        70       80  90 

Time  in  days 
contraction  of  concretes. 


*  Fig.  296. — Expansion  and  contraction  of  concretes.    Air  and  water  storage. 

W 

water  for  2  years,  and  a  portion  from  the  gravel  concrete  base  of  the  same  walk  expanded 
about  0.12%  in  the  same  period. 

The  results  of  a  number  of  tests  of  concrete  made  under  various  auspices  are  shown  by  Fig. 
296.  Curves  I,  II,  and  III  show  the  changes  in  length  of  concretes  tested  by  A.  T.  Goldbeck 
in  the  laboratory  of  the  Office  of  Public  Roads,  U.  S.  Department  of  Agriculture  {Proc.  Am.  Soc. 
Test.  Mat.,  vol.  11).    The  specimens  were  8  in.  square  and  5  ft.  long.    Specimens  I  and  II 


L 


254 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-34 


were  stored  in  air;  specimen  III  was  wrapped  in  burlap  which  was  kept  moist  continuously. 
Curves  IV,  V,  VI,  and  VII  are  derived  from  tests  niade  by  Prof.  H.  C.  Berry  in  the  laboratories 
of  the  University  of  Pennsylvania  {Proc.  Am.  Soc.  Test.  Mat.,  vol.  11).  The  specimens  were 
9  in.  square  and  the  gaged  length  was  20  in.  Specimens  IV  and  V  were  stored  in  air  while  speci- 
mens VI  and  VII  were  stored  in  water.  Curve  VIII  is  the  record  of  a  test  of  a  slab  of  concrete 
12  in.  wide,  6  in.  deep,  and  10  ft.  long  between  gage  points,  made  by  Prof.  B.  P.  Fleming  of  the 
State  University  of  Iowa.  The  slab  was  exposed  in  the  air  of  the  laboratory  throughout  the 
period  of  observation.  Its  behavior  is  notable  in  one  respect  in  that  a  pronounced  expansion 
was  observed  for  the  first  10  days,  amounting  to  about  ,0.012%.  After  about  12  days  it  con- 
tracted continuously  for  about  75  days  longer,  at  which  time  it  shows  a  net  contraction  of  about 
0.03%.  Mr.  Goldbeck  states  that  some  of  his  mixtures  showed  a  tendency  to  expand  in  the 
early  hardening  period  of  a  few  days  but  the  amount  of  expansion  was  very  slight. 

The  tests  of  Fig.  296  indicate  that  the  changes  in  volume  of  concretes  when  exposed  in 
either  a  wet  or  a  dry  situation  are  rather  variable  with  different  cements  and  aggregates.  It 
appears,  however,  that  a  concrete  which  dries  out  in  the  air  may  be  expected  to  contract  from 
0.02  to  0.05%,  and  when  immersed  in  water  may  expand  at  least  half  this  amount.  If  the 
concrete  in  a  structure  is  so  restrained  that  it  is  not  free  to  expand  or  contract,  it  is  possible 
therefore  that  stresses  amounting  to  from  400  to  1000  lb.  per  sq.  in.  in  tension  may  occur,  E 
being  considered  to  be  2,000,000  lb.  per  sq.  in.  This  means  that  the  tensile  strength  of  concrete 
is  exceeded  and  the  concrete  will,  and  commonly  does,  crack.  Difficulty  caused  by  the  expan- 
sion of  concrete  in  a  damp  or  wet  situation  is  not  so  commonly  encountered,  and  the  stresses 
introduced  will  never  cause  compressive  failure.  They  may,  however,  cause  a  buckling  action 
in  the  case  of  continuous  surfaces  of  large  extent. 

DURABILITY  OF  CEMENT  MORTAR  AND  CONCRETE 

34.  Fire -resistance  Properties. — Concrete  ranks  highly  as  a  fire-resistant  and  fireproofing 
material  principally  because  it  possesses  a  low  rate  of  heat  conductivity  and  has  a  low  coeffi- 
cient of  expansion  practically  equal  to  that  of  steel,  in  addition  to  being  incombustible.  Other 
masonry  materials  like  some  of  the  natural  stones  and  terra-cotta  are  no  less  incombustible 
than  concrete,  but  are  inferior  to  the  latter  as  a  fireproofing  material  because  they  possess  either 
greater  conductivity  or  a  higher  coefficient  of  expansion. 

Tests  of  the  conductivity  of  concretes  made  by  Prof.  Ira  H.  Woolson  {Proc.  Am.  Soc.  Test. 
Mat.,  vols.  5,  6,  and  7)  led  to  the  conclusions:  "  That  all  concretes " — stone  gravel,  and  cinder — 
"have  a  very  low  thermal-conductivity,  and  herein  lies  their  ability  to  resist  fire.  That  when 
the  surface  of  a  mass  of  concrete  is  exposed  for  hours  to  a  high  heat,  the  temperature  of  the 
concrete  1  in.  or  less  beneath  the  surface  will  be  several  hundred  degrees  below  the  outside. 
That  a  point  2  in.  beneath  the  surface  would  stand  an  outside  temperature  of  1500°F.  for  2  hr. 
with  a  rise  of  only  500°  to  700°,  and  points  with  3  in.  or  more  of  protection  would  scarcely  be 
heated  above  the  boiling  point  of  water." 

The  low  thermal-conductivity  of  concrete  is  partly  due  to  its  porosity,  air  spaces  affording 
efficient  protection  against  conduction,  and  partly  due  to  the  absorption  of  heat  of  vaporiza- 
tion by  the  water  of  combination  in  the  set  cement  when  the  temperature  of  dehydration  of  the 
latter  is  reached.  This  dehydration  probably  begins  at  about  500°F.  and  is  completed  at  about 
900°F.  (S.  B.  Newberry,  Cement,  May,  1902,  p.  95).  The  absorption  of  heat  by  the  surface 
material  in  becoming  itself  dehydrated  retards  the  dehydration  of  the  underlying  material. 
The  surface  concrete  which  is  injured  by  heat,  but  which  remains  in  place,  affords  protection 
for  the  material  beneath,  for  it  becomes  a  poorer  conductor  than  the  original  concrete.  The 
Joint  Committee  on  Concrete  and  Reinforced  Concrete  recommends  that  "metal  be  protected 
by  a  minimum  of  2  in.  of  concrete  on  girders  and  columns,  1}^  in.  on  beams,  and  1  in.  on  floor 
slabs." 

The  experience  gained  in  great  conflagrations  like  the  Baltimore  fire,  the  San  Francisco 


Sec.  6-35] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


255 


fire,  the  Edison  plant  fire,  etc.,  has  been  that  concrete  exposed  to  intense  heat  for  considerable^ 
periods  becomes  calcined  to  a  depth  of  from  3^  to  in.  but  shows  no  tendency  to  spall  ofT 
except  at  exposed  corners  and  edges  (see  reports  of  Captain  J.  S.  Sewell  to  the  Chief  of  Engineers, 
U.  S.  A.,  and  of  Prof.  Norton  to  the  Insurance  Engineering  Experiment  Station,  on  the  Balti- 

j;  more  fire,  Eng.  News,  March  24,  and  June  2,  1904;  the  report  of  S.  A.  Reed  to  the  National  Board 
of  Fire  Underwriters  on  the  San  Francisco  fire,  Eng.  News,  vol.  56,  p.  137;  the  comments  of 
various  engineers  upon  the  Edison  plant  fire,  Eng.  News,  vol.  73,  p.  38;  and  the  report  on  the 
Edison  fire  of  the  National  Fire  Protective  Association,  obtainable  in  booklet  form  from  the 
New  York  Board  of  Fire  Underwriters). 

Prof.  Norton  and  others  have  concluded  that  there  is  little  difference  in  the  action  of  fire 

I  on  stone  concrete  and  cinder  concrete. 

35.  Weathering  Qualities. — The  principal  agencies  affecting  the  durability  of  concretes 
and  mortars  which  are  classed  as  weathering  agencies  are  changes  of  atmospheric  temperature, 
wind  and  rain,  and  changes  of  atmospheric  moisture.  The  expansion  and  contraction  of  mor- 
tars and  concretes  subjected  to  variations  of  temperature  and  moisture  conditions  are  respon- 
sible for  practically  all  failures  of  these  materials  under  conditions  of  exposure  to  the  weather. 
Either  temperature  effects  or  moisture  effects  may  be  alone  operative,  or  both  effects  may  be 
combined.  Temperature  stresses  caused  by  the  shrinkage  of  continuous  large  surface  areas 
are  particularly  apt  to  cause  cracking.  This  cannot  be  wholly  prevented,  but  cracks  can  be 
made  less  harmful  by  the  use  of  steel  reinforcement  so  placed  that  a  multitude  of  small  cracks, 
which  do  not  open  up  much,  replace  a  few  large  and  deep  cracks.  In  the  average  situation  the 
introduction  of  dangerous  stresses  caused  by  a  tendency  to  expand  or  contract  is  more  apt  to 
be  due  to  moisture  changes  than  to  temperature  changes,  because  the  volumetric  changes  in 
the  latter  case  are  less  marked.  The  expansion  and  contraction  of  rich  mortars  and  concretes 
is  considerably  more  extensive  than  that  of  leaner  mixes  when  the  moisture  condition  varies, 
and  the  same  thing  appears  to  be  true  to  a  lesser  extent  when  the  temperature  varies.  This 
circumstance  is  responsible  for  the  difficulty  often  encountered  in  causing  a  surface  coating  of 
comparatively  rich  material  plastered  upon  a  leaner  base  material  to  adhere  permanently  if 
the  bond  between  the  two  is  at  all  defective.  The  surface  material  tends  to  expand  and  con- 
tract more  than  the  underlying  material  not  only  because  it  is  richer  in  cement,  but  also  be- 
cause it  protects  the  underlying  material  from  as  extensive  temperature  and  moisture  changes 
as  it  itself  experiences.  The  result  is  the  introduction  of  excessive  stresses  in  the  surface 
material,  the  opening  up  of  tension  cracks,  or  buckling  due  to  compressive  stress,  and  the 
ultimate  spalling  off  of  the  surface  layer.  The  principal  preventive  measures  which  may  bo 
adopted  are  the  use  of  as  lean  a  surface  coat  as  is  practicable,  the  use  of  as  thin  a  plaster  coating 
as  possible  thus  favoring  the  formation  of  many  small  cracks  rather  than  a  few  large  ones, 
and  the  adoption  of  all  measures  tending  to  make  a  strong  bond  between  the  two  classes  of 
material.  An  excessive  amount  of  troweling  of  surfaces  is  to  be  avoided  because  of  the  flush- 
ing to  the  surface  of  a  film  of  nearly  neat  cement  which  will  tend  to  peel  off  in  some  cases. 

36.  Abrasive  Resistance. — The  abrasive  resistance  of  mortars  "is  primarily  of  importance 
in  the  determination  of  the  best  mortar  for  use  in  the  top  coat  of  concrete  floors,  walks,  and  pave- 
ments. Resistance  to  abrasion  will  always  be  dependent  not  only  upon  the  cement,  as  regards 
the  tenacity  with  which  it  clings  to  the  sand  grains,  which  will  be  largely  dependent  upon  its 
fineness  and  its  lime  content,  but  also  upon  the  hardness  of  the  sand  used.  Abrasion  either 
wears  away  the  cement  and  the  sand  grains,  or  it  pulls  the  sand  grains  out  of  the  cement  matrix. 

"With  soft  sand  particles  the  resistance  to  abrasion  with  a  given  cement  decreases  con- 
stantly as  the  percentage  of  sand  is  increased.  With  hard  sand  grains  the  abrasive  resistance 
increases  as  the  proportion  of  sand  increases,  until  the  volume  of  cement  becomes  relatively 
too  small  to  bind  the  sand  grains  together  thoroughly.  This  limit  is  found  to  be  reached  when 
the  mortar  contains  not  more  than  two  parts  of  sand  to  one  of  cement."  ("  Materials  of  Con- 
struction," by  A.  P.  Mills.)  The  abrasive  resistance  of  concretes  is  dependent  almost  wholly 
upon  that  of  the  mortar  made  by  its  cement  and  fine  aggregate.    The  coarse  aggregate  is  prac- 


256 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  6-37 


tically  always  forced  back  from  the  surface  of  concrete  exposed  to  abrasion.  If  it  is  exposed, 
the  same  considerations  of  relative  hardness  of  the  stone  particles  and  proportion  of  the  mix 
applicable  in  the  case  of  mortars  apply  to  the  concrete. 

37.  Action  of  Sea  Water. — The  behavior  of  concrete  in  sea  water  is  a  problem  which 
has  occupied  much  of  the  attention  of  engineers  for  many  years.  The  question  has  often 
been  discussed,  and  many  attempts  have  been  made  to  determine  experimentally  the  exact 
action  of  sea  water  upon  concrete,  and  the  causes  of  that  action.  The  amount  of  accurate  in- 
formation available  is  rather  meager,  however,  and  the  results  of  experimental  investigations 
are  inconclusive  and  often  contradictory.  Many  concrete  structures  in  sea  water  out  of  the 
range  of  frost  action  have  remained  intact  and  uninjured  for  many  years.  Others  have  been 
seriously  disintegrated,  particularly  between  high  and  low  tide  levels.  The  disintegration  is 
evidently  often  due  in  part  to  frost  action,  but  chemical  action  is  frequently  indicated  by  the 
softening  of  the  mortar,  and  the  complete  disintegration  of  mortar  and  concrete  specimens 
by  subjection  to  the  action  of  sea  water  at  normal  temperatures  in  the  laboratory  has  been 
accomplished.  The  exact  nature  of  the  chemical  action  involved  cannot  be  definitely  stated. 
It  is  commonly  believed,  however,  that  the  magnesium  sulphate  in  the  sea  water  is  the  most 
injurious  constituent,  and  that  the  magnesium  chloride  and  calcium  chloride  are  somewhat 
less  active.  The  magnesium  sulphate  attacks  the  lime  in  the  cement,  also  the  alumina,  form- 
ing large  and  rapidly  growing  crystals  of  hydrated  magnesia  and  calcium  sulpho-aluminate. 
Both  magnesium  chloride  and  sodium  chloride  attack  the  silicates  of  the  cement. 

The  chemical  action  is  accompanied  by  various  physical  phenomena.  Sometimes  the  mass 
swells,  cracks,  and  gradually  falls  apart;  sometimes  the  mortar  softens  and  becomes  disinte- 
grated leaving  the  coarse  aggregate  exposed  and  finally  permitting  it  to  fall  away;  and  occa- 
sionally a  crust  forms  on  the  surface  which  later  cracks  off. 

An  important  symposium  of  European  investigators'  studies  of  the  problem  of  concrete 
in  sea  water  is  afforded  by  the  several  papers  of  Chapter  XVII  of  the  Proceedings  of  the  Sixth 
Congress  of  the  International  Association  for  Testing  Materials  held  in  New  York  in  1912. 

The  conclusions  arrived  at  from  a  study  of  important  German  and  Scandinavian  tests, 
have  been  expressed,  in  part,  as  follows  {Concrete  and  Constructional  Engineering,  January,  1910) : 

1.  Good  Portland  cements  such  as  are  now  on  the  European  market,  are  very  resistant  to  the  action  of  sea 
water.  A  marked  difference  in  the  behavior  of  cements  of  slightly  different  composition  has  not  been  found,  ex- 
cept that  a  high  proportion  of  aluminates  tends  to  cause  disintegration. 

2.  In  a  dense  mortar,  the  chemical  action  is  confined  to  an  outer  layer  of  small  depth,  further  action  being 
checked  by  the  slowness  of  diffusion.  A  porous  mortar,  by  admitting  salt  water  to  the  interior,  is  apt  to  crack  by 
expansion  owing  to  chemical  change. 

3.  The  main  agency  in  the  destruction  of  mortar  and  concrete  in  marine  embankments,  harbor  works,  groynes, 
etc.,  is  not  chemical  action,  but  the  alternations  of  saturation,  drying  in  the  sun,  freezing,  etc.,  due  to  the  alternate 
exposure  and  covering  by  the  rise  and  fall  of  the  tide. 

4.  The  denser  the  mortar  the  better  (1  cement  :3  sand  is  too  poor).  An  admixture  of  fine  sand  with  the 
ordinary  sand  increases  the  closeness  of  the  mixture.  A  well-graded  aggregate  would  be  advantageous  for  the 
same  reason. 

5.  The  addition  of  finely  ground  silica  or  trass  to  the  cement  before  mixing  is  possibly  advantageous  in  the 
case  of  weaker  mortars.    It  is  very  doubtful  whether  anything  is  gained  by  adding  trass  to  the  richer  mortars. 

6.  The  destructive  action  of  the  sea  being  mainly  physical  and  mechanical,  and  not  chemical,  tests  by  mere 
immersion  in  still  sea  water  are  of  very  little  value  in  determining  the  behavior  of  concrete  in  marine  engineering 
works.  A  mixture  which  disintegrates  under  this  test  is  certainly  useless,  but  a  mixture  which  passes  the  test 
may  disintegrate  under  the  more  stringent  conditions  of  practical  use. 

7.  As  long  a  period  as  is  practicable  should  be  allowed  for  the  hardening  of  concrete  blocks  before  placing 
in  the  sea. 

8.  The  behavior  of  test  specimens  for  the  first  12  months  is  very  irregular,  and  definite  conclusions  can  only 
be  drawn  from  the  results  of  long-period  tests. 

The  most  notable  American  investigations  of  the  subject  are  one  made  by  the  Bureau 
of  Standards  {Tech.  Paper  12)  and  one  begun  in  1908  by  the  Aberthaw  Construction  Co.  in 
cooperation  with  the  United  States  Navy  Department  (reported  in  a  pamphlet  issued  by  the 
Aberthaw  Construction  Co.  in  1914;  also  in  Eng.  Rec,  March  21,  1914).    Few  general  conclu- 


Sec.  &-38] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


257 


sions  may  be  drawn  from  the  results  of  the  first  5  years'  observations  of  the  Aberthaw  tests. 
This  is  particularly  true  since  European  experience  has  shown  that  the  first  indications  of 
injury  to  many  concretes  appear  only  after  from  5  to  10  years'  exposure,  and  in  some  cases  only 
after  more  than  20  years.  The  most  notable  indications  afforded  by  the  Aberthaw  tests  after 
5  years'  exposure  in  a  latitude  involving  wide  variations  of  temperature  and  frequent  freezing 
and  thawing,  are: 

1.  Concrete  which  is  alternately  immersed  and  exposed  as  the  tide  rises  and  falls  is  most 
subject  to  injury. 

2.  Lean  mixtures  (1:3:6)  are  very  much  more  subject  to  attack  than  rich  mixtures  (1:1 
:2),  and  medium  mixtures  (1:2:4)  are  more  vulnerable  than  rich  ones. 

3.  Concrete  mixed  with  a  plastic  or  even  a  very  wet  consistency  appears  to  withstand  sea 
water  attack  better  than  concrete  of  a  dry  consistency. 

4.  The  relative  immunity  from  attack  by  sea  water  of  concretes  made  with  cements  of 
various  classes,  including  a  low-iron  cement,  high-  low-  and  average-alumina  cements,  an  iron- 
ore  cement,  and  a  slag  Portland  cement,  has  not  been  conclusively  established. 

The  Joint  Committee  makes  the  following  recommendations  for  concrete  placed  in  sea 
water: 

To  effect  the  best  resistance  to  sea  water,  the  concrete  must  be  proportioned,  mixed,  and  placed  so  as  to 
prevent  the  penetration  of  sea  water  into  the  mass  or  through  the  joints.  The  aggregates  should  be  carefully 
selected,  graded,  and  proportioned  with  the  cement  so  as  to  secure  the  maximum  possible  density;  the  concrete 
should  be  thoroughly  mixed;  the  joints  between  old  and  new  work  should  be  made  water-tight;  and  the  concrete 
should  be  kept  from  exposure  to  sea  water  until  it  is  thoroughly  hard  and  impervious. 

38.  Action  of  Alkali. — The  effect  of  alkali  on  concrete  is  a  problem  resembling  in  many 
respects  that  of  the  action  of  sea  water  on  concrete.  The  problem  is  of  especial  interest  in 
connection  with  concrete  construction  in  the  arid  regions  of  the  West,  where  soluble  salts  are 
present  in  the  soil  to  an  extent  not  usually  found  elsewhere. 

The  principal  salts  encountered  in  alkali  waters  usually  include:  magnesium  sulphate, 
calcium  sulphate  and  sodium  sulphate,  magnesium  chloride,  sodium  chloride,  and  potassium 
chloride,  together  with  carbonates  of  magnesium,  sodium,  and  potassium.  Of  these  the 
sulphates  appear  to  be  most  active  in  causing  disintegration  of  concrete;  the  chlorides  also  are 
active,  while  the  carbonates  appear  to  be  without  effect. 

The  attempts  at  an  explanation  of  the  manner  of  attack  of  these  salts  upon  concrete 
have  hitherto  encountered  the  same  difficulty  found  in  the  case  of  sea  water — an  unsatisfactory 
knowledge  of  the  constitution  of  cement.  From  the  physical  point  of  view  the  action  exactly 
resembles  the  action  of  frost  except  that  it  is  more  rapid.  There  exists,  apparently,  a  disruptive 
force  which  quickly  destroys  the  bond  and  causes  disintegration.  This  action  appears  to 
proceed  most  rapidly  in  the  parts  of  a  structure  subjected  to  alternate  wetting  with  alkali 
water  and  drying  in  the  air.  In  porous  concrete  the  action  proceeds  much  more  rapidly  than  in 
dense  concrete,  where,  indeed,  it  may  make  no  progress  at  all. 

As  in  the  case  of  the  injurious  action  of  sea  water  on  concrete,  instances  of  failure  caused 
by  alkali  waters  are  merely  isolated  ones,  presenting  an  interesting  field  for  study,  but  not 
constituting  a  very  serious  menace  to  the  future  of  concrete  construction  in  the  arid  regions 
of  the  West.  The  remedy  in  the  present  state  of  our  knowledge  is,  as  in  the  case  of  marine 
structures,  a  matter  of  the  possible  physical  precautions  only — the  securing  of  the  densest 
possible  concrete,  thus  preventing  injury  by  the  exclusion  of  the  salt-bearing  waters. 

39.  Action  of  Acids,  Oils,  and  Sewage.— The  Joint  Committee  Report  makes  the  following 
statements  concerning  the  effect  of  acids  and  oils  upon  concrete : 

Dense  concrete  thoroughly  hardened  is  affected  appreciably  only  by  acids  which  seriously  injure  other 
materials.  Substances  like  manure,  that  contain  acids,  may  injuriously  affect  green  concrete,  but  do  not  affect 
concrete  that  is  thoroughly  hardened. 

Concrete  is  unaffected  by  such  mineral  oils  as  petroleum  and  ordinary  engine  oils.    Oils  which  contain  fatty 
acids  produce  injurious  effects,  forming  compounds  with  the  lime  which  may  result  in  a  disintegration  of  the  con- 
crete in  contact  with  them. 
17 


258 


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[Sec.  5-40 


The  use  of  concrete  sewer  pipes  has  led  to  considerable  study  of  the  effect  of  sewage  and 
sewage  gases  upon  concrete.  Sidney  H.  Chambers  concluded  from  an  investigation  reported 
before  the  Concrete  Institute  (Great  Britain)  in  1910: 

That  the  gases  in  solution  in  sewage  and  those  expelled  from  it,  arising  from  its  decomposition,  do  act  in- 
juriously upon  Portland-cement  concrete,  notwithstanding  the  fact  that  the  concrete  is  constituted  of  sound  and 
good  materials,  when  the  following  conditions  prevail:  (1)  A  high  degree  of  putrescence  of  the  sewage;  (2)  a  mois- 
tened surface,  which  held  or  absorbed  the  putrid  gases;  (3)  the  presence  of  a  free  air  supply.  Further,  that  in  the 
absence  of  one  or  the  other  of  the  above-enumerated  factors  little  danger  from  erosion  need  be  feared. 

Rudolph  Hering  is  responsible  for  the  following  statements  concerning  the  effect  of  the 
acids  in  sewage  upon  concrete  (quoted  from  a  report  to  the  President  of  the  Borough  of  Brook- 
lyn in  1908  by  Gustave  Kaufman  in  Proceedings  of  the  National  Association  of  Cement  Users, 
vol.  8,  1912,  p.  725). 

Portland  cement  used  for  the  manufacture  of  concrete  pipes  is  attacked  by  certain  strong  acids,  such  as 
sulphuric  acid,  which  converts  the  carbonate  into  sulphate  of  lime,  which  is  comparatively  soft  and  easily  eroded. 
Therefore  cement  pipe  cannot  be  used  where  strong  acids  are  known  to  enter  the  sewers. 

The  acid  question  should  be  viewed  in  a  reasonable  light.  When  the  dilution  of  sewage  is  sufficient  the 
discharge  of  a  small  amount  of  even  strong  acid  will  not  cause  objectionable  effects,  as  evidenced  by  European 
cities  where  the  use  of  concrete  sewers  is  almost  exclusive  in  some  cities,  as  Paris  and  Vienna.  In  England  concrete 
sewers  are  also  very  common. 

The  greasy  substance  which  is  usually  found  to  coat  the  perimeter  of  a  sewer  under  the  water  line  tends 
to  protect  the  cement  from  the  action  of  acids  to  some  extent. 

Over  400  miles  of  concrete  sewer  pipe  laid  in  the  City  of  Brooklyn  during  a  period  of  over 
50  years  are  giving  eminent  satisfaction. 

40.  Electrolysis  in  Concrete. — Experience  and  laboratory  tests  have  shown  that  under 
certain  conditions  concrete  may  be  seriously  damaged  by  electrolytic  action  caused  by  the 
flow  of  electric  current  between  the  concrete  and  iron  or  steel  embedded  therein.  The  phe- 
nomena assumes  importance  under  certain  conditions  of  use  of  reinforced  concrete,  also  the  use 
of  concrete  foundations  and  footings  in  which  the  bases  of  columns  of  buildings,  bridges,  and 
elevated  railway  structures  are  embedded.  A  very  important  laboratory  and  field  study  of 
the  entire  problem  has  been  made  by  the  U.  S.  Bureau  of  Standards,  and  the  conclusions  arrived 
at  in  this  investigation  constitute  the  authority  for  the  statements  made  here  {Tech.  Paper 
18,  Bureau  of  Standards). 

The  electrolytic  effect  differs  according  to  the  direction  of  flow  of  the  current.  If  elec- 
trically positive  iron  or  steel  is  in  contact  with  concrete  the  iron  will  become  corroded  provided 
the  concrete  is  moist  or  wet  and  the  potential  gradient  is  high  enough  to  heat  the  junction  to  a 
temperature  not  below  about  45°C.  (113°F.).  The  minimum  potential  gradient  found  effective 
in  causing  corrosion  in  moist  concrete  was  about  60  volts  per  ft.  Iron  when  corroded  expands 
to  about  2.2  times  its  original  volume  and  causes  mechanical  pressure  found  in  some  cases  to 
reach  values  as  high  as  4700  lb.  per  sq.  in.  This  causes  cracking  of  the  concrete.  The  passivity 
of  iron  below  45°C.  is  due  chiefly  to  the  inhibiting  effect  of  Ca(0H)2  in  the  concrete,  and  on 
this  account  old  concrete  in  which  the  Ca(0H)2  has  been  largely  carbonated  is  probably  more 
susceptible  to  electrolysis  than  new  concrete  in  the  same  moisture  condition.  For  air-dried 
concrete  a  much  higher  potential  gradient  is  required  to  produce  the  temperature  at  which 
corrosion  becomes  dangerous  than  for  moist  concrete.  Under  actual  conditions,  therefore, 
corrosion  from  stray  currents  may  be  expected  only  under  special  or  extreme  conditions. 
Normal  wet  concrete  carrying  current  also  increases  its  resistance  a  hundredfold  in  the  course 
of  a  few  weeks,  owing  partly  to  the  precipitation  of  CaCOs  which  fills  up  the  pores.  This 
further  lessens  danger  of  trouble. 

Electrolysis  of  the  concrete  in  contact  with  negative  iron  is  manifested  in  a  different  way. 
The  concrete  near  the  cathode  becomes  softened,  beginning  at  the  cathode  surface,  and  extend- 
ing to  a  depth  of  in.  or  more.  This  softening  practically  completely  destroys  the  bond 
between  iron  or  steel  and-concrete.  While  the  anode  effect  becomes  serious  in  normal  concrete 
only  on  comparatively  high  voltages,  decreases  much  more  rapidly  than  the  voltage,  and  almost 


Sec.  5-41] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


259 


I  disappears  at  voltages  likely  to  be  encountered  in  practice,  the  cathode  effect  develops  at  all 
I  voltages,  the  rate  being  roughly  proportional  to  the  voltage.    The  softening  effect  is  due  to 
the  gradual  concentration  of  alkalies,  Na  and  K,  near  the  cathode,  these  finally  becoming  strong 
enough  to  attack  the  cement.    The  cathode  effect  is  wholly  limited  to  the  vicinity  of  the  cath- 
ode, the  strength  of  the  mass  of  the  concrete  not  being  affected. 

Salt  or  calcium  chloride,  even  in  very  small  amounts  (a  fraction  of  1%),  multiplies  the 
rate  of  corrosion  of  iron  at  the  anode  many  hundredfold  because  it  increases  the  conductivity 
of  wet  concrete,  destroys  the  passivity  of  iron  at  ordinary  temperatures,  and  prevents  the 
increase  in  resistance  with  flow  of  current  by  preventing  the  precipitation  of  CaCOs.  Salt 
should  therefore  not  be  used  in  structures  subject  to  electrolytic  action,  and  special  considera- 
tion should  be  given  to  the  possibility  of  electrolytic  action  in  the  cases  of  all  concretes  exposed 
to  sea  water  or  salt  brine. 

The  danger  of  electrolysis  of  reinforced-concrete  structures  through  the  operation  of 
stray  currents  has  been  overestimated.    Certain  precautions  are  necessary  under  special 
conditions,  but  there  is  no  cause  for  serious  alarm.    Non-reinforced-concrete  structures  are 
1  practically  immune  from  injury  by  electrolysis. 

I  The  precautions  to  be  adopted  in  the  special  cases  where  electrolysis  is  to  be  feared  include 
avoidance  of  grounds  in  direct-current  circuits  in  buildings;  providing  insulating  joints  in 

'pipe  lines  which  enter  buildings  outside  the  walls;  completely  isolating  the  buildings  by  in- 
sulating joints  in  pipe  lines  which  enter  the  building  and  also  continue  on  beyond;  providing 
a  copper  cable  shunt  around  the  building  if  the  potential  drop  is  large;  isolating  from  the  con- 
crete lead-covered  cables  entering  the  building;  and  interconnecting  all  metal  work  in  the 
building  if  practicable,  but  without  connecting  this  metal  work  to  ground  plates  or  to  pipe 
lines  outside  of  the  insulating  joints. 

41.  Effect  of  Manure. — Manure,  is  occasionally  used  to  cover  up  fresh  concrete  in  freezing 
weather,  not  only  because  it  is  a  poor  conductor  of  heat  when  rather  dry,  but  also  because  its 
decomposition  is  a  source  of  heat.  Experience  has  shown  (see  Eng.  Neivs,  vol.  49,  pp.  11,  104, 
126,  127,  and  175;  also  Journal  of  the  New  England  Waterworks  Association,  vol.  22,  p.  242) 
that  manure  not  onlj^  discolors  the  work,  but  that  it  also  has  a  marked  disintegrating  effect  if 
placed  in  contact  with  freshly  placed  concrete.  The  injury  is  especially  pronounced  if  rain 
wets  the  manure  during  the  early  hardening  period  and  carries  the  uric  acid  into  the  concrete. 

ij  The  use  of  manure  as  a  preventive  of  freezing  of  fresh  concrete  may  be  considered  permissible 
j  only  if  the  work  is  covered  first  by  a  material  which  will  be  sufficiently  impermeable  to  prevent 
Ij  the  seepage  of  acid  into  the  concrete. 

j  Concrete  which  has  once  thoroughly  hardened  appears  not  to  be  susceptible  to  injury 
by  contact  with  manure  except  that  it  is  in  some  cases  somewhat  discolored. 

MISCELLANEOUS  PROPERTIES  OF  CEMENT 
j  MORTAR  AND  CONCRETE 

42.  Rise  of  Temperature  in  Setting. — The  chemical  combination  of  water  with  Portland 

cement  is  an  endothermic  reaction,  the  heat  evolved  being  sufficient  to  materially  raise  the 
temperature  of  mortars  and  concretes  during  the  period  of  setting  and  hardening.  The  total 
rise  in  temperature,  the  rate  of  increase,  and  the  time  interval  before  the  maximum  temperature 

I  is  reached  are  all  variable,  depending  upon  the  character  of  the  cement  used,  the  proportions  of 
the  mixture,  the  size  of  specimen  or  bulk  of  material  involved  (in  so  far  as  this  determines  the 
distance  of  the  point  at  which  temperatures  are  measured  from  any  exposed  surface  of  the 

i  material),  external  temperature  conditions,  the  amount  of  water  used  in  mixing,  etc. 

j  [  The  results  of  observations  of  temperatures  acquired  at  the  center  of  12-in .  cubes  of  cements 
and  mortars  tested  at  the  Watertown  Arsenal  (''Tests  of  Metals,"  1901,  p.  493),  are  shown  by 
Fig.  30a.    With  these  specimens  the  maximum  temperature  was  attained  in  from  12  to  18 


260 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-42 


hr.  except  in  the  case  of  natural  cements  which  reached  their  maximum  temperature  much  ear- 
lier. The  heating  effect  is  less  than  one-half  as  great  with  1 : 1  mortar  as  with  neat  cement,  and 
is  quite  small  with  leaner  mixtures. 


£12 
194 

1 158 
.0  140 

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S.86 
,2?  68 
50 
X 


100 
90 
80 
70 
p  60 


50 
§40 
30 
SO 
10 
0 


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Porn 

ind 

Portia 

nd 

p 

jrti 

ind 

i:3 

le    14    16   16    EO    22-  24  26   E8  30   32  34  36  38  40 

Time  in  hours 


Fig.  30a. — Rise  in  temperature  of  cement  and  mortar  in  setting  and  hardening.    (12-in.  cubes.) 

Radiation  has  a  great  deal  to  do  with  the  temperatures  observed  at  the  centers  of  these 
comparatively  small  specimens,  as  is  shown  by  comparison  of  the  curves  for  mortars  with  Fig. 
306  which  shows  the  rise  in  temperature  of  a  1  : 23^  :  6  concrete,  the  temperature  having  been 
measured  in  the  midst  of  a  very  large  mass  of  concrete  with  the  thermometer  covered  by  a 


Si 

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l5 

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lOE 

9a 

94 
90 
86 
82 
78 
74. 
70 
66 
62 
58 
54 

50 
46 


r  25' 


Approximate  depth 

4'  6.5' 


of  concrete  over  tViermometer 

6.5'  9' 


-. 

J 

t..: 

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«i 

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-\ 

- 

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u 

r— 
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icrete 

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1 

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1 

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-r 

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t- 

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4 

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4. 

T 

4 
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i  over 

1 

t- 

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1 

r 

t 

O. 

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p- 

1 

1 

t- 

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1 

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t- 

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1 

4- 

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1 

4 

t 

V 

t- 

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+ 
4 

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8 

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V 

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«. 

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1  with  fresh  concrete  | 

t 

1 

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r 

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+ 

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4 

-4 

4 

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1 

4 

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1 

1 

1 

\ 

1 

T 

s 

^ 

EG 


40 


60  80  100 

Time  in  hours 


120 


140 


160 


180 


Fig.  306. — Rise  in  temperature  of  mass  concrete  in  setting  and  hardening. 

II  part  sand-cement, 
parts  sand. 
D  parts  gravel, 
2  parts  large  cobbles. 
Dotted  lines  indicate  daily  variation  in  atmospheric  temperature. 


depth  of  from  1  to  9  ft.  of  concrete  as  indicated.  Fig.  306  constitutes  a  portion  of  a  report 
upon  an  investigation  of  the  temperature  changes  in  mass  concrete  made  during  the  construc- 
tion of  the  Arrowrock  Dam  by  the  United  States  Reclamation  Service  near  Boise,  Idaho  ("Tem- 
perature Changes  in  Mass  Concrete"  by  Charles  H.  Paul  and  A.  B.  Mayhew,  Tran^,  Am.  Soc. 


Sec.  5-43]  CEMENT  MORTAR  AND  PLAIN  CONCRETE  261 

C.  E.,  vol.  79,  p.  1225,  1915).  A  summary  of  the  results  obtained  in  these  tests  is  given  in  the 
following  table. 


Temperature  Changes  in  Mass  Concrete 
Arrowrock  Dam  Tests 


Proportions  of  mix  (parts  by  volume) 

Distance 
to  nearest 
face  (ft.) 

Depth  of 
concrete  over 

Rise  in 
temperature 

Highest 
temperature 

Time 
reaching 
highest  tem- 
perature, hr. 

Sand  cement 

Sand 

Gravel 

Cobbles 

thermometer 
(ft.) 

in  degrees 
Fahr. 

in  degrees 
Fahr. 

*1 

2 

4 

23^ 

1.0 

2.0 

2.5 

78.0 

1 

*1 

2 

4 

2.0 

1.5 

3.6 

77.6 

1 

5 

2 

10.0 

35.0 

16.6 

91.6 

32 

2 

1^ 

3.0 

3.0 

19.5 

74.5 

5 

2^ 

6 

2 

19.5 

3.5 

20.6 

64.6 

15 

2M 

4 

3.5 

6.0 

26.9 

69.8 

5 

2^ 

6 

2 

76.0 

15.5 

27.5 

94.0 

31 

23^ 

2^ 

31.0 

80.0 

35.7 

96.2 

101 

2^ 

6 

2 

20.0 

28.5 

36.7 

86.2 

45 

*  Thermometer  bedded  in  fresh  concrete  in  shallow  trench  dug  in  concrete  11  days  old. 


Similar  tests  made  during  the  construction  of  the  Kensico  Dam  at  Valhalla,  N.  Y.,  by- 
George  T.  Seabury,  are  reported  to  have  established  that  {Proc.  Am.  Soc.  C.  E.,  vol.  29,  p.  1247- 
1253): 

With  the  1:3:6  concrete  used,  thermometers  being  inserted  as  soon  as  the  concrete  was  placed  and  immedi- 
ately covered  to  as  great  a  depth  as  possible,  the  rise  in  temperature  was  uniformly  about  40°F. 

The  maximum  concrete  temperature  reached  was  often  well  above  100°F.  in  summer,  in  one  instance,  118.5". 
This  maximum  was  usually  reached  in  about  15  days. 

The  rate  of  increase  in  temperature  was  about  1**  per  hr.  for  4  or  5  hr.  gradually  increased  to  8°-10°  per  hr. 
during  the  period  of  final  set  of  the  cement,  and  then  dropped  suddenly  to  about  H**  per  hr.  for  a  considerable 
time.    A  total  rise  in  temperature  of  from  25"  to  SO^F.  often  occurred  subsequent  to  the  period  of  final  setting. 

43.  Porosity. — The  porosity  of  a  mortar  or  concrete  is  expressed  by  the  percentage  of  void 
space  (space  filled  by  air  or  uncombined  water)  in  terms  of  the  total  volume.  It  is  determined 
experimentally  by  subtracting  from  the  total  apparent  volume  the  volume  of  solid  matter  and 
dividing  by  the  total  apparent  volume.  The  total  apparent  volume  may  be  determined  by 
direct  measurement  or  by  determination  of  the  volume  of  water  it  displaces,  absorption  being 
prevented  by  a  waterproof  coating  of  grease  or  varnish.  The  volume  of  solid  matter  is  deter- 
mined by  weighing  the  specimen  dry  in  air,  and  subsequently  in  water  after  the  pores  of  the 
material  have  been  thoroughly  impregnated  with  water.  The  difference  in  these  weights 
divided  by  the  weight  of  a  unit  volume  of  water  is  the  volume  of  solid  matter.  Extreme  accu- 
racy in  determining  porosity  is  not  possible  because  of  the  difficulty  encountered  in  completely 
fiilling  all  the  voids  in  the  material. 

The  porosity  of  mortars  and  concretes  is  principally  dependent  upon  the  consistency  of  the 
mixture,  and  the  granularmetric  composition  of  the  aggregates.  Plastic  or  wet  consistencies 
will  in  general  produce  mortars  having  less  void  space,  and  therefore  lower  porosity,  than  dry 
consistencies,  and  a  well-graded  aggregate  will  form  less  porous  mortar  than  one  whose  particles 
are  not  well  graded  in  size.  A  concrete  will  usually  be  considerably  less  porous  than  a  mortar 
because  of  its  proportion  of  comparatively  non-porous  coarse  aggregate,  and  a  fine-sand  aggre- 
gate will  in  general  produce  more  porous  mortar  than  a  coarse  sand  because  of  the  larger  amount 
of  water  required  in  gaging  the  latter. 

The  porosity  of  mortars  will  usually  be  found  within  the  limits  of  15%  and  30%,  an  average 
1 : 2  mortar  showing  20  to  25 %  porosity.    Concretes  show  from  about  12  to  about  20  %  porosity, 


262 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  5-44 


the  lower  figure  applying  to  concretes  having  a  relatively  large  proportion  of  coarse  aggregate 
and  the  higher  figure  to  concretes  having  a  relatively  low  proportion  of  coarse  aggregate. 

44.  Permeability  and  Absorptive  Properties. — The  permeability  of  mortar  or  concrete  is  a 
measure  of  the  rate  at  which  water  under  a  given  pressure  will  pass  through  a  given  thickness 
of  the  material.  The  absorptive  properties  of  a  mortar  or  concrete  constitute  a  measure  of  the 
rate  at  which  moisture  will  be  absorbed  when  the  material  is  exposed  in  damp  situations  or 
covered  with  water  under  negligibly  small  heads. 

Permeability  is  an  important  consideration  where  water-tightness  of  walls,  etc.,  is  re- 
quired and  percolation  of  water  is  not  admissible. 

Absorptive  properties  of  a  mortar  determine  its  value  as  a  dampproofing  coat,  particularly 
in  the  event  of  its  use  as  a  plaster  over  metal  lath,  which  must  be  protected  to  prevent  corrosion. 
In  view  of  the  disintegrating  effect  of  expansion  and  contraction  of  mortars  used  as  a  plaster, 
etc.,  the  moisture  content  (which  largely  affects  this  expansion  and  contraction)  should  not  be 
greatly  variable.  Thus  the  least  absorptive  mortar  will  be  most  durable,  up  to  the  limit 
reached  when  the  cement  content  is  relatively  so  high  that  the  expansion  and  contraction  is 
disproportionately  increased. 

The  determining  of  precise  information  concerning  each  of  these  properties  is  dependent 
upon  a  standardization  of  methods  of  conducting  tests.  Such  standard  methods  have  not 
yet  been  adopted,  and  it  is  therefore  impossible  to  quote  data  as  to  the  absolute  permeability 
or  absorptive  power  of  mortars. 

Tests  to  determine  the  relative  permeability  and  absorptive  power  of  mortars  were  made 
at  the  Structural  Materials  Laboratory  as  St.  Louis  in  1909,  and  are  reported  in  Technologic 
Paper  3  of  the  Bureau  of  Standards.  Owing  to  the  small  number  of  tests  made  and  certain 
unsatisfactory  features  of  the  testing  method  employed,  only  a  few  general  conclusions  will 
be  drawn  from  the  report  of  these  tests.  (1)  Permeability  decreases  rapidly  for  all  mixtures 
with  increase  in  age  of  the  specimens  when  tested;  (2)  permeability  decreases  considerably 
with  the  continuation  of  the  flow;  (3)  permeability  increases  with  the  leanness  of  the  mixture, 
the  dryness  of  the  mixture,  and  increased  coarseness  of  the  sand. 

Absorption  was  found  to  be  dependent  upon  the  same  factors:  it  decreased  with  the  age 
of  the  mortar  as  a  rule,  but  not  as  rapidly  as  did  the  permeability  (especially  with  the  leaner 
mixtures);  it  decreased  but  slightly  with  increased  richness  of  the  mixtures;  and  the  wetter 
mixtures  were  slightly  less  absorptive  than  the  dryer  mixtures. 

The  permeability  of  mortars  and  concrete  is  closely  related  to  the  porosity,  but  the  relation- 
ship is  not  always  direct,  and  is  by  no  means  constant,  since  the  continuity  and  size  of  the  pores 
determines  permeability  more  than  does  the  actual  percentage  of  voids. 

The  Joint  Committee  Report  says  concerning  the  permeability  and  the  waterproofing  of 
concrete : 

Many  expedients  have  been  resorted  to  for  rendering  concrete  impervious  to  water.  Experience  shows, 
however,  that  when  concrete  or  mortar  is  proportioned  to  obtain  the  greatest  practicable  density  and  is  mixed  to 
the  proper  consistency,  the  resulting  mortar  or  concrete  is  impervious  under  moderate  pressure. 

On  the  other  hand,  concrete  of  dry  consistency  is  more  or  less  pervious  to  water,  and  though  compounds  of 
various  kinds  have  been  mixed  with  the  concrete  or  applied  as  a  wash  to  the  surface,  in  an  effort  to  offset  this 
defect,  these  expedients  have  generally  been  disappointing,  for  the  reason  that  many  of  these  compounds  have  at 
best  but  temporary  value,  and  in  time  lose  their  power  of  imparting  impermeability  to  the  concrete. 

In  the  case  of  subways,  long  retaining  walls  and  reservoirs,  provided  the  concrete  itself  is  impervious,  cracks 
may  be  so  reduced,  by  horizontal  and  vertical  reinforcement  properly  proportioned  and  located,  that  they  will 
be  too  minute  to  permit  leakage,  or  will  be  closed  by  infiltration  of  silt. 

Asphaltic  or  coal-tar  preparations  applied  either  as  a  mastic  or  as  a  coating  on  felt  or  cloth  fabric,  are  used 
for  waterproofing,  and  should  be  proof  against  injury  by  liquids  or  gases. 

For  retaining  and  similar  walls  in  direct  contact  with  the  earth,  the  application  of  one  or  two  coatings  of 
hot  coal-tar  pitch,  following  a  painting  with  a  thin  wash  of  coal-tar  dissolved  in  benzol,  to  the  thoroughly  dried 
surface  of  concrete  is  an  efficient  method  of  preventing  the  penetration  of  moisture  from  the  earth. 

45.  Protection  of  Embedded  Steel  From  Corrosion.^ — The  Joint  Committee  Report  says 
concerning  the  corrosion  of  metal  reinforcement  in  concrete : 


Sec.  &-46] 


CEMENT  MORTAR  AND  PLAIN  CONCRETE 


263 


Tests  and  experience  indicate  that  steel  sufficiently  embedded  in  good  concrete  is  well  protected  against 
corrosion,  no  matter  whether  located  above  or  below  water  level.  It  is  recommended  that  such  protection  be  not 
less  than  1  in.  in  thickness.  If  the  concrete  is  porous  so  as  to  be  readily  permeable  by  water,  as  when  concrete  is 
laid  with  a  very  dry  consistency,  the  metal  may  corrode  on  account  of  the  presence  of  moisture  and  air. 

The  historic  tests  made  by  Prof.  C,  L.  Norton  for  the  Insurance  Engineering  Station  in 
Boston  in  1902  led  to  the  following  conclusions  the  validity  of  which  has  never  been  disproved  by 
either  tests  or  experience  {Eng.  News,  vol.  48,  p.  333) : 

1.  Neat  Portland  cement,  even  in  thin  layers,  is  an  effective  preventive  of  rusting. 

2.  Concretes,  to  be  effective  in  preventing  rust,  must  be  dense  and  without  voids  or  cracks.  They  should 
be  mixed  quite  wet  where  applied  to  the  metal. 

3.  The  corrosion  found  in  cinder  concrete  is  mainly  due  to  the  iron  oxide,  or  rust,  in  the  cinder,  and  not 
to  the  sulphur. 

4.  Cinder  concrete,  if  free  from  voids  and  well  rammed  when  wet,  is  about  as  effective  as  stone  concrete  in 
protecting  steel. 

Further  tests  made  by  Prof.  Norton  in  1903  showed  conclusively  that  steel  reinforcement, 
corroded  before  being  embedded  in  concrete,  does  not  corrode  further,  provided  only  that  it 
has  a  continuous  unbroken  coating  of  concrete.  This  fact  is  important  since  it  is  almost  impos- 
sible to  prevent  exposure  of  reinforcing  steel  on  construction  work  to  the  elements,  and  a  large 
proportion  of  such  steel  is  therefore  corroded  when  placed  in  the  work. 

Experience  has  abundantly  shown  that  if  concrete  be  mixed  sufficiently  wet  so  that  it  will 
flow  about  the  reinforcement  with  only  a  moderate  amount  of  puddling,  the  thin  film  of  rich 
mortar  which  coats  the  steel  affords  a  perfect  preventive  of  corrosion. 

46.  Weight  of  Mortar  and  Concrete. — The  weight  of  mortars  and  concretes  varies  with  the 
proportions  of  the  mixture,  the  consistency  used  in  mixing,  and  the  character  and  granular- 
metric  composition  of  the  aggregates.  William  B.  Fuller  found  the  following  range  of  weights 
of  mortars  of  various  proportions  made  with  the  same  sand  and  cement : 


1:1 

1:2 

1:3 

1:4 

1:5 

1:6  1:7 

145.1 

143.3 

140.0 

137.7 

138.6 

135.5  137.6 

The  Bureau  of  Standards  found  the  following  relation  between  weight  of  gravel  concrete 
and  the  proportions  of  mixture  (Tech.  Paper  58): 


Proportions  of  mixture  

1:1:2 

1:13^:3 

1:2:4 

1:23^:5 

1:3:6 

1:4:8 

Ave.  weight  (lb.  per  cu.  ft.)  

147 

145 

144 

143 

142 

140 

The  same  series  of  tests  of  the  Bureau  of  Standards  indicate  the  following  relations  to  hold 
between  weight  and  consistency: 

The  cinder  concrete  appears  to 
be  slightly  heavier  the  wetter  the 
mixture,  but  all  of  the  rock  con- 
cretes are  slightly  heavier  the  drier 
the  mixture.  No  universally  appli- 
cable relation  between  weight  of 
concrete  and  the  class  of  aggregate 
used  is  shown  by  tests.  Different 
gravel  concretes,  for  instance,  will 
show  greater  variations  in  weight 
than  the  difference  in  average  weight  of  gravel  concretes  and  granite  concretes.  For  pur- 
poses of  design  the  weight  of  any  class  of  stone  concrete  may  be  assumed  to  be  150  lb.  per 
cu.  ft.,  while  cinder  concrete  may  be  assumed  to  weigh  115  lb.  per  cu.  ft. 


Proportions  by 
volume 
1:2:4 
Coarse  aggregate 

Weight  per  cubic  foot 

Watery  or 

fluid 
consistency 

Soft,  mushy 
consistency 

Stiff  quaking 
consistency 

Cinder  

115.2 

114.9 

113.1 

Granite  

147.6 

147.7 

148.9 

139.6 

142.7 

144.5 

Limestone  

144.7 

145.9 

147.8 

SECTION  6 


GENERAL  PROPERTIES  OF  REINFORCED  CONCRETE 

1.  Advantages  of  Combining  Concrete  and  Steel.— Steel  can  be  put  into  a  form  to  resist 
a  given  tensile  stress  much  more  cheaply  than  to  resist  an  equal  amount  of  compressive  stress. 
This  comes  from  the  fact  that  the  solid  bar  is  well  adapted  to  take  tensile  stresses,  while  for 
compressive  stresses  the  steel  must  be  made  into  forms  of  more  extended  cross-section  in  order 
to  provide  sufficient  lateral  rigidity.  Other  facts  to  be  noted  are  the  lack  of  durability  of 
steel  in  many  locations  and  its  failure  to  stand  up  under  a  high  heat. 

Concrete,  on  the  other  hand,  cannot  be  used  in  tension  except  to  a  very  limited  extent, 
but  its  compressive  strength  is  sufficiently  high  to  be  of  structural  importance.  It  is  also  a  good 
fireproof  material  and  has  great  durability.  In  addition,  concrete  is  a  cheaper  material  than 
I  steel,  can  readily  be  obtained  in  almost  any  locality,  and  tests  and  the  results  of  observations 
show  that  it  thoroughly  protects  embedded  steel  from  corrosion. 

From  the  above  considerations  it  follows  that  the  advantages  to  be  gained  by  using  con- 
crete reinforced  with  steel  instead  of  either  material  separately  will  vary  with  different  types 
of  structures.  In  structural  members  subjected  to  both  tension  and  compression,  as  in  all 
forms  of  beams,  the  proper  combination  of  the  two  materials  meets  with  the  best  success. 
Steel  rods  embedded  in  the  lower  side  of  the  beam  carry  the  tensile  stresses  while  the  compressive 
stresses  are  carried  by  the  concrete.  Here  the  steel  is  used  in  its  cheapest  form  and  the  con- 
struction may  be  made  strong,  economical,  and  very  durable.  In  compressive  members  of 
appreciable  length,  such  as  columns,  a  combination  of  the  two  materials  is  also  quite  advanta- 
geous, although  to  a  varying  degree  depending  upon  whether  the  reinforcing  steel  is  used  in 
the  form  of  small  rods  or  as  structural-steel  shapes. 

2.  Bond  Between  Concrete  and  Steel. — Most  of  the  tests  on  bond  have  been  made  by 
embedding  a  short  reinforcing  bar  in  a  block  of  concrete  and  pulling  it  out  in  a  testing  machine. 
In  the  kind  of  tests  referred  to,  the  concrete  is  in  compression  and  conditions  do  not  correspond 
to  those  ordinarily  encountered  in  beams  and  slabs.  Pull- 
out  tests  of  this  character,  however,  have  been  found  to  be 
of  valuable  aid  in  determining  actual  values  for  bond.  This 
conclusion  was  reached  through  an  extended  series  of  ex- 
periments at  the  University  of  Illinois  during  the  period 
1909-1912;  a  series  which  include  both  pull-out  tests  and  Fig.  l. 

beam  tests,  as  described  further  on  in  this  article. 

In  a  series  of  experiments  made  at  the  University  of  Wisconsin,  test  beams  were  arranged 
as  shown  in  Fig.  1,  the  reinforcing  bars  being  embedded  only  a  short  distance  from  each  end, 
leaving  the  middle  portion  exposed.  The  stress  in  the  rods  were  computed  from  the  observed 
deformations.  The  beam  was  prevented  from  failing  in  the  early  stages  of  the  tests,  by  an 
upper  set  of  auxiliary  rods.  Failure  finally  occurred  by  the  pulling  out  of  the  lower  rods,  as 
intended.  Pull-out  tests  were  also  made  with  concrete  cylinders  and  rods  arranged  as  shown 
in  Fig.  2.  Cylinders  designated  as  (a)  were  tested  in  the  ordinary  way  with  their  upper  surfaces 
bedded  against  the  lower  face  of  the  puUing  head.  In  cylinders  (6)  tension  was  applied  to 
both  upper  and  lower  rods,  bringing  tension  also  in  the  concrete.  The  principal  conclusions 
arrived  at  were  as  follows  (the  word  static  is  used  in  connection  with  beams  progressively 
tested  to  failure  under  loads  gradually  applied,  and  the  word  repeated  occurs  in  connection 
with  those  beams  subjected  to  repeated  loadings)  :^ 

1  Bull.  5,  vol.  5,  University  of  Wisconsin. 

265 


266 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  6-2 


The  static  bond  between  1:2:4  concrete  and  plain  round  steel  rods  increases  with  age  at  least  up  to  6  months. 
About  80%  of  the  6  months'  bond  strength  is  developed  in  1  month. 

Owing  to  the  variation  in  the  results  of  individual  tests  and  the  difference  between  laboratory  and  practical 
working  conditions,  it  does  not  seem  as  though  the  maximum  static  bond  between  concrete  of  the  class  used  and 
plain  rods  less  than  %  in.  diameter  should  be  assumed  greater  than  250  lb.  per  sq.  in.  or  for  the  rods  or  larger  size 
200  lb.  per  sq.  in. 

The  method  of  making  bond  tests  by  pulling  a  rod  from  a  cylinder  of  concrete  in  such  a  manner  that  the 
concrete  around  the  rod  is  compressed  gives  results  which  are  neither  of  quantitative  nor  qualitative  value.  The 
results  obtained  are  dependent  largely  upon  the  compressive  stress  acting  on  the  head  of  the  cylinder.  Cylinder 
tests  in  which  the  rod  and  concrete  are  both  subjected  to  a  tensile  stress  give  results  more  in  accord  with  the  bond 
values  obtained  from  beam  tests. 

The  static  bond  between  the  class  of  concrete  employed  and  corrugated  bars  is  about  twice  as  great  as  that 
which  can  be  developed  with  plain  round  rods  of  about  the  same  size.  The  static  bond  between  concrete  and  rusted 
rods  is  very  much  greater  than  that  obtained  where  plain  round  rods  are  used. 

From  the  tests  under  repeated  loadings  it  seems  evident  that  50  to  60%  of  the  static  bond  between  concrete 
and  plain  round  rods  may  be  repeated  a  large  number  of  times  without  failure  in  bond;  that  60  to  70%  are  the 
corresponding  figures  for  corrugated  bars.  Under  repeated  loadings  the  bond  between  concrete  and  rusted  round 
rods  is  considerably  greater  than  that  between  concrete  and  plain  round  rods. 

Considering  the  severity  of  the  tests  made  there  seems  to  be  no  valid  reason  for  believing  that  the  bond  be- 
tween concrete  and  plain  round  rods  will  be  destroyed  under  repeated  loadings,  providing  a  proper  working  value  is 
used.    Such  a  value  for  concrete  of  the  class  used  in  these  tests  should  not  be  over  50  lb.  per  sq.  in. 

1Q In  tests  at  the  University  of  Illinois,  attention  was  given  to 
_ .  j-y    obtaining  accurate  measurement  of  slip  of  bar  through  the  concrete 
i!         i     as  the  loading  progressed,  in  both  the  ordinary  pull-out  tests  and  in 
■—-^          '■ '         '•     tests  on  beams.    In  the  beams  of  this  series  the  concrete  was  not  cut 
away  from  the  rods  as  in  the  tests  at  the  University  of  Wisconsin. 

In  the  pull-out  tests  the  amount  of  movement  of  the  free  end 
of  the  embedded  bar  was  measured  by  means  of  an  Ames  gage. 
In  the  beam  tests,  the  Ames  gage  was  used  to  measure  center  deflec- 
tions and  the  movement  of  the  ends  of  the  reinforcing  bars.  In 
many  of  the  tests,  observations  were  also  made  on  the  amount  of 
slip  of  the  reinforcing  bar  with  respect  to  the  adjacent  concrete  at 
several  points  along  the  length  of  the  beam. 

The  concrete  blocks  used  in  the  pull-out  tests  were  usually  8  in. 
in  diameter  and  8  in.  long,  with  the  bar  embedded  axially.  The 
beams  tested  were  8  by  12  in.  in  section  with  an  effective  depth  of  10 
in.  The  span  length  was  generally  6  ft.  All  beams  were  tested 
with  two  symmetrical  loads,  generally  at  the  one-third  points  of  the 
span.  With  the  exception  of  six  tests,  the  longitudinal  reinforce- 
ment consisted  of  a  jingle  bar  of  large  diameter  placed  horizontally  throughout  the  length  of 
the  beam.    The  principal  results  of  these  tests  and  the  conclusions  reached  were  as  follows:^ 


(a) 


Fig.  2. 


Pull-out  Tests 

Bond  between  concrete  and  steel  may  be  divided  into  two  principal  elements,  adhesive  resistance  and  sliding 
resistance.  The  source  of  adhesive  resistance  is  not  known,  but  its  presence  is  a  matter  of  universal  experience 
with  materials  of  the  nature  of  mortar  and  concrete.  Sliding  resistance  arises  from  inequalities  of  the  surface  of 
the  bar  and  irregularities  of  its  section  and  alignment  together  with  the  corresponding  conformations  in  the  con- 
crete. The  adhesive  resistance  must  be  overcome  before  sliding  resistance  comes  into  action.  In  other  words, 
the  two  elements  of  bond  resistance  are  not  effective  at  the  same  time  at  a  given  point.  Many  evidences  of  the 
tests  indicate  that  adhesive  resistance  is  much  the  more  important  element  of  bond  resistance. 

Relation  of  Bond  Stress  to  Slip  of  Bar  as  Load  Increases. — Pull-out  tests  with  plain  bars  show  that  a  con- 
siderable bond  stress  is  developed  before  a  measurable  slip  is  produced.  Slip  of  bar  begins  as  soon  as  the  adhesive 
resistance  is  overcome.  After  the  adhesive  resistance  is  overcome,  a  further  slip  without  an  opportunity  of  rest 
is  accompanied  by  a  rapidly-increasing  bond  stress  until  a  maximum  bond  resistance  is  reached  at  a  definite  amount 
of  slip  (see  Fig.  3). 

1  Bull.  71,  Engineering  Experiment  Station,  University  of  Illinois. 


Sec.  6-2] 


GENERAL  PROPERTIES  OF  REINFORCED  CONCRETE 


267 


The  true  relation  of  slip  of  bar  to  bond  stress  can  best  be  studied  by  considering  the  action  of  a  bar  over  a 
very  short  section  of  the  embedded  length.  The  difficulties  arising  from  secondary  stresses  made  it  impracticable 
to  conduct  tests  on  bars  embedded  very  short  lengths.  The  desired  results  (Fig.  3)  were  obtained  by  varying 
the  forms  of  the  specimens  in  such  a  way  that  the  effect  of  different  combinations  of  dimensions  could  be  studied. 

Pull-out  tests  with  plain  bars  of  the  same  size  embedded  different  lengths  furnish  data  which  suggest  the 
values  of  bond  resistance  over  a  very  short  length  of  embedment,  or  indicate  values  of  bond  resistance  which  are 
independent  of  the  length  of  embedment.  Tests  with  bars  of  different  size  which  were  embedded  a  distance 
proportional  to  their  diameters  give  the  true  relation  when  the  effect  of  size  of  bar  is  eliminated.  Two  series  of 
tests  of  this  kind  on  plain  round  bars  of  ordinary  mill  surface  gave  almost  identical  values  for  bond  resistance  after 
eliminating  the  effect  of  length  of  embedment  and  size  of  bar,  and  we  may  consider  that  these  values  represent  the 
stresses  which  were  developed  in  turn  over  each  unit  of  area  of  the  embedded  bar  as  it  was  withdrawn  by  a  load 
applied  by  the  method  used  in  these  tests.  These  tests  showed  that  for  concrete  of  the  kind  used  (a  1  :  2  : 4  mix, 
stored  in  damp  sand  and  tested  at  the  age  of  about  60  days)  the  first  measurable  slip  of  bar  came  at  a  bond  stress 
of  about  260  lb.  per  sq.  in.,  and  that  the  maximum  bond  resistance  reached  an  average  value  of  440  lb.  per  sq.  in. 
If  we  conclude  that  adhesive  resistance  was  overcome 
at  the  first  measurable  slip,  it  will  be  seen  that  the  ad- 
hesive resistance  was  about  60%  of  the  maximum  bond 
resistance.  This  ratio  did  not  vary  much  for  a  wide 
range  of  mixes,  ages,  size  of  bar,  condition  of  storage, 
etc. 

Sliding  resistance  reached  its  maximum  value 
for  plain  bars  of  ordinary  mill  surface  at  a  slip  of 
about  0.01  in.  The  constancy  in  the  amount  of  slip 
corresponding  to  the  maximum  bond  resistance  for  a 
wide  range  of  mixes,  ages,  sizes  of  bar,  conditions  of 
storages,  etc.,  is  a  noteworthy  feature  of  the  tests. 
With  further  slip  the  sliding  resistance  decreased 
slowly  at  first,  then  more  rapidly,  until  with  a  slip  of 
0.1  in.  the  bond  resistance  was  about  one-half  its  maxi- 
mum value. 

Bond  Resistance  in  Terms  of  Compressive 
Strength  of  Concrete. — Pull-out  tests  with  plain  round 
bars  show  end  slip  to  begin  at  an  average  bond  stress 
equal  to  about  one-sixth  the  compressive  strength  of 
6-in.  cubes  from  the  same  concrete;  the  maximum  bond 
resistance  is  equal  to  about  one-fourth  the  compres- 
sive strength  of  6-in.  cubes.  These  values  were  about 
the  same  for  a  wide  range  of  mixes,  ages,  and  conditions 
of  storage.  In  terms  of  the  compressive  strength  of  8 
by  16-in.  concrete  cylinders  these  values  would  be  about 
13%for  first  end  slip  and  19%  for  the  maximum  bond 
resistance. 

Distribution  of  Bond  Stress  Along  a  Bar. — The 

tests  indicate  that  bond  stress  is  not  uniformly  dis- 
tributed along  a  bar  embedded  any  considerable  length 
and  having  the  load  applied  at  one  end.  Slip  of  bar 
begins  first  at  the  point  where  the  bar  enters  the  con- 
crete, and  the  bond  stress  must  be  greater  here  than  elsewhere  until  a  sufficient  slip  has  occurred  to  develop  the 
maximum  bond  resistance  at  this  point.  SUp  of  bar  begins  last  at  the  free  end  of  the  bar.  After  slip  becomes 
general,  there  is  an  approximate  equality  of  bond  stress  throughout  the  embedded  length. 

Variation  of  Bond  Resistance  with  Size,  Shape,  and  Condition  of  Surface  of  Bar. — The  maximum  bond 
resistance  was  not  materially  different  for  bars  of  different  diameters. 

Rusted  bars  gave  bond  resistances  about  15%  higher  than  similar  bars  with  ordinary  mill  surface. 

The  tests  with  flat  bars  showed  wide  variations  of  bond  resistance  and  were  not  conclusive.  Square  bars 
gave  values  of  unit  stress  about  75  %  of  those  obtained  with  plain  round  bars. 

T-bars  gave  lower  unit  bond  resistance  than  plain  round  bars,  but  gave  about  double  the  bond  resistance 
per  unit  of  length  that  was  found  for  the  plain  round  bars  of  the  same  sectional  area. 

With  polished  bars  the  bond  resistance  is  due  almost  entirely  to  adhesion  between  the  concrete  and  steel. 
Numerous  tests  with  polished  bars  embedded  in  1:2:4  concrete  and  tested  at  60  days  indicated  a  maximum  bond 
resistance  of  about  160  lb.  per  sq.  in.,  or  about  60%  of  the  bond  resistance  of  bars  of  ordinary  surface  at  small 
amounts  of  slip. 

Adhesive  resistance  must  be  destroyed,  sliding  resistance  largely  overcome,  and  the  concrete  ahead  of  the 
projections  must  undergo  an  appreciable  compressive  deformation  before  the  projections  on  a  deformed  bar 
become  effective  in  taking  bond  stress.  The  tests  indicate  that  the  projections  do  not  materially  assist  in  re- 
sisting a  force  tending  to  withdraw  the  bar  until  a  sUp  has  occurred  approximating  that  corresponding  to  the 


1 
to  200 


100 


Fig.  3. 


•  /g-/n  corrugated  rounds, 

Embedmeni-  varable. 

♦  l^-in  plain  rounds, 

Embedment-  mriable. 
o  Plain  rounds,  D/amefer 
and  embednient  yar/ab/e 


IS -4  concref-e. 
Age  about  2  monttis. 

I    I    I  I  L 


.01 


.OZ  .03  .04-  .05 

Slip  of  Bar -Inches 

-Relation  of  bond  to  slip  of  bar  as  load  increases. 


268 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  6-2 


maximum  sliding  resistance  of  plain  bars.  As  slip  continues  a  larger  and  larger  portion  of  the  bond  stress  is  taken 
by  direct  bearing  of  the  projections  on  the  concrete  ahead. 

In  determining  the  comparative  merits  of  deformed  bars,  the  bar  which  longest  resists  beginning  of  slip 
should  be  rated  highest,  other  considerations  being  equal. 

The  concrete  cylinders  of  the  pull-out  specimens  with  deformed  bars  were  reinforced  against  bursting  or 
splitting,  because  it  was  desired  to  study  the  load-slip  relation  through  a  wide  range  of  values.  In  only  a  few  tests 
was  the  maximum  bond  resistance  reached  at  an  end  slip  less  than  0.1  in.  It  should  be  recognized  that,  in  general, 
the  bond  stresses  reported  for  deformed  bars  at  end  slip  of  0.05  and  0.1  in.  could  not  have  been  developed  with 
bars  embedded  in  unreinforced  blocks.  These  high  values  of  bond  resistance  must  not  be  considered  as  available 
under  the  usual  conditions  of  bond  action  in  reinforced-concrete  members.  In  the  tests  in  which  the  blocks  were 
not  reinforced,  evidence  of  splitting  of  the  blocks  was  found  at  end  slips  of  0.02  to  0.05  in. 

The  normal  components  of  the  bearing  stresses  developed  by  the  projections  on  a  deformed  bar  may  pro- 
duce very  destructive  bursting  stresses  in  the  surrounding  concrete.  The  bearing  stress  between  the  projections 
and  the  concrete  in  the  tests  with  certain  types  of  commercial  deformed  bars  was  computed  to  be  from  5800  to 
14,000  lb.  per  sq.  in.  at  the  highest  bond  stresses  considered  in  these  tests.  The  large  slip  and  the  high  bearing 
stresses  developed  in  the  later  stages  of  the  tests  show  the  absurdity  of  seriously  considering  the  extremely  high 
values  that  are  usually  reported  to  be  the  true  bond  resistance  of  many  types  of  deformed  bars. 

Round  bars  with  standard  V-shaped  threads  gave  much  higher  bond  resistance  at  low  slips  than  the  com- 
mercial deformed  bars.  The  average  bond  resistance  at  an  end  slip  of  0.001  in.  was  612  lb.  per  sq.  in.  The  maxi- 
mum bond  resistance  was  745  lb.  per  sq.  in.  These  were  the  only  deformed  bar  tests  in  which  failure  came  by 
shearing  the  surrounding  concrete. 

The  1-in.  twisted  square  bars  gave  a  bond  resistance  per  unit  of  surface  at  an  end  slip  of  0.001  in.,  only  88% 
of  that  for  the  plain  rounds.  Following  an  end  slip  of  about  0.01  in.,  these  bars  showed  a  decided  decrease  in  bond 
resistance,  and  a  slip  of  5  to  10  times  this  amount  was  required  to  cause  the  bond  resistance  to  regain  its  first 
maximum  value.  After  this,  the  bond  resistance  gradually  rose  as  the  bar  was  withdrawn.  Some  of  the  bars  were 
withdrawn  2  or  3  in.  before  the  highest  resistance  was  reached.  The  apparent  bond  stresses  at  these  slips  were 
very  high;  but,  of  course,  such  stresses  and  slips  could  not  be  developed  in  a  structure  and  could  not  have  been 
developed  in  the  tests  had  the  blocks  not  been  reinforced  against  bursting.  Such  values  are  entirely  meaningless 
under  any  rational  interpretation  of  the  tests. 

Anchoring  of  Reinforcing  Bars. — The  tests  with  plain  round  bars  anchored  by  means  of  nuts  and  with  washers, 
only  showed  that  the  entire  bar  must  slip  an  appreciable  amount  before  these  forms  of  anchorage  come  into  action. 
Anchorages  of  the  dimensions  used  in  these  tests  did  not  become  effective  until  the  bar  had  slipped  an  amount 
corresponding  to  the  maximum  bond  resistance  of  plain  bars.  With  further  movement  the  apparent  bond  re- 
sistance was  high,  but  was  accompanied  by  excessive  bearing  stresses  on  the  concrete. 

The  load-slip  relation  for  bars  anchored  by  means  of  hooks  and  bends  was  not  determined.^ 

Influence  of  Method  of  Curing  Concrete. — Tests  on  specimens  stored  under  different  conditions  indicate  that 
concrete  stored  in  damp  sand  may  be  expected  to  give  about  the  same  bond  resistance  and  compressive  resistance 
as  that  stored  in  water.  Water-stored  specimens  gave  values  of  maximum  bond  resistance  higher  in  each  instance 
than  the  air-stored  specimens;  the  increase  for  water  storage  ranged  from  10  to  45%.  The  difference  seemed  to 
increase  with  age.  The  presence  of  water  not  only  did  not  injure  the  bond  for  ages  up  to  3  years,  but  it  was  an 
important  factor  in  producing  conditions  which  resulted  in  high  bond  resistances.  However,  it  was  found  that 
specimens  tested  with  the  concrete  in  a  saturated  condition  gave  lower  values  for  bond  than  those  which  had  been 
allowed  to  dry  out  before  testing.  The  bars  in  specimens  which  had  been  immersed  in  water  as  long  as  3H  years 
showed  no  signs  of  rust  or  other  deterioration. 

Influence  of  Freezing  of  Concrete. — Specimens  made  outdoors  in  freezing  weather,  where  they  probably 
froze  and  thawed  several  times  during  the  period  of  setting  and  hardening,  were  almost  devoid  of  bond  strength. 

Influence  of  Age  and  Mix  of  Concrete. — Pull-out  tests  made  at  early  ages  gave  surprisingly  high  values  of 
bond  resistance.  Plain  bars  embedded  in  1  :  2  : 4  concrete  and  tested  at  2  days  did  not  show  end  slip  of  bar  until  a 
bond  stress  of  75  lb,  per  sq.  in.  was  developed.  Bond  resistance  increases  most  rapidly  with  age  during  the  first 
month.  The  richer  mixes  show  a  more  rapid  increase  than  the  leaner  ones.  The  tests  on  concrete  at  ages  of 
over  1  year  showed  that  the  bond  resistance  of  specimens  stored  in  a  damp  place  may  be  expected  ultimately  to 
reach  a  value  as  much  as  twice  that  developed  at  60  days. 

The  load-sUp  relation  of  leaner  and  richer  mixes  was  similar  to  that  for  1:2:4  concrete.  For  a  wide  range  of 
mixes  the  bond  resistance  was  nearly  proportional  to  the  amount  of  cement  used.  This  relation  did  not  obtain 
in  a  mix  from  which  the  coarse  aggregate  had  been  omitted. 

Effect  of  Continued  and-  Repeated  Load. — When  the  application  of  load  was  continued  over  a  considerable 
period  of  time  or  when  the  load  was  released  and  reapplied,  the  usual  relation  of  slip  of  bar  to  bond  resistance  was 
considerably  modified.  The  few  tests  which  were  made  indicate  that  the  bond  stress  corresponding  to  beginning 
of  slip  is  the  highest  stress  which  can  be  maintained  permanently  or  be  reapplied  indefinitely  without  failure  of 
bond. 

1  Other  tests  have  shown  that  a  semicircular  hook  of  4  times  the  diameter  of  the  bar  and  well  embedded 
in  concrete  may  be  assumed  to  develop  the  elastic  limit  of  the  steel  without  exceeding  the  bearing  strength  of 
the  concrete.  The  curved  ends  should  consist  of  bends  through  180  deg.  with  a  short  length  of  straight  rod 
beyond  the  bend,  A  short  cross  rod  aids  greatly  in  distributing  the  bearing  stress  in  the  concrete.  Short 
square  hooks  upon  the  ends  of  bars  are  not  of  great  value. 


Sec.  6-2] 


GENERAL  PROPERTIES  OF  REINFORCED  CONCRETE 


Effect  of  Concrete  Setting  Under  Pressure. — Bond  resistance  of  plain  bars  is  greatly  increased  if  the  con- 
crete is  caused  to  set  under  pressure.  With  a  pressure  of  100  lb.  per  sq.  in.  on  the  fresh  concrete  for  5  days  after 
molding,  the  maximum  bond  resistance  was  increased  92  %  over  that  of  similar  bars  in  concrete  which  had  set, 
without  pressure.  The  greater  density  of  the  concrete  and  its  more  intimate  contact  with  the  bar  seems  to  be 
responsible  for  the  increased  bond  resistance.  Light  pressures  gave  an  appreciable  increase  in  bond  resistance. 
With  polished  bars  the  effect  of  pressure  was  slight. 

As  might  have  been  expected,  the  compressive  resistance  of  concrete  setting  under  pressure  was  increased  in 
much  the  same  ratio  as  the  bond  resistance.  At  the  age  of  80  days  the  initial  modulus  of  elasticity  in  compression 
for  concrete  which  set  under  a  pressure  of  100  lb.  per  sq.  in.  was  about  37  %  higher  and  the  compressive  strength 
was  increased  by  about  73  %  over  that  of  concrete  which  had  set  without  pressure.  The  density  of  the  concrete, 
as  determined  by  the  unit  weights,  was  increased  about  4  %  by  a  pressure  of  100  lb.  per  sq.  in.  on  the  fresh  con- 
crete. The  increase  in  strength  and  density  was  relatively  greater  for  the  low  than  for  the  high  pressures.  A 
pressure  continued  for  1  day,  or  until  the  concrete  had  taken  its  final  set  and  hardening  had  begun,  seems  to  have 
produced  the  same  effect  in  increasing  the  strength  and  elastic  properties  of  the  concrete  as  when  the  pressure 
was  continued  for  a  much  longer  period. 

Beam  Tests 


Number 
of  tests 

First  end 
slip  of  bar 

End  slip 
of  0.001 
in. 

Maximum 
bond 
stress 

1  and  l^-in.  plain  round.  .  . 

28 

245 

340 

375 

^4 -in.  plain  round  

3 

186 

242 

274 

^i-in.  plain  round  

3 

172 

235 

255 

1-in.  plain  square  

6 

190 

248 

278 

1-in.  twisted  square  

3 

222 

289 

337 

l^i-in.  corrugated  round. .  .  . 

9 

251 

360 

488 

The  mean  computed  values  for  bond  stresses  in  the  6-ft.  beams  in  the  series  of  1911  and  1912  were  as  given 
below.  All  beams  were  of  1  :  2  :  4  concrete,  tested  at  2  to  8  months  by  loads  applied  at  the  one-third  points  of  the 
span.    Stresses  are  given  in  pounds  per  square  inch. 

In  the  beams  reinforced  with 
plain  bars  end  slip  begins  at  67  %  of 
tlie  maximum  bond  resistance;  for 
the  corrugated  rounds  this  ratio  is 
51%,  and  for  the  twisted  squares, 
66%. 

The  bond  unit  resistance  in 
beams  reinforced  with  plain  square 
bars,  computed  on  the  superficial 
area  of  the  bar,  was  about  75%  of 
that  for  similar  beams  reinforced 
with  plain  round  bars  of  similar  size. 

Beams  reinforced  with  twisted 
square  bars  gave  values  at  small  slips  about  85%  of  those  found  for  plain  rounds.    At  the  maximum  load,  the 
bond-unit  stress  with  the  twisted  bars  was  90  %  of  that  with  plain  round  bars  of  similar  size. 

In  the  beams  reinforced  with  IJ'i-in.  corrugated  rounds,  slip  of  the  end  of  the  bar  was  observed  at  about  the 
same  bond  stress  as  in  the  plain  bars  of  comparable  size.  At  an  end  slip  of  0.001  in.,  the  corrugated  bars  gave  a 
bond  resistance  about  6  %  higher  and  at  the  maximum  load,  about  30  %  higher  than  the  plain  rounds. 

The  beams  in  which  the  longitudinal  reinforcement  consisted  of  three  or  four  bars  smaller  than  those  used  in 
most  of  the  tests  gave  bond  stresses  which,  according  to  the  usual  method  of  computation,  were  about  70%  of 
the  stresses  obtained  in  the  beams  reinforced  with  a  single  bar  of  large  size.  It  seems  probable  that  the  lower 
computed  bond  stresses  in  these  tests  are  due  to  errors  in  the  assumptions  made  as  to  the  distribution  of  bond 
stress  and  not  to  actual  differences  of  bond  resistance  in  the  bars  of  different  size. 

The  tests  on  beams  with  the  loads  placed  in  different  positions  with  respect  to  the  span  gave  little  variation 
in  bond  resistance  during  the  early  stages  of  the  tests.  The  maximum  bond  resistances  increased  rapidly  as  the 
load  approached  the  supports.  These  tests  indicate  that  the  variation  in  the  maximum  bond  stresses  must  be  due 
to  the  presence  of  other  than  normal  beam  action. 

The  bond  stresses  developed  in  the  beam  tests  indicate  that  with  beams  of  the  same  cross-section  the  bond 
stresses  are  distributed  in  the  same  way  during  the  early  stages  of  the  test  in  beams  varying  widely  in  span  length 
and  loading.  During  the  later  stages  of  the  test,  the  distribution  of  bond  stress  seems  to  depend  largely  upon 
the  conditions  of  stress  in  the  concrete  through  the  region  of  the  span  where  beam  bond  stresses  are  high.  The 
distribution  of  bond  stresses  in  beams  of  different  cross-section  apparently  varies  with  the  relative  dimensions  of 
the  beam  and  the  reinforcing  bars. 

In  the  reinforced-concrete  beams  it  was  found  that  very  small  amounts  of  slip  at  the  ends  of  the  bar  repre- 
sented critical  conditions  of  bond  stress.  For  beams  failing  in  bond  the  load  at  an  end  slip  of  0.001  in.  was  89  to 
94  %  of  the  maximum  load  found  in  beams  reinforced  with  plain  bars,  and  79  %  of  the  maximum  load  for  similar 
beams  reinforced  with  corrugated  bars.  As  soon  as  slip  of  bar  became  general,  other  conditions  were  introduced 
which  soon  caused  the  failure  of  the  beam. 

The  bond  stresses  developed  in  a  reinforced-concrete  beam  by  a  load  applied  as  in  these  tests  varies  widely 
over  the  region  in  v/hich  beam  bond  stresses  are  present.  High  bond  stresses  are  developed  just  outside  the  load 
points  at  comparatively  low  loads.  The  load  which  first  developed  a  bond  stress  nearly  equal  to  the  maximum 
bond  resistance  in  the  region  of  beam  bond  stresses  produced  a  stress  near  the  support  which  was  not  more  than 
about  15  to  40  %  of  the  maximum  bond  resistance.  As  the  load  is  increased,  the  region  of  high  bond  stress  is  thrown 
nearer  and  nearer  the  support,  and  at  the  same  time  the  bond  stress  over  the  region  just  outside  the  load  point 


270 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  6-3 


becomes  steadily  smaller.  This  indicates  a  piecemeal  development  of  the  maximum  bond  stress  as  the  load  is 
increased.  The  actual  bond  stresses  in  certain  tests  varied  from  less  than  one-half  to  more  than  twice  the  average 
bond  resistance  computed  in  the  usual  manner. 

Slip  of  bar  in  a  reinforced-concrete  beam  has  a  marked  influence  in  increasing  the  center  deflection  during 
the  later  stages  of  loading. 

The  comparison  of  the  bond  stresses  developed  in  beams  and  in  puU-out  specimens  from  the  same  materials 
is  of  interest.  Such  a  comparison  should  be  made  for  similar  amounts  of  slip.  In  the  pull-out  tests  the  maximum 
bond  resistance  came  at  a  slip  of  about  0.01  in.  for  plain  bars.  The  mean  bond  resistance  for  the  deformed  bars 
tested  was  not  materiallv  different  from  that  of  the  plain  bars  until  a  sHp  of  about  0.01  in.  was  developed;  with  a 
continuation  of  slip  the  projections  came  into  action  and  with  much  larger  slip  high  bond  stresses  were  developed. 
The  beam  tests  showed  that  about  79  to  94  %  of  the  maximum  bond  resistance  was  being  developed  when  the  bar 
had  slipped  0.001  in.  at  the  free  end;  hence  the  bond  stress  developed  at  an  end  slip  of  0.001  in.  was  used  as  a  basis 
of  the  principal  comparisons  in  the  pull-out  tests.  However,  it  is  recognized  that,  under  certain  conditions,  the 
stresses  developed  at  larger  amounts  of  slip  may  have  an  important  bearing  on  the  effective  bond  resistance  of 
the  bar. 

The  pull-out  tests  and  beam  tests  gave  nearly  identical  bond  stresses  for  similar  amounts  of  slip  in  many 
groups  of  tests,  but  it  seems  that  this  was  the  result  of  a  certain  accidental  combination  of  dimensions  in  the  two 
forms  of  specimens  and  did  not  indicate  that  the  computed  stresses  in  the  beams  were  the  correct  stresses.  How- 
ever, it  is  believed  that  a  properly  designed  pull-out  test  does  give  the  correct  value  of  bond  resistance,  and  gives 
values  which  probably  closely  represent  the  bond  stresses  which  actually  exist  in  a  beam  or  other  member  as 
slipping  is  produced  from  point  to  point  along  the  bar.  The  relative  position  of  the  bar  during  molding  may  be 
expected  to  influence  the  values  of  bond  resistance  found  in  the  tests. 

A  working  bond  stress  equal  to  4  %  of  the  compressive  strength  of  the  concrete  tested  in  the  form  of  8  by  16- 
in.  cylinders  at  the  age  of  28  days  (equivalent  to  80  lb.  per  sq.  in.  in  concrete  having  a  compressive  strength  of 
2000  lb.  per  sq.  in.)  is  as  high  a  stress  as  should  be  used.  This  stress  is  equivalent  to  about  one-third  that  causing 
first  slip  of  bar  and  one-fifth  of  the  maximum  bond  resistance  of  plain  round  bars  as  determined  from  pull-out  tests. 
The  use  of  deformed  bars  of  proper  design  may  be  expected  to  guard  against  local  deficiencies  in  bond  resistance 
due  to  poor  workmanship  and  their  presence  may  properly  be  considered  as  an  additional  safeguard  against  ulti- 
mate failure  by  bond.  However,  it  does  not  seem  wise  to  place  the  working  bond  stress  for  deformed  bars  higher  than 
that  used  for  plain  bars. 

3.  Length  of  Embedment  of  Reinforcing  Bars  to  Provide  for  Bond. — Let  fs  be  the  working 
tensile  strength  of  the  steel,  As  the  area  of  bar,  o  the  circumference  of  bar,  d  the  diameter  or 
thickness  of  bar,  u  the  working  unit  bond  strength,  and  x  the  required  length  of  embedment 
(or  grip)  for  the  above  values  of  f,  and  u.  Then,  to  develop  the  strength  of  the  steel,  using 
either  round  or  square  bars, 

XOU  =  A,fs  J» 

or 

4.  Ratio  of  the  Moduli  of  Elasticity. — ^Let  fs  =  unit  stress  in  steel,  fc  =  unit  stress  in  con- 
crete, Es  =  modulus  of  elasticity  of  steel,  and  Ec  =  modulus  of  elasticity  of  concrete.  Since 
the  modulus  of  elasticity  of  a  material  is  the  ratio  of  stress  to  deformation,  it  follows  that,  for 
equal  deformations,  the  stresses  in  the  steel  and  concrete  will  be  as  their  moduli  of  elasticity. 
Thus, 

fs  ^Es 
fo  Eo 

This  ratio  of  the  moduli  is  generally  denoted  by  the  letter  n,  or 

fs  =  nfc 

The  equation  just  given  shows  that  if  the  stress  in  either  the  steel  or  concrete  of  a  concrete 
column  is  known,  the  stress  in  the  other  material  can  be  found,  and  this  relation  is  made  use  of 
in  the  derivation  of  column  formulas.  Fig.  26,  Sect.  5,  page  250,  shows  that  the  modulus  of 
elasticity  of  concrete  in  compression  is  less  for  the  greater  loads,  and  hence  the  value  of  n  is 
greater.  Thus,  it  is  plain  that  with  increasing  loads  in  concrete  columns  the  steel  receives  a 
greater  proportionate  stress,  the  variation  in  the  amount  carried  by  the  steel  depending  on  the 
variation  in  the  value  of  n.    In  order  to  take  account  of  the  fact  that  under  increasing  loads  the 


Sec.  6-5]         GENERAL  PROPERTIES  OF  REINFORCED  CONCRETE  271 

steel  receives  an  increasing  proportion,  it  is  desirable  to  use  a  value  of  n  in  the  computations 
for  design  somewhat  larger  than  that  which  is  obtained  by  taking  a  value  of  Ec  corresponding 
to  working  loads  on  small  prisms  (about  10).  A  value  of  15  for  n  may  well  be  used  for  the  ordi- 
nary 1:2:4  mix. 

In  concrete  beams,  experiments  show  that  the  tension  which  remains  in  the  concrete  just 
below  the  neutral  axis,  and  properly  not  allowed  for  in  the  derivation  of  the  beam  formulas, 
has  its  effect  in  the  position  of  the  neutral  axis  and  the  strength  of  the  beam.  It  is  found  that 
a  value  of  15  for  n  is  not  too  large  for  calculations  of  strength  of  beams,  assuming  the  ordinary 
1  :2  :4mix,  although  great  accuracy  in  this  respect  is  not  necessary.  This  value  of  15  for 
n  is  the  one  most  generally  used,  but  a  value  of  12  is  also  frequently  employed.  The  value  of 
15  corresponds  to  a  value  of  Ec  of  2,000,000  which  is  somewhat  low  as  determined  by  compressive 
tests. 

For  the  proper  values  of  n  to  use  for  other  mixtures  see  recommendations  of  the  Joint 
Committee,  Appendix  B. 

Comparatively  few  tests  have  been  made  on  the  elasticity  of  concrete  in  tension,  but  these 
seem  to  indicate  that  for  small  stresses,  it  is  practically  the  same  as  in  compression,  although 
probably  slightly  less. 

5.  Behavior  of  Reinforced  Concrete  Under  Tension. — Early  tests  indicated  that  the  ulti- 
mate stretch  of  reinforced  concrete  in  tension  is  as  much  as  10  times  that  of  plain  concrete, 
but  such  results  were  due  to  the  fact  that  it  was  found  extremely  difficult  to  determine  just  when 
the  concrete  begins  to  crack.  Cracks  do  not  become  noticeable,  even  on  very  close  examination, 
until  a  stretching  occurs  corresponding  to  a  tensile  stress  much  beyond  the  ultimate  tensile 
strength  of  the  concrete.  The  steel  causes  a  uniform  elongating  of  the  concrete  so  that  the 
cracks  which  open  up  are  very  small  and  remain  invisible  for  some  time. 

A  method  of  detecting  minute  cracks  in  the  tensile  side  of  beams  was  accidentally  discovered 
in  1901-02  in  some  experiments  made  at  the  University  of  Wisconsin.  It  was  found  that  when 
beams  were  hardened  in  water  and  only  partially  dried  before  testing,  very  fine  hair-cracks  be- 
came noticeable  at  a  moderate  load.  Before  these  cracks  occurred,  however,  dark  wet  lines 
appeared  across  the  beam,  and  it  was  observed  that  each  of  these  lines  was  later  followed  by  a 
very  fine  crack.  These  water-marks  were  proven  to  be  incipient  cracks  by  the  sawing  out  of 
a  strip  of  concrete  along  the  outer  part  of  the  beam.  Careful  measurements  of  extension  showed 
that  these  streaks,  or  water-marks,  occurred  at  practically  the  same  deformation  at  which  the 
concrete  ruptured  when  not  reinforced.  This  same  phenomenon  has  since  been  observed  by 
many  careful  experimenters,  and  the  fact  is  now  generally  established  that  concrete,  reinforced 
with  steel,  does  not  elongate  under  tensile  stress  to  any  greater  extent  before  cracking  than  plain 
concrete. 

A  reinforced-concrete  beam  for  working  loads  is  usually  more  heavily  stressed  on  the  ten- 
sion side  than  the  ultimate  tensile  strength  of  plain  concrete — enough  steel  being  usually  em- 
bedded near  the  lower  face  to  permit  the  full  allowable  compressive  strength  of  the  concrete 
to  be  utilized.  The  presence,  then,  of  the  cracks  above  referred  to,  accurring  long  before  a 
reinforced-concrete  beam  has  obtained  its  working  load,  must  seriously  affect  the  tensile  strength 
of  the  concrete.  The  moment  formulas  now  in  most  general  use  for  the  design  of  reinforced- 
concrete  beams  neglect  entirely  the  tensile  strength  of  the  concrete. 

Experiments  have  shown  that  concrete  when  well  placed  and  mixed  somewhat  wet,  com- 
pletely protects  the  steel  in  the  tensile  side  of  a  beam  from  corrosion,  even  when  the  unit  stress 
in  the  steel  somewhat  exceeds  the  elastic  hmit. 

6.  Shrinkage  and  Temperature  Stresses. — In  reinforced-concrete  structures  which  are 
free  to  contract  and  expand,  the  stresses  occurring  from  temperature  changes  and  from  shrink- 
age in  hardening  are  due  wholly  to  the  mutual  action  of  the  steel  and  concrete.  Of  the  stresses 
produced  from  these  two  causes,  those  which  result  from  hardening  are  the  greater,  but  experi- 
ments show  that  even  these  are  not  sufficient  to  be  of  practical  importance.    In  regard  to  the 


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CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  6-7 


temperature  stresses,  they  are  negligible  by  reason  of  the  nearly  equal  rates  of  expansion  of  the 
two  materials. 

On  the  other  hand,  if  reinforced-concrete  structures  are  restrained  by  outside  forces,  or  if 
they  are  of  such  dimensions  that  they  cannot  be  considered  as  sufficiently  well  bonded  to  act 
as  a  unit — such  as  long  retaining  walls — then  the  stresses  resulting  are  much  greater,  and  the 
tensile  strength  of  the  concrete  will  be  reached  (this  will  occur  with  a  drop  in  temperature  some- 
where between  10  and  20°F.),  thus  producing  cracks,  called  contraction  cracks.  To  prevent 
plainly  noticeable  cracks  due  to  shrinkage  and  lowering  of  the  temperature,  all  exposed  surfaces 
should  be  reinforced  with  about  0.3  of  1  %  of  steel,  based  on  the  cross-section  of  the  concrete. 
This  is  less  than  the  amount  required  theoretically,  but  experience  shows  this  amount  to  give 
very  satisfactory  results  where  the  foundations  are  stable.  If  the  structure  is  fixed  in  two 
directions,  the  reinforcement  must  be  placed  accordingly.  The  above  percentage  of  steel 
should  be  figured  for  an  area  of  cross-section  of  maximum  thickness  of  about  12  in. 

No  amount  of  reinforcement  can  entirely  prevent  contraction  cracks.  The  steel  can, 
however,  if  of  small  diameter  and  placed  close  to  the  surface,  force  the  cracks  to  take  place  at 
such  frequent  intervals  that  the  required  deformation  occurs  without  any  one  crack  becoming 
large.  No  cracks  will  open  up  to  be  plainly  noticeable  until  the  steel  is  stressed  beyond  its 
elastic  limit.  The  amount  of  steel  should  be  such,  then,  that  without  being  stressed  beyond  its 
elastic  limit,  it  will  withstand  the  tensile  stress  resulting  from  the  maximum  fall  of  temperature 
(usually  considered  to  be  50°)  in  the  steel  itself  plus  the  tensile  stress  necessary  to  crack  the  con- 
crete.   A  high  elastic-limit  steel  is  thus  advantageous. 

The  size  and  spacing  of  the  cracks  will  also  depend  upon  the  bond  strength  of  the  rein- 
forcing rods.  The  distance  between  cracks  in  any  given  case  will  be  the  length  required  to 
develop  a  bond  strength  equal  to  the  tensile  strength  of  the  concrete.  Thus,  bars  with  ir- 
regular surfaces  which  provide  a  mechanical  bond  with  the  concrete  are  in  general  more  effective 
than  -smooth  bars. 

7.  "Weight  of  Reinforced  Concrete. — Reinforcing  steel  in  the  usual  proportions  adds  from 
3  to  5  lb.  to  the  weight  of  plain  concrete  per  cubic  foot.  The  weight  of  plain  concrete  for  the 
various  kinds  of  aggregate  may  be  found  on  page  263.  Reinforced  concrete  is  usually  assumed 
as  150  lb.  per  cu.  ft.  in  making  computations  for  design. 


SECTION  7 


BEAMS  AND  SLABS 


RECTANGULAR  BEAMS  AND  SLABS 

1.  Forces  to  be  Resisted. — As  expressed  by  the  Joint  Committee  the  forces  to  be  resisted 
are  those  due  to : 

1.  The  dead  load,  which  includes  the  weight  of  the  structure  and  fixed  loads  and  forces. 

2.  The  live  load,  or  the  loads  and  forces  which  are  variable.  The  dynamic  effect  of  the 
live  load  will  often  require  consideration.  Allowance  for  the  latter  is  preferably  made  by  a 
proportionate  increase  in  either  the  live  load  or  the  live-load  stresses.  The  working  stresses 
recommended  (see  Appendix  B)  are  intended  to  apply  to  the  equivalent  static  stresses  thus 
determined. 

2.  Distribution  of  Stress  in  Homogeneous  Beams. — The  following  statements  and  for- 
mulas are  in  accordance  with  the  theory  of  homogeneous  beams : 

1.  At  any  cross-section  the  internal  forces,  or  stresses,  may  be  resolved  into  normal  and 
tangential  components.  The  components  normal  to  the  section  are  stresses  of  tension  and 
compression,  while  the  tangential  components  add  together  and  form  a  stress  known  as  the 
resisting  shear. 

2.  The  shear  at  any  cross-section  is  borne  by  the  tangential  stresses  in  that  section.  The 
moment  at  any  section  is  borne  by  the  component  stresses  normal  to  that 
section. 

3.  The  neutral  axis  passes  through  the  center  of  gravity  of  the  cross- 
section. 

4.  The  intensity  of  stress  normal  to  the  section  increases  directly  with 
the  distance  from  the  neutral  axis  and  is  a  maximum  at  the  extreme  fiber 
(Fig.  1).  The  intensity  of  this  stress  at  any  given  point  in  the  cross-sec- 
tion is  given  by  the  formula 


Compression 


/  = 


My 


in  which  /  =  unit  fiber  stress  at  distance  y  from  neutral  axis. 

M  =  external  bending  moment  at  section  in  inch-pounds. 
y  =  distance  in  inches  from  neutral  axis  to  any  fiber. 
/  =  moment  of  inertia  of  the  cross-section  about  the  neutral  axis. 
5.  The  general  formula  which  gives  the  longitudinal  shear  per  square  inch  (y)  at  any 
desired  point  in  the  cross-section  is 

VQ 


in  which  V 
'  Q 


=  total  shear  at  the  section  in  pounds. 

=  statical  moment  about  the  neutral  axis  of  that  portion  of  the  cross-section  lying 
either  above  or  below  (depending  upon  whether  the  point  in  question  is  above 
or  below  the  neutral  axis)  an  axis  drawn  through  the  point  in  question  parallel 
to  the  neutral  axis. 

=  moment  of  inertia  of  the  cross-section  about  the  neutral  axis. 

=  width  of  beam  at  the  given  point. 

273 


18 


274 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-2 


a^y/////////. 


Area  of 
cross-hcrtched 
portion-  A' 


Fig.  2. 


In  the  above  formula,  by  the  term  statical  moment  is  meant  the  product  of  the  area  mentioned 
by  the  distance  between  its  center  of  gravity  and  the  neutral  axis.  For  example,  the  longi- 
tudinal shearing  intensity  at  a  point  c  in  a  rectangular  beam.  Fig.  2,  may  be  expressed  as 
follows : 

VA'r 

For  rectangular  beams  and  all  beams  of  uniform  width,  the  largest  value  of  v  for  any  given  sec- 
tion will  occur  at  the  neutral  axis  since  the  statical  moment 
Q  has  its  maximum  value  for  a  point  on  this  axis,  and  h  is 
constant. 

6.  If  a  beam  is  of  constant  cross-section  throughout,  the 
maximum  values  of  /  and  v  will  occur  at  the  section  where 
M  and  V  respectively  have  maximum  values. 

7.  In  addition  to  the  longitudinal  or  horizontal  shear  at 
any  point  there  coexists  a  vertical  shear  and  the  intensity  of 
this  vertical  shear  is  equal  to  the  intensity  of  the  horizontal 
shear. 

8.  The  intensity  of  the  shear  at  the  top  and  bottom  of  a  beam  is  zero  and  the  intensity 
of  shear  (horizontal  and  vertical)  along  a  vertical  cross-section  for  a  rectangular  beam  varies 
as  the  ordinates  to  a  parabola,  as  shown  graphically  in  Fig.  3.    The  maximum  value  occurs 

the  average  intensity,  or  2  • 

9.  At  the  neutral  plane  there  exists  a  tension  and  compression  at  angles  of  45  deg.  to  the 
horizontal,  and  the  intensity  of  these  forces  is  equal  to  that  of  the  shear. 

10.  At  the  end  of  a  simply  supported  beam  where  the  shear  is  a 
maximum  and  the  bending  moment  a  minimum,  the  stresses  lie  prac- 
tically at  45  deg.  to  the  horizontal  throughout  the  entire  depth  of 
beam. 

11.  At  the  section  of  maximum  moment,  the  shear  is  zero  and  the 
stresses  are  horizontal. 

12.  If  /  represents  the  intensity  of  horizontal  fiber  stress  and  v  the  intensity  of  vertical 
or  horizontal  shearing  stress  at  any  point  in  a  beam,  the  intensity  of  the  inclined  stress  will  be 
given  by  the  formula 


at  the  neutral  axis  and  is 


Fig.  3. 


and  the  direction  of  this  stress  by  the  formula 

tan  2K  =  y 

where  K  is  the  angle  of  the  stress  with  the  horizontal. 

13.  At  any  given  point  maximum  compressive 
stress  and  maximum  tensile  stress  make  an  angle  of 
90  deg.  with  each  other. 

14.  The  directions  of  the  maximum  stresses  for 
a  simply  supported  beam  uniformly  loaded  are  as 
given  in  Fig.  4.  The  general  direction  of  the  stresses 
in  a  beam  with  any  given  loading  may  be  determined 
by  means  of  the  formulas  for  t  and  K  given  above. 

15.  The  common  theory  of  flexure  gives  the  unit  stress  correctly  at  the  important  section 
of  maximum  moment  and  also  for  the  extreme  fibers  in  other  sections,  since  at  these  points 
the  shear  is  zero.  Where  the  shear  is  not  zero  an  inclined  stress  is  the  result  and  the  flexure 
formula  gives  only  the  horizontal  component  of  this  stress — namely,  the  fiber  stress. 


Lines  of  maximum  tensidn 
Lines  of  maximum  compression 

Fig.  4. 


Sec.  7-3] 


BEAMS  AND  SLABS 


27.5 


Fig.  5. 


Fig,  6. 


3.  Assumptions  in  Theory  of  Flexure  for  Homogeneous  Beams. — The  two  main  assump- 
tions in  the  common  theory  of  flexure  are : 

1.  If,  when  a  beam  is  not  loaded,  a  plane  cross-section  be  made,  this  cross-section  will  still 
be  a  plane  after  the  load  is  put  on  and  bending  takes  place  (Navier's  hypothesis). 

2.  The  stress  is  proportional  to  the  deformation — namely,  to  the 
amount  of  elongation  or  compression  per  unit  of  length  (Hooke's  Law). 

From  the  first  assumption  it  follows  that  the  unit  deformations  of  the 
fibers  at  any  section  of  a  beam  are  proportional  to  their  distance  from 
the  neutral  axis.  By  means  of  the  second  assumption  the  important 
principle  is  established  that  the  unit  stresses  in  the  fibers  are  also  pro- 
portional to  the  distances  of  the  fibers  from  the  neutral  axis. 

4.  Plain  Concrete  Beams. — The  first  assumption  in  the  common 
theory  of  flexure,  as  given  in  the  preceding  article,  may  be  applied  directly 
to  plain  concrete  and  also  to  reinforced-concrete  beams.  Careful  measurements  seem  to  show 
some  deviation  from  a  plane,  but  in  general  this  assumption  seems  to  be  warranted.  From 
this  fact  it  follows  (as  stated  above)  that  deformations  of  the  fibers  are  proportional  to  the 
distances  of  the  fibers  from  the  neutral  axis.    OS  in  Fig.  5  is  the  stress-deformation  diagram 

for  concrete  in  compression  with  the  deformations  repre- 
sented vertically.  The  curve  OT  is  the  stress-deforma- 
tion diagram  for  concrete  in  tension.  For  working  loads 
the  curves  OS  and  07"  do  not  vary  materially  from  straight 
lines  and  the  unit  stresses  in  the  fibers  at  any  section  of  a 
plain  concrete  beam  may  thus  be  assumed  to  vary  directly 
as  the  deformations  and  consequently  as  the  distances  of  the  fibers  from  the  neutral  axis. 
Hence,  the  common  flexure  formula  for  homogeneous  beams  applies  when  the  loads  are  work- 
ing loads.    For  ultimate  loads,  however,  ths  formula  does  not  strictly  apply. 

A  plain  concrete  beam  will  fail  by  cracks  opening  up  along  the  uneven  lines  which  are 
shown  in  Fig.  4  on  account  of  the  low  strength  of  concrete  in  tension.  If  concrete  were  only 
stronger  in  tension,  then  the  plain  concrete  beam  might  be  of 
some  structural  value.  In  order  to  offset  this  disadvantage  of 
plain  concrete,  steel  is  used. 

6.  Purpose  and  Location  of  Steel  Reinforcement. — Steel 
reinforcement  should  have  the  general  directions  shown  in  Fig.  Fig.  7. 

6  in  order  to  take  the  tension  in  the  beam  and  prevent  the 

cracks  starting  along  the  lines  indicated.  Fig.  7  is  the  simplest  method  of  reinforcement 
and  quite  often  used  for  light  loads.  In  beams  highly  stressed,  curved  or  inclined  reinforce- 
ment is  needed,  in  addition  to  the  horizontal  rods.  The  most  common  method  is  to  use  several 
bars  for  the  horizontal  reinforcement  and  then  to  bend  up  some  of  these  at  an  angle  of  from  30 
to  45  deg.  as  they  approach  the  end  of  the  beam  and  where  they  are  not  needed  to  resist  bending 

stresses.  The  concrete  is  depended  upon  to  take  care  of 
the  compressive  and  pure  shearing  stresses,  its  resistance 
to  such  stresses  being  large. 

6.  Tensile  Stress  Lines  in  Reinforced-concrete 
Beams. — ^Lines  of  maximum  tension  in  the  concrete  of  re- 
inforced-concrete beams  are  considerably  inchned  imme- 
diately above  the  line  of  the  steel.  The  inclination  of 
these  lines  is  greater,  the  greater  the  shear,  and  the  less 
the  horizontal  tension.  The  inclination,  therefore,  increases  toward  the  end  of  the  beam.  At 
points  nearer  the  neutral  plane,  the  horizontal  tensile  stresses  become  less  and  the  inclined  ten- 
sion approaches  the  value  of  the  shearing  stress,  while  its  inclination  approaches  45  deg.  Fig. 
8  is  an  attempt  to  represent  roughly  the  general  direction  of  the  inclined  tensile  stresses  in  a 
simply  supported  beam  uniformly  loaded  and  with  horizontal  reinforcement. 


Diagonal-tension  -'' 
cracks  UKely  to  occur 


-Very  little  tension  in 
the  concrete  here  (if  any) 
on  account  of  concrete 
cracking  across  the 
tension  face 


Pig.  8. 


27.0 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-7 


7.  Flexure  Formulas  for  Reinforced-concrete  Beams. — A  great  many  varieties  of  flexure 
formulas  have  been  proposed  from  time  to  time  to  be  used  in  the  design  of  reinforced-concrete 
beams.  As  might  be  expected,  many  of  the  earlier  formulas  considered  the  concrete  to  carry 
its  share  of  the  tension  which  we  know  now  cannot  be  done  with  safety.  Only  two  classes  of 
flexure  formulas  are  at  the  present  time  in  practical  use.  In  each  of  these  classes,  tension  in 
the  concrete  is  neglected  and  a  plane  section  before  bending,  is  assumed  to  be  a  plane  after 
bending  takes  place. 

The  formulas  almost  universally  used  and  made  standard  by  the  Joint  Committee 
relate  to  working  stresses  and  safe  loads,  and  are  based  on  the  straight-line  theory  of  stress 
distribution.  The  other  formulas  referred  to  above  relate  to  ultimate  strength  and  ultimate 
loads  and  the  stress-deformation  curve  for  concrete  in  compression  is  assumed  to  be  a  full 
parabola.  Ultimate-load  formulas  are  used  to  such  a  limited  extent  that  only  a  few  pages  of 
this  handbook  are  devoted  to  their  consideration — ^namely.  Arts.  10  and  11. 

8.  Assumptions  in  Flexure  Calculations. — The  following  assumptions  are  made  in  deriving 
the  flexure  formulas:  (1)  the  adhesion  of  concrete  to  steel  is  perfect  within  the  elastic  limit  of 

the  steel;  (2)  no  initial  stresses  are  con- 
^  sidered  in  either  the  concrete  or  the  steel 

Tl  ^M^W^  to  contraction  or  expansion;  (3)  the 

applied  forces  are  parallel  to  each  other 
and  perpendicular  to  the  neutral  surface 
of  the  beam  before  bending;  (4)  sectional 
planes  before  bending  remain  plane  sur- 
faces after  bending  within  the  elastic  limit 
of  the  steel ;  (5)  no  tension  exists  in  the  con- 
crete; (6)  modulus  of  elasticity  of  concrete 
is  constant. 

9.  Flexure  Formulas  for  Working  Loads — Straight-line  Theory. — The  unit  stress  in  the 
steel  is  within  the  elastic  limit,  and  the  unit  stresses  in  the  concrete  at  the  given  section  of  the 
beam  are  considered  to  vary  as  the  ordinates  to  a  straight  line  (see  Fig.  9).  Tension  in  the 
concrete  is  neglected.    The  formulas  follow^  (see  Notation,  Appendix  D): 

1  The  formulas  may  be  derived  as  follows: 

Total  compressive  resistance  =  total  tensile  resistance,  or 

Vzfckbd  =  Asf^  (o) 
From  the  assumption  that  deformations  vary  as  the  distances  of  the  fibers  from  the  natural  axis  and  assuming 
stress  proportional  to  deformation 

fc  fs 


Diagram 


Fig.  9. 


Eckd  E,da 


k) 


which  reduces  to 


fs  =  fen 


■*  or  fc 


fsk 


n(l  -  k) 


,  or  k  = 


The  total  resisting  moment  of  the  beam  is  the  sum  of  the  moments  of  the  total  compressive  stresses  and  of 
the  total  tensile  stresses  about  the  neutral  axis,  or 


M  =  %kd{y2fckhd)  +  d(l  -  k)Asfs 
=  \ifckW  +  Asfsdil  -  k) 

Eliminating  k  between  equations  (o)  and  (6),  the  following  formula  for  steel  ratio  results 

fc^nfc^  ) 

Introducing  the  value  of  fs  from  equation  (6)  into  equation  (a),  we  have 

Yik'^hd  -  A^nCl  -  A;)  =  0 
y2k%  -  p6n(l  -  A;)  =  0 


Sec.  7-9] 


BEAMS  AND  SLABS 


277 


k  =  ■\/2pn  -f  (pn)2  —  pn  = 


V  = 


J  =  1  -  3^  A;  (2) 
hd     fs  (fs  ^  ,  \     2/,  (3) 


ff4  +  l) 
fc  \nfa  / 


M.^VMd^     or  or     /.  =  (4) 

Ms  =  ?>/J(6rf2),     or     bd^  or     /.  =  (5) 

/-^^  -  ;^.)  («) 

The  above  formulas  show  that  for  a  given  ratio  of      p  and  k  remain. the  same  for  all  sizes 

fc 

of  beams.  The  formula  for  Mc  gives  the  resisting  moment  when  the  maximum  allowable  value 
of  fc  is  introduced  as  the  limiting  factor  and  the  formula  for  Ms  gives  the  resisting  moment 
when  the  maximum  allowable  value  of  fs  is  the  limiting  factor.  The  lesser  of  these  two  re- 
sisting moments,  when  proper  working  values  are  assigned  to  fc  and  fs,  is  the  safe  resisting 
moment  of  the  beam  in  question. 

Unlike  steel  beams,  reinforced-concrete  beams  require  a  preliminary  formula  to  be  solved 
before  the  formula  for  resisting  moment  may  be  employed.  Solving  this  preliminary  formula 
locates  the  position  of  the  neutral  axis  which  is  in  the  same  position  only  for  beams  of  a  given 
percentage  of  steel  reinforcement. 

The  method  of  procedure  in  flexure  formulas  is  to  determine  the  vertical  section  of  the  beam 
where  the  moment  is  a  maximum  and  apply  the  formulas  at  that  section.  Either  formula  for 
p,  containing  the  values  of  fc  and  fs,  determines  the  amount  of  steel  reinforcement  which  is 
needed  to  cause  the  beam  to  be  of  equal  strength  in  tension  and  compression.  The  formulas 
for  resisting  moment  determine  the  bending  moment  which  a  beam  will  safely  withstand  (for  an 
existing  structure)  or  the  size  of  the  beam  needed  to  resist  a  given  bending  moment  (for  a  pro- 
posed structure). 

If  a  beam  is  over-reinforced,  its  resisting  moment  depends  on  Mc,  and  if  under-reinforced 
on  Ms. 

If  it  is  desired  to  find  the  fiber  stresses  in  concrete  and  steel  of  a  given  beam,  the  formulas 

/,  =  — ~and/c  =  -r~-  (or /c  =  ^{'^^  should  be  used,  where  M  is  the  external  bending 
Asjd  kjbd^  \  k  / 

2M  M 

moment  in  each  case.    For  a  given  external  M,  either  bd^  =  or  bd"^  =  may  be  used  to  de- 

fckj  pfsj 


from  which 


k  =  \/2pn  +  (pn.)^  —  pn 
Substituting  the  value  of  Asfs  from  (o)  into  (c),  we  get 

Mc  =  V2fck(l  -  H  k)bd^ 

Mc  =  Hfckjbd^ 

Substituting  the  value  of  fc  from  (a)  into  (c),  and  remembering  that  As  =  pbd, 

Ms  =  pfsjbd^ 

Equation  (a)  may  be  solved  to  give 

2f,p  fck 
/c  =  — ,  or  p  = 


278 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-9 


termine  cross-section,  when  the  p  used  is  obtained  from  the  formula  p  = 

fck  .  . 
V  =  — '  in  which  k  = 
2/. 


fc  \nfc  I 


or  from 


1  + 


Illustrative  Problem. — What  will  be  the  resisting  moment  (Af)  for  a  beam  whose  breadth  (b)  is  8  in.  with 
a  distance  from  the  center  of  the  reinforcement  to  the  compression  surface  {d)  of  12  in.,  the  area  of  steel  section  being 
0.96  sq.  in.?    Assume  n  =  15;  /<,  =  650  lb.  per  sq.  in.;  and  /s  =  16,000  lb.  per  sq.  in. 


O.f 


(8) (12) 


0.01 


From  (1) 

From  (4) 
From  (5) 


k 
J 

Mc 
Ms 


\/(2)(0.01)(15)  +  (0.01)2(15)2 
0.861 


(0.01)(15)  =  0.418 


1/^(650) (0.418) (0.861) (8) (12)2  ^  134,700  in.-lb. 
(0.01) (16,000) (0.861) (8) (12)2  ^  158,700  in.-lb. 


Mc  is  the  lesser  of  the  two  resisting  moments  and  hence  controls  in  the  design. 

Illustrative  Problem. — Assume  the  beam  of  the  preceding  problem  to  be  14  in.  deep  and  subjectetl  to  a 
bending  moment  of  130,000  in.-lb.    Compute  the  maximum  unit  stresses  in  the  steel  and  concrete. 


0.96 
(8)(14) 


=  0.0086 


From  (1) 


From  (4) 


From  (5) 


k 
j 

130,000 

fc 

130,000 


a/(2)  (0.0086)  (15)  +  (0.0086)2(15)  = 
0.868 

(0.395)  (0.868)  (8)  (14)2 
480  lb.  per  sq.  in. 

(0.0086)  Us)  (0.868)  (8)  (14)2 
11,100  lb.  per  sq.  in. 


(0.0086)  (15)  =  0.395 


Illustrative  Problem. — A  beam  is  to  be  designed  to  withstand  a  bending  moment  of  300,000  in.-lb.  and  to 
have  equal  strength  in  tension  and  compression.  A  1  :  2  :  4  concrete  will  be  used  with  Ec  =  2,000,000  and/c  =  600 
lb.  per  sq.  in.    The  pull  in  the  steel  is  to  be  limited  to  14,000  lb.  per  sq.  in.    Its  modulus  of  elasticity  Es  is  30,000,000. 


^»  _  1  ^  ^  _  Z2 
Ec~  fc  ~  3 


From  (1)  and  (2) 


From  (3) 


^  +  (15) (600) 
(600)  (0.391) 


0.391  and  j  =  0.870 


0.0084 


(21)(14,000) 

Either  (4)  or  (5)  may  now  be  used  in  determining  b  and  d  since  the  amount  of  steel  to  be  employed  will  cause 
simultaneous  maximum  working  stresses. 

From  (5) 


6^2  = 


300,000 


2930 


293,  or  d  =  17H  in. 


(0.0084)  (14,000)  (0.870) 
Many  different  values  of  b  and  d  will  satisfy  the  last  equation.    If  b  is  taken  as  10  in.,  then 
„  2930 

=-Io- 

Finally 

As  =  (0.0084)  (10)  (17.25)  =  1.45  sq.  in. 
If  IH  in.  is  allowed  between  the  tension  surface  of  the  concrete  and  the  center  of  the  steel,  the  entire  depth  of  the 
beam  should  be  19  in. 


Sec.  7-10] 


BEAMS  AND  SLABS 


279 


10.  Flexure  Formulas  for  Ultimate  Loads. — The  stress-deformation  curve  for  concrete  in 
compression  is  assumed  to  be  a  full  parabola.  Experiments  show  this  to  be  very  nearly  the 
case  for  ultimate  loads.  The  amount  of  reinforcement  is  considered  as  sufficient  to  develop 
the  full  compressive  strength  of  the  concrete  without  stressing  the  steel  beyond  its  yield  point. 
Failure  under  such  conditions  (Fig.  10)  will  occur  by  crushing  the  concrete. 


Average  compressive 
stress  -  I  fc 


Total,  compressive 
stress- 1  fcbkd. 


Fig  10. 


The  formulas  follow  (see  Notation,  Appendix  D) : 


^  =  \  3pn  +  (^pn\  ^  -  ^pn  =  

1  -h; 


2nfa 


V  = 


Mo  =  Hfckjibd^),  or  bd' 
Ms  =  pfsjihd^),     or  bd' 


2  fck 
M 


Hfckj 


fc 


2k 


M 

Pfsj 


(1) 

(2) 
(3) 

(4) 
(5) 
(6) 


In  the  above  formulas,  /,  =  elastic  limit  of  the  steel,  and  fc  =  ultimate  compressive  strength 
of  concrete. 

When  using  the  above  formulas,  it  should  be  remembered  that  the  amount  of  steel  in  the  beam 
is  assumed  as  sufficient  to  cause  the  ultimate  resisting  moment  to  be  due  to  the  concrete.  Thus, 
the  resisting  moment  of  the  beam  may  be  figured  by  using  the  formula  for  Mc.  Xf  an  amount 
of  steel  is  used  such  that  the  ultimate  strength  of  the  concrete  and  the  elastic  limit  of  the.  steel 
would  be  reached  simultaneously,  either  Mc  or  Ms  may  be  used  to  determine  the  ultimate 
resisting  moment.  If  a  less  amount  of  steel  is  used  than  the  amount  just  mentioned,  the  condi- 
tions of  the  assumption  do  not  hold,  and  the  formulas  given  above  cannot  be  used.  When  this 
happens  the  ultimate  moment  may  be  figured  by  means  of  formulas  based  on  a  parabolic  varia- 
tion of  compression  in  the  concrete  and  applicable  for  any  load  up  to  the  ultimate.  The  para- 
bola for  such  a  case  is  not  a  full  one  and  the  formulas  are  cumbersome  to  use  and  not  at  all 
fitted  for  practical  use. 

The  formulas  for  ultimate  loads,  however,  can  readily  be  employed  to  design  a  beam  for 

equal  strength  in  tension  and  compression.    The  method  is  to  first  find  the  required  amount 

MM 

or  bd^  =  — .  may  be  used  to  determine  the  size  of  beam 


of  steel.    Then  either  bd^  = 


fckj 


necessary. 


Illustrative  Problem. — A  beam  is  to  be  designed  to  have  equal  strength  in  tension  and  compression  and 
to  safely  withstand  a  bending  moment  of  150,000  in.-lb.,  the  ultimate  compressive  strength  of  the  concrete  being 
taken  at  2000  lb.  per  sq.  in.  and  the  elastic  limit  of  the  steel  at  40,000  lb.  per  sq.  in.     Assume  n  =  15. 


280 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-11 


k  ^  — 


1  + 


20 


0.698 


30 

1  -  Hk  =  0.775 
2  0.598 


J 

^  "  3  '  20 

With  a  factor  of  safety  of  4,  the  ultimate  bending  moment  is  600,000  in.-lb.  and 


0.02 


With  &  =  8  in.,  then 


Also, 


d2 


600,000 


(^3X2000)  (0.598)  (0.775) 


=  972 


972 
8 


121.5,  or  d  =  11  in. 


As  =  (0.02)  (8)  (11)  =  1.76  sq.  in. 


11.  Flexure  Formulas  for  "Working  Loads  and  for  Ultimate  Loads  Compared. — Formulas 
for  ultimate  loads  are  open  to  the  objection  that  when  a  factor  of  safety  is  applied  which  will 
bring  the  stress  in  the  concrete  to  about  a  good  working  stress,  the  stress  in  the  steel  becomes 
unduly  low  from  a  standpoint  of  economy.  A  factor  of  safety  of  3  or  4,  as  is  usually  taken, 
leaves  a  high  stress  in  the  concrete  with  the  stress  in  the  steel  far  below  what  is  usually  consid- 
ered a  safe  stress.  Beams  designed  by  the  ultimate  load  formulas  will  generally  be  of  smaller 
cross-sectional  dimensions  than  when  the  straight-line  formulas  are  employed;  but,  on  the  other 
hand,  a  larger  amount  of  steel  is  required.  Practically  identical  results  will  be  obtained  by  the 
two  classes  of  formulas  if  about  15%  lower  compressive  stress  is  permitted  in  the  concrete  by 
the  ultimate  load  formulas  than  by  the  formulas  based  on  the  straight-line  theory.  There 
seems  to  be  no  good  reason  why  the  simple  formulas  based  on  the  theory  of  straight-line  stress 
variation  should  not  be  used  for  purposes  of  design,  safe  working  stresses  being  employed. 

12.  Lengths  of  Simply-supported  Beams. — The  span  length  for  beams  and  slabs  simply 
supported  should  be  taken  as  the  distance  from  center  to  center  of  supports,  but  need  not  be 
taken  to  exceed  the  clear  span  plus  the  depth  of  beam  or  slab. 

13.  Shearing  Stresses. — In  Fig.  11  is  shown  a  small  portion  of  a  concrete  beam,  so  short 
that  no  appreciable  portion  of  the  load  on  the  beam  acts  directly  upon  it.    The  opposing  total 

compressive  forces  are  denoted  by  C  and  C;  and  the  tension 
in  the  steel  on  each  face  by  T'  and  T.  The  tension  in  the 
concrete  may  be  neglected.  Let  V  be  the  total  shear  on 
this  small  portion  of  the  beam.  From  conditions  of  equili- 
brium, C  =  T'  and  C  =  T.  The  total  horizontal  shearing 
stress  upon  a  horizontal  section  immediately  above  the  steel 
is  T'  —  T,  and  if  h  denotes  the  breadth  of  the  beam  and  v 
the  unit  shear  (horizontal  or  vertical)  at  any  point  between 
the  neutral  axis  and  the  steel,  then 


T 


 Neafrai  <t 


Fig.  1] 


hx 


(1) 


The  various  couples  acting  upon  the  element  produce  equilibrium ;  hence 

Vx  =  {T  -  T)jd 

or 

Vx 

Substituting  this  value  in  equation  (1)  there  results 

V  (2) 

which  is  the  value  of  shear  intensity  at  any  point  between  the  neutral  axis  and  the  steel. 


Sec.  7-14] 


BEAMS  AND  SLABS 


281 


The  value  of  j  for  working  loads  varies  within  narrow  limits  and  v  will  change  but  sHghtly 
if  the  different  values  of  j  are  inserted  in  equation  (2).  The  average  value  of  j  for  beams  in 
ordinary  construc{ion  is         Using  this  value,  equation  (2)  reduces  to 


bd 


(3) 


Fig.  12. 


I 

IP  Shearing  stress  is  the  same  at  all  points  between  the  neutral  axis  and  the  steel,  and  above 
the  neutral  axis  it  follows  the  parabolic  law.  Fig.  12  represents  the  distribution  of  shearing 
stress  on  a  vertical  cross-section  assuming  no  tension  in  the  concrete. 

The  longitudinal  tension  in  the  concrete  near  the  end  of  beam  modifies  the  distribution 
of  the  shear,  increasing  the  shearing  stress  somewhat  at  the  neutral  axis  and  decreasing  it  at 
the  level  of  the  reinforcement.  Equation  (3),  however,  gives  results  ^ 
which  are  sufficiently  accurate  and  are  derived  for  beams  having  the 
horizontal  bars  straight  throughout.  When  any  web  reinforcement  is 
used,  the  distribution  and  the  amount  of  the  shearing  stresses  at  the  end 
of  a  simply  supported  beam  are  materially  different  from  the  foregoing. 
The  analysis  of  the  stresses  becomes  more  complex  and  a  determination 
of  their  value  impracticable.  Even  here,  however,  the  above  formula 
serves  a  useful  purpose.  It  is  found  that  shear  is  the  chief  factor  in  the 
failure  of  a  beam  by  diagonal  tension  and  either  formula  (2)  or  formula  (3)  may  be  used  in  de- 
sign if  properly  controlled  by  the  results  of  experiments. 

Failure  by  the  actual  shearing  of  the  concrete  in  a  beam  is  not  a  likely  occurrence  under 
any  conditions  as  the  shearing  strength  of  concrete  is  at  least  one-half  the  crushing  strength. 

14.  Methods  of  Strengthening  Beams  Against  Failure  in  Diagonal  Tension. — The  in- 
tensity of  the  diagonal  tensile  stress  at  any  point  in  a  beam  depends  upon  the  shear  and  hori- 
zontal tension  in  the  concrete,  with  shear  as  the  chief  factor.  The  percentage  of  horizontal 
reinforcement  must  also  be  considered,  since  the  amount  of  steel  employed  affects  the  hori- 
zontal deformation  and  consequently  the  tension  in  the 
concrete.  Thus  beams  may  be  strengthened  against 
failure  in  diagonal  tension  by  keeping  the  horizontal 
tension  small  through  the  use  of  considerable  horizontal 
steel  at  points  of  heavy  shear,  by  avoiding  heavy  shear- 
ing stresses,  and  by  providing  some  type  of  web  rein- 
forcement. A  low  unit  working  stress  in  whatever 
type  of  web  reinforcement  is  employed  is  also  much  to 
be  preferred. 

The  most  unfavorable  part  of  a  beam  as  regards 
diagonal  tension  is  at  points  of  excessive  shear  com- 
bined with  considerable  bending  moment.  A  sufficient 
number  of  reinforcing  rods  should  be  extended  horizon- 
tally to  the  ends  of  the  beam  to  provide  for  bending 
with  low  unit  stresses  in  the  steel.  In  small  beams,  ver- 
tical stirrups  looped  about  the  horizontal  rods  may  be  employed  throughout  for  web  reinforce- 
ment but  in  large  beams  under  heavy  shearing  stresses,  both  stirrups  and  bent  rods  should  be 
used.  The  stirrups  in  large  beams  should  be  securely  fastened  to  the  longitudinal  rods  in 
such  a  way  as  to  prevent  slipping  of  bar  past  the  stirrup.  Inclined  web  members  may  also 
be  used  in  place  of  vertical  stirrups  if  securely  attached  to  the  horizontal  rods.  Vertical 
stirrups  may  be  made  in  various  forms,  as  indicated  in  Fig.  13. 

15.  Moment  and  Diagonal-tension  Tests — General.^ — When  a  beam  begins  to  fail  by 
yielding  of  the  steel  at,  or  near,  the  section  of  maximum  bending  moment,  any  further  load 

1  For  detailed  treatment  of  this  subject,  see  "Concrete,  Plain  and  Reinforced"  by  Taylor  and  Thompson 
(1916  Edition). 


282 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-15 


rapidly  increases  the  deformation,  large  cracks  open  up  in  the  concrete  on  the  tension  side,  the 
neutral  axis  rises  on  this  account,  and  the  ultimate  failure  soon  occurs  by  the  crushing  of  the 
concrete.  A  steel  tension  failure  is  found  to  occur  when  the  amount  of  steel  used  is  less  than 
the  amount  determined  by  theoretical  formulas  which  makes  the  beam  of  equal  strength  in 
tension  and  compression.  This  result  agrees,  then,  with  what  is  expected.  Likewise  it  is 
found  that  with  a  larger  amount  of  steel  than  is  theoretically  required,  the  yield  point  of  steel 
is  not  reached  and  the  beam  fails  directly  by  crushing  of  the  concrete.  Beams  with  no  web 
reinforcement  and  with  the  existence  of  large  shearing  and  moment  stresses, 
fail  by  inclined  cracks  opening  up  in  the  concrete,  thus  substantiating  to  a 
considerable  degree  the  theoretical  deductions  regarding  the  internal  stresses  in 
beams. 

The  results  of  breaking  tests  on  reinforced  beams  with  different  percent- 
ages of  steel  reinforcement  compare  well  with  the  results  derived  from  the- 
oretical formulas.  Considering  the  nature  of  the  material,  the  calculations  by 
the  two  assumptions  of  stress  variation  are  found  to  agree  sufficiently  with 
the  experimental  results  to  justify  their  use  in  problems  of  design. 

Another  method  of  testing  reinforced-concrete  beams  is  by  the  use  of  ex- 
tensometers  to  measure  distortions,  so  that  the  deformation  of  the  steel  and  of 
the  extreme  fiber  of  the  concrete  may  be  calculated  and  the  neutral  axis  determined.  In 
making  beam  tests  it  is  customary  to  place  equal  loads  at  points  dividing  the  length  into 
three  equal  parts.  The  advantage  of  this  arrangement  lies  in  the  fact  that  the  bending 
moment  is  practically  uniform  between  the  loads  and,  if  measuring  devices  are  attached,  the 
deformations  of  the  fibers  at  the  top  and  at  the  bottom  may  be  easily  determined.  If  in  Fig. 
14  the  deformations  be  aa'  and  hb',  the  neutral  axis  0  is  located  by  connecting 
a'  and  b'  with  a  straight  line,  intersecting  ab  at  0. 

In  moment  calculations,  the  position  of  the  neutral  axis  is  of  prime  im- 
portance and  once  this  is  known,  the  actual  strength  may  be  determined  with 
little  uncertainty.  The  formula  for  k  shows  that  the  position  of  the  neutral 
axis  depends  only  upon  the  percentage  of  steel  employed  and  upon  the  ratio 
E 

or  n.    The  value  of  Ec  is  the  only  value  in  the  formula  which  is  uncertain. 

It  might  be  well  to  take  the  value  as  determined  by  the  ordinary  compression 
test  for  use  in  theoretical  formulas,  but  closer  results  can  be  obtained  from 
these  formulas  if  the  value  of  n  is  taken  so  that  for  average  conditions  the  neu- 
tral axis  is  in  as  nearly  as  possible  the  same  position  theoretically  and  experimentally.  The 
reason  that  Ec,  as  thus  determined,  will  give  better  results  at  working  loads,  is  due  to  the  effect 
of  the  remaining  tension  in  the  concrete  below  the  neutral  axis — a  stress  which  is  properly  not 
allowed  for  in  the  resisting  moment. 

In  making  the  experiments  above  described,  it  was  observed  that  the  neutral  axis  raised 
as  the  loading  increased,  k  being  approximately  H  at  working  loads.    It  was  also  noted  that 

for  the  lower  loads  the  neutral  axis  as  deter- 
mined from  the  theoretical  formulas  is  more 
uncertain  and  generally  lower  in  the  beam 
than  for  the  higher  loads.  This  is  undoubtedly 
due  to  the  relatively  large  influence  of  the  ten- 
sile strength  of  the  concrete  in  such  cases.  This 
rise  of  the  neutral  axis  as  the  load  increases  is 
shown  in  Fig.  15.  Consider  aibi  to  be  the  plane 
ab  after  a  bending  takes  place  just  sufficient  to  bring  the  maximum  tensile  stress  in  the  concrete 
to  its  ultimate  value.  When  loads  are  applied  which  cause  a  greater  bending  moment,  the 
concrete  in  tension  becomes  broken  by  fine  cracks,  and  the  steel  takes  a  greater  part  of  the 
tensile  stress.    The  elongation  at  b  now  increases  faster  than  at  a,  and  the  neutral  axis  rises 


Fig.  16. 


Sec.  7-15] 


BEAMS  AND  SLABS 


283 


rapidly.  When  working  loads  are  reached,  the  position  of  the  neutral  axis  moves  but  little, 
and  the  steel  takes  all  the  tension. 

Fig.  16  illustrates  a  typical  diagonal  tension  failure  in  beams  reinforced  with  only  horizontal 
bars.  The  initial  crack  forms  at  a  and  branches  toward  b.  A  little  later  the  concrete  begins  to 
fail  in  a  horizontal  tension  crack  just  above  the  rods,  running  from  a  toward  the  end  of  the  beam. 
This  horizontal  crack  is  brought  about  by  the  new  conditions  which  exist  after  the  concrete 
has  become  cracked  along  the  diagonal  line  and  the  normal  diagonal  tension  has  thus  ceased 
to  act.  Sometimes  this  horizontal  crack  does  not  extend  to  the  end  of  the  beam — the  final 
failure  occurring  either  by  the  diagonal  crack  extending  to  the  top  of  the  beam  or  the  horizontal 
rods  pulling  out.  Thus  final  failure  often  occurs  from  stresses  which  are  developed  after  initial 
failure  has  occurred.  However,  the  initial  failure  and  its  cause  is  what  is  of  importance  in 
design. 

Tests  show  that  it  is  possible  to  provide  sufficient  web  reinforcement  by  means  of  stirrups 
and  bent  bars  to  develop  the  full  strength  of  the  beam  whether  governed  by  the  crushing  strength 
of  the  concrete  or  the  elastic  limit  of  the  steel.  It  is  found  that  part  of  the  diagonal  tension  is 
taken  by  the  concrete  so  that  web  reinforcement  need  not  be  designed  to  take  all  the  diagonal 
tensile  stresses. 

Vertical  stirrups  spaced  a  distance  apart  equal  to,  or  greater  than,  the  depth  of  beam  help 
but  little  in  preventing  diagonal  cracks  between  successive  stirrups.  They  may  prevent  final 
failure,  however,  by  preventing  the  extension  of  a  crack  horizontally  along  the  reinforcing  rods. 
Stirrups  are  found  by  tests  to  be  most  effective  when  spaced  a  distance  apart  equal  to  one-third 
the  depth  of  beam.  To  give  the  best  results  they 
should  be  securely  fastened  to  the  longitudinal  bars 
in  the  tension  side  of  the  beam. 

Tests  in  which  curved  and  inclined  rods  were 
used,  but  in  which  no  rods  continued  straight  for 
the  entire  length  of  the  beam,  showed  results  very 
little  better  than  for  straight  rods. 

Vertical  stirrups  and  bent  rods  combined  are 
found  by  tests  to  give  the  very  best  results.  Tests  also  seem  to  indicate  that  too  much  re- 
liance should  not  be  placed  upon  one  or  two  bent  rods.  For  this  reason,  even  if  one  or  two 
rods  are  bent  up  properly  to  take  the  diagonal  tension,  it  would  be  good  design  to  consider  this 
rod,  or  rods,  as  not  taking  any  diagonal  tensile  stress  and  to  provide  a  thorough  web  reinforce- 
ment by  means  of  stirrups. 

Tests  show  that  bent  bars  may  be  inclined  at  any  angle  between  30  and  45  deg.  without 
the  beam  showing  any  marked  difference  in  strength.  Beams  having  sharp  bends  in  the  rein- 
forcing bars  are  found  to  have  less  strength  than  beams  with  bars  having  circular  bends  of  a 
radius  about  12  diameters. 

Fig.  17  represents  the  conditions  which  developed  in  the  test  of  a  beam.  The  cracks  are 
numbered  in  the  order  of  their  appearance,  final  failure  occurring  at  crack  No.  4  and  being  due 
to  inadequate  web  reinforcement.    The  stirrups  were  stressed  beyond  their  yield  point. 

It  appears  from  tests  of  beams  in  which  bent  rods  were  employed  with  a  good  anchorage  at 
their  ends,  that  the  anchorage  is  quite  advantageous  in  increasing  web  resistance.  This  form 
of  construction  is  also  found  to  be  an  insurance  against  failure  at  low  loads  through  defective 
concrete  or  insufficient  bond. 

Hooks  at  the  ends  of  the  horizontal  tensile  bars  prevent  slipping  of  the  bars  in  the  concrete 
and  are  found  to  increase  the  strength  of  the  beam  materially. 

The  results  of  experiments  show  that  the  ultimate  compressive  strength  of  concrete  in  a 
beam  is  at  least  equal  to  its  crushing  strength  as  determined  by  tests  on  cubes  hardened  under 
similar  conditions;  also,  that  the  yield  point  of  the  steel  should  be  regarded  as  ultimate  strength 
as  far  as  reinforced  beams  are  concerned.  When  the  steel  reaches  its  yield  point,  the  beam  de- 
flects, and  failure  soon  occurs  by  the  crushing  of  the  concrete. 


284 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-16 


16.  Bond  Stress. — The  tension  in  the  horizontal  steel  near  the  lower  surface  of  a  reinf orced- 
concrete  beam  is  a  maximum  near  the  center  of  beam  and  decreases  each  way  toward  the  end. 
The  difference  in  the  tension  between  any  two  points  is  transmitted  to  the  concrete  by  the  bond 
between  the  steel  and  the  concrete. 

A  formula  for  bond  may  be  derived  for  beams  in  which  the  reinforcement  is  horizontal 
or  straight  throughout.  The  total  shearing  stress  per  linear  inch  between  the  steel  and  the 
concrete,  considering  a  length  of  beam  equal  to  x,  is 

T'  -  T 

X 

From  Fig.  11 

Vx  =  (T'  -  T)jd 

or 

T'  —  T  V 

  =  -rr  (bond  stress  per  linear  inch) 

V 

and  the  bond  stress  per  square  inch  of  the  surface  of  the  steel  bars  is      divided  by  the  sum 

in  inches  of  the  circumference  of  the  bars  at  the  given  vertical  cross-section.  If  u  =  unit 
bond  stress,  and  2o  the  total  circumference  of  all  bars  in  a  beam  at  the  given  section,  then 

V 

The  above  formula  shows  that  theoretically  the  bond  stress  is  a  simple  function  of  the 
shear  and  varies  with  the  shear.  Thus,  shear  diagrams  may  be  used  to  represent  the  variation 
of  bond  stress  along  a  beam.  When  using  the  above  formula,  the  average  value  of  j  =  J-^ 
may  be  taken. 

If  we  consider  simply  supported  beams,  tests  on  rectangular  and  T-beams  loaded  at  the 
quarter  points  show  that  when  stirrups  are  used  the  beam  is  stiffened  and  the  bond  stress  along 
the  horizontal  rods  near  the  end  of  beam  is  somewhat  reduced.  A  reason  for  this  may  be 
shown  in  the  fact  that,  after  the  concrete  begins  to  crack  from  diagonal  tension,  the  stirrups 
aid  in  carrying  part  of  the  tensile  stress  which  results  from  the  bending  moment  then  existing 
at  the  line  of  the  diagonal  crack;  the  stress  in  the  horizontal  rods  at  the  end  of  beam  is  thus 
reduced  and  likewise  the  liability  of  failure  through  bond.  A  greater  reduction  of  the  bond 
stress  has  been  found  to  exist  when  the  web  reinforcement  is  provided  by  means  of  bent  rods 
and  stirrups.  The  reduction  becomes  considerable  when  about  one-half  of  all  the  rods  are  bent 
up,  provided,  however,  that  a  sufficient  number  of  rods  be  thus  employed.  Results  seem  to 
indicate  that  no  reduction  should  be  considered  in  design  unless  the  number  of  rods  bent 
be  greater  than  two  or  three  and  that  the  bends  be  made  at  least  at  two  points  at  each  end  of 
beam.  Tests  show  that  for  conditions  especially  favorable,  an  average  of  50%  more  bond  stress 
may  safely  be  allowed  on  the  horizontal  rods  at  the  end  of  beam  than  would  be  considered 
safe  by  the  above  formula.  No  allowance  should  be  made  when  only  stirrups  are  employed 
for  the  web  reinforcement. 

It  has  been  found  in  the  testing  of  simply  supported  T-beams  with  steel  straight  throughout 
and  loaded  at  the  one-third  points,  that  the  bond  stress  along  the  horizontal  steel  is  affected  by 
the  presence  of  tensile  stresses  in  the  concrete  and  that  this  bond  stress  is  usually  a  maximum 
just  outside  the  load  points.  The  observed  bond  stress  at  these  points  was  in  some  cases  as 
much  as  50%  greater  than  the  computed  stress. 

In  beams  reinforced  for  diagonal  tension  the  bond  stresses  along  the  horizontal  bars  are 
not  distributed  as  uniformly  as  in  beams  having  the  reinforcement  horizontal  or  straight  through- 
out. The  bond  stresses  are  found  to  be  concentrated  at  and  near  stirrups  and  at  and  near 
points  of  bending  of  the  longitudinal  rods.  Such  concentration  of  bond  stress  causes  local  slip 
of  the  longitudinal  bars  unless  the  web  reinforcement  is  well  distributed  along  the  beam.  If  a 
stirrup  is  not  rigidly  attached  to  the  horizontal  rods  and  local  slip  of  bars  occurs,  the  effective- 
ness of  the  stirrup  is  somewhat  impaired. 


Sec.  7-17] 


BEAMS  AND  SLABS 


285 


The  bond  stress  in  continuous  beams  is  treated  in  Art.  39. 

The  bond  strength  of  vertical  (or  inclined)  stirrups  may  be  insufficient  to  develop  the  re- 
quired strength  of  the  stirrups  with  respect  to  tension.  This  possibiHty  must  also  be  investi- 
gated in  the  design  of  beams  having  web  reinforcement  in  the  form  of  bent  rods.  Tests  show 
that  it  is  safe  to  assume  that  the  stress  in  a  stirrup  or  bent-up  bar  may  be  transferred  to  the 
concrete  above  a  point  0.6  the  depth  of  beam  from  the  upper  surface.  In  most  cases  it  is  found 
that  stirrups  must  have  hooked  ends. 

For  illustrative  problem,  see  page  298. 

17.  Web  Reinforcement  in  General. — Inclined  web  reinforcement  may  be  separate  mem- 
bers firmly  connected  with  the  horizontal  reinforcement  to  prevent  slipping,  or  some  of  the 
horizontal  bars  may  be  bent  up  near  the  ends  of  the  beam  where  they  are  not  needed  to  resist 
bending.  The  vertical  reinforcement  may  be  used  separately  or  in  combination  with  inclined 
reinforcement,  depending  upon  the  preference  of  the  designer  and  upon  the  amount  of  diagonal 
tension  to  be  provided  for.  Vertical  stirrups  should  be  looped  around  the  horizontal  bars  and 
in  important  beams  should  also  be  firmly  secured  to  these  bars  by  wiring  or  otherwise.  Stir- 
rups should  usually  be  looped  or  hooked  at  the  top  in  order  to  prevent  slipping  due  to  insuffi- 
cient bond  (see  Art.  19). 

The  proportioning  of  web  reinforcement  cannot  be  done  with  any  degree  of  exactness  since 
very  little  experimental  work  has  been  performed  along  this  line.  Howler,  rough  determina- 
tions of  what  is  required  may  be  obtained  on  rational  grounds.  The  only  information  from 
tests  is  the  value  of  the  maximum  shearing  stress  which  measures  diagonal  tension  failure — (1) 
for  beams  with  horizontal  bars  only,  and  (2)  for  beams  having  an  effective  system  of  web  rein- 
forcement. Also,  tests  on  beams,  with  and  without  web  reinforcement,  show  that  when  rein- 
forcement is  provided  for  diagonal  tension,  the  concrete  may  be  assumed 
to  carry  its  full  value  of  the  shear  and  the  steel  the  remainder.    It  is  I     t  I 

generally  conceded  as  safe  practice  in  the  designing  of  beams  to  use 
only  two-thirds  of  the  external  vertical  shear  in  making  calculations  of 
the  stresses  to  be  taken  by  the  web  reinforcement. 

Consider  now  Fig.  18,  in  which  V  represents  the  average  total  shear 
over  the  portion  s  of  the  beam.  Let  v'  represent  average  unit  horizon- 
tal shear  on  any  plane  below  the  neutral  axis.    Then  (see  Art.  13) 

bjd 

The  total  shear  over  any  such  horizontal  plane  is  v'bs',  whence 

V  OS  =  -TT 

Jd 

The  function  of  stirrups,  either  vertical  or  inclined,  is  to  resist  by  their  tensile  strength 
that  portion  of  the  above  shearing  stress  which  is  not  carried  by  the  concrete. 

Assume  a  vertical  stirrup  to  be  placed  at  the  section  A- A,  and  to  oppose  the  shear  over  the 
portion  of  the  beam.  The  total  stress  in  the  stirrup  is  Asfs  (in  a  U-shaped  stirrup,  As  is  the  sum 
of  the  areas  of  the  two  legs),  and  it  is  produced  by  that  part  of  the  total  shear  over  the  horizontal 
plane  bs  not  taken  by  the  concrete.  Assuming  the  steel  to  take  two-thirds  of  the  total  shear, 
then 


1  I 


U.-J 

Fig.  18. 


AJs  = 


'bs  =  ^--V, 


Vs 
jd 


Solving 


As  = 


s 


fsjd 


(vertical  stirrups) 


(1) 


(2) 


286 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-18 


For  inclined  members  and  bent-up  bars,  the  lines  on  a  beam  representing  the  direction  in 
which  the  diagonal  tensile  cracks  are  likely  to  occur,  are  crossed  more  times  per  unit  of  length 
for  a  given  horizontal  spacing  than  would  be  the  case  if  vertical  stirrups  were  employed;  that  is, 
a  given  amount  of  inclined  steel  is  much  more  effective  in  taking  diagonal  tension  than  the  same 
amount  of  vertical  steel.    It  may  be  assumed  that  the  allowable  stress  in  the  inclined  bars  is 

approximately    — and  the  required  area  of  steel,  assuming  the  steel  to  take  two-thirds  of 
sin  4o 

the  shear,  is 

2  0.7(Vs) 

or 

s      2  0.77 

Since  tests  show  that  bent  bars  may  be  inclined  at  any  angle  between  30  and  45  deg.  without 
a  beam  showing  any  marked  difference  in  strength  (see  Art.  15),  the  Joint  Committee  recom- 
mends that  the  longitudinal  spacing  of  vertical  stirrups  should  not  exceed  one-half  (3^)  the  depth 
of  beam  and  that  of  inclined  members  and  bent-up  bars  should  not  exceed  three-fourths  {^i) 
of  the  depth  of  beam. 

18.  Region  Where  No  Web  Reinforcement  is  Required. — There  is  a  region  near  the  center 
of  most  beams  in  which  the  shear  does  not  exceed  that  permissible  for  plain  concrete.  In  this 
region  no  shear  reinforcement  is  required.  The  distance  from  one  support  to  a  point  beyond 
which  no  stirrups  are  required  may  be  found  as  follows  for  a  uniformly  loaded  beam. 

Let 

I  =  span  of  beam  in  feet. 
w  =  uniform  load  in  pounds  per  foot. 

Xi  =  distance  in  feet  from  left  support  beyond  which  no  stirrups  are  required. 

Vi  =  unit  working  shear  for  plain  concrete, 

Vi  =  total  working  shear,  producing  unit  shear  of  Vi. 
From  equation  (2)  on  page  280,  it  is  obvious  that,  where  Vi  =  v,  no  stirrups  are  recjuired. 
At  this  point 

^  Wd 


But 
Whence 

or,  in  terms  of  v  at  the  end  of  beam, 


Xi 


wl 

_  I  Vibjd 
~  2  wT 


Xi 

When  V  at  the  end  of  beam  equals  3^1,  then 

/ 

=  3 

This  derivation  applies  only  to  a  static  uniformly  distributed  load  over  the  whole  span. 

Suppose  a  10-ft.  beam  {h  =  10  in.  and  d  =  20  in.)  is  uniformly  loaded  with  a  static  load  of  2900  lb.  per  ft. 
and  assume  vi  =  40  lb.  per  sq.  in.  according  to  recommendation  of  Joint  Committee  for  2000-lb.  concrete.  Also 
assume  jd  =  lid.  Then 

10  (40)(10)(17.5) 
XI  =  y  290"0          =  2.6  ft. 

When  designing  for  floor  systems  it  is  often  more  proper  to  consider  the  uniform  load  to 


Sec.  7-18] 


BEAMS  AND  SLABS 


287 


Diagram  I 


10  15  5 

Spacing  of  U-5tirrups  in  inches 

80  30  10 

Spacing  of  W- Stirrups  »n  inches 


0  5  10  15 

Spacing  of  U-Stirrupjs  m  inches 
30  0  lO  20  30 

Spacing  of  W-S+irrups  in  Inches 


Diagram  II 


10  \5  5 

Spacing  of  U-5tirrups  in  inches 

80  30  10  20 

Spacing  of  W-5tirrups  in  inches 

Diagram  III 


0  5  10  15 

Spacing  of  U-5firrups  in  inches 
0  10  20  30 

Spacing  of  W-SfirrupS  in  inches 


VO  \5  5 

Spacing  of  U-Stirrups  in  inches 

20  30  \0 

Spacing  of  W-Sfirrops  in  inches 


0  5  10  15 

Spacing  of  U-5tirrups  in  inches 
O  10  20  30 

Spacing  of  W-5tirrupS  in  inchea 


288  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  7-18 


Diagram  IV 


P  5  10  15  5  10  15  0  5  10  15 

Spacing  of  U-5tirrups  In  inches  Spacing  of  U-Stirrups  in  inches 

O  10  20  30  10  20  30  0  (0  20  30 

Spacing  of  W- Stirrups  in  inches  Spacing  of  W-Stirrups  in  inches 


Diagram  V 


0                 5                 10                 15                  5  10                15                0                 5                 10  15 

Spacing  of  U-Stirrups  in  inches  Spacing  of  U-Sttrrups  in  inches 

0                 10                20                30                10  ?0               30                0                 10                20  30 

Spacing  of  W-Stirfups  in  inches  Spacing  of  W-Stirrups  in  inches 


Diagram  VI 


spacing  of  U-Stirrups  in  inches  Spacing  of  U-S+irrups  m  inches 

O  10  20  30  10  20  30  O  10  ZO  3Q 

Spacing  of  W-5tirrvp6  in  inches  Spacing  of  W-Stirrwp*  in  jnche^ 


Sec.  7-19] 


BEAMS  AND  SLABS 


289 


Diagram  VII 


10  15  5  10 

Spacing  of  U-5+irrups  in  inches 

20  30  10  ZO 

5p<Jcing  of  W-S+trrups   in  inches 

Diagram  VIII 


15  O  5  10  15 

Spacmg  of  U-S+irrups  in  fnches 

30  0  10  20  3Q 

Spacing  of  W- Stirrups  in  inches 


10  IS  5 

Spacing  of  U-Sfirrups  <n  Inches 

20  30  10 

Spacing  of  W-Stirrups  In  inches 


10  15  0  5  \0  15 

Spacing  of  U- Stirrups  in  inches 

ZO  30  O  10  20  30 

Spacing  of  W- Stirrups  in  inches 


be  a  moving  load.    In  this  case  the  shear  at  the  center  of  the  span  is  not  zero,  but  is  equal  at 

maximum  to      •  where  w'  is  the  live  load  per  foot.    When  plotting  the  shear  diagram  this  value 

should  be  plotted  at  the  center  of  the  beam  and  the  total  end  shear  at  the  support.  The  varia- 
tion in  shear  between  these  two  points  may  be  safely  assumed  to  be  a  straight  line.  The  shear 
to  be  carried  by  the  concrete  being  known,  the  point  in  the  beam  beyond  which  no  shear  rein- 
forcement is  required  may  be  quickly  located. 

19.  Vertical  Stirrups. — The  required  total  area  of  cross-section  of  a  vertical  stirrup  may 
be  determined  by  the  formula  (see  page  285) 

A  -^-^ 
'     3  hjd 

assuming  the  web  reinforcement  to  carry  two-thirds  of  the  total  shear.  (For  U-shaped  stirrup, 
As  is  the  sum  of  the  areas  of  the  two  legs.)  With  a  given  size  of  stirrup,  this  formula  may  be 
solved  to  give  the  spacing  required,  or 

_  3  Asfsjd 
^  "  2'  V 

19 


290 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-19 


The  value  of  V  should  be  taken  at  the  section  where  the  spacing  is  desired.  This  spacing 
formula  may  be  solved  directly  by  means  of  Diagrams  1  to  VIII  inclusive  for  three  sizes  of 
stirrups.^ 

If  the  shear  diagram  is  drawn  for  any  given  beam,  it  is  convenient  to  use  the  above  formula 
in  the  form 

3  A,f..jd 
2'  s 


V  = 


and,  for  various  even-inch  spacings  (s)  of  the  stirrups,  to  solve  for  the  corresponding  total 
external  shears.  At  the  point  where  the  ordinate  to  the  shear  diagram  scales  a  computed  total 
shear,  there  the  spacing  may  be  made  the  even  inch  used  for  s  in  the  formula. 

Tests  have  shown  that  little  or  no  value  is  derived  from  stirrups  spaced  a  distance  apart 
equal  to,  or  greater  than,  d  (see  page  283).  A  practical  limit  suggested  by  the  Joint  Com- 
mittee is  one-half  the  depth. 

In  restrained  beams  the  first  stirrup  should  be  placed  no  farther  than  one-half  the  mini- 
mum spacing  from  the  edge  of  support  and,  in  beams  simply  supported,  the  first  stirrup  should 
be  placed  not  farther  than  one-half  the  minimum  spacing  from  the  center  of  support. 

The  variation  of  shear  intensity  along  a  uniformly  loaded  beam  is  shown  in  Fig.  19,  The 

area  ABCD  represents  the  total  stress  to  be  taken 
by  the  stirrups  at  each  end  of  beam.  The  ordi- 
nate AB  represents  two-thirds  of  the  shear  at  the 
support  per  1-in.  length  of  beam. 

Some  attention  must  be  paid  to  the  diameter 
of  stirrup  which  it  will  be  possible  to  employ  in  any 
given  case.  The  diameter  should  not  be  so  small 
that  the  stirrups  will  be  placed  too  close  together 
for  convenience  in  construction,  yet  not  so  far 
apart  that  the  limiting  value  }4d  is  exceeded. 
Fig.  19.  But,  in  addition  to  such  consideration,  the  bond 

strength  of  the  stirrup  must  be  investigated  if  the 
stirrups  are  not  made  with  hooked  ends,  since  the  danger  of  slipping  determines  the  maxi- 
mum diameter  which  may  be  employed. 

The  distribution  of  bond  stresses  developed  on  the  surface  of  the  stirrups  is  indeterminate. 
Evidently  it  must  not  be  expected  that  tension  will  be  transferred  through  bond  to  the  con- 
crete until  the  compression  area  of  the  beam  is  reached,  or  until  a  point  but  little  below  is 
reached.  Experiments  show  that  it  is  safe  to  assume  the  grip  of  a  stirrup  to  be  0.6  the  depth 
of  beam.    Using  notation  on  page  270. 

fsAs  =  0.6  dou 


A  A 

i  -§ 

•  -l<o 

1  +B 

■  i 

y    Y  . 

^^^^ 

mmMmMWMM  concrete>^ 

A' 

<  

=0.6^^ 

0  fs 


But,  for  round  or  square  stirrups,  letting  i  =  maximum  diameter  of  stirrup, 


Then 


1  . 


(-3 


If  each  end  of  the  stirrup  is  bent  into  a  prong  or  hook,  then  stirrups  of  larger  diameter  may  be 
used  than  is  indicated  by  the  above  formula.    Tests  show  that  if  hooks  with  a  semicircular 

1  Diagrams  similar  to  those  by  Frank  S.  Bailey  in  E7ia.  News.  Oct.  12.  1916. 


Sec.  7-20] 


BEAMS  AND  SLABS 


291 


bend  of  4  diameters  are  well  embedded  in  concrete,  the  stress  in  the  bar  will  reach  the  elastic 
limit  before  slipping  takes  place  (see  page  268). 

It  is  considered  good  practice  to  use  ^ie-'m.  stirrups  with  hooked  ends  for  beams  from  10 
to  25  in.  deep,  ^^-in.  stirrups  for  beams  from  25  to  40  in.  deep,  and  3^-in.  stirrups  for  beams  from 
40  to  60  in.  deep. 

Illustrative  Problem. — A  simply  supported  beam  is  9  by  16  in.  in  cross-section  and  the  tension  rein- 
forcement is  2  in.  above  the  lower  face  of  the  beam.  Span  of  the  beam  is  8.5  ft.  Uniform  load  of  1800  lb.  per  ft. 
If  necessary,  the  web  is  to  be  reinforced  against  diagonal  tension  using  vertical  stirrups.  Allowable  =  10,000; 
J,  =  40;  w  =  80. 

V  7650 

=6^  =  T9)moA)  =  p^'- 

The  allowable  shear  is  40  lb.  per  sq.  in.,  hence  stirrups  are  necessary. 

The  diameter  of  a  stirrup  without  any  prong  or  hook  should  not  exceed 


80 


0.27  in. 


If  the  stirrups  are  to  be  bent  at  the  upper  end,  Me-in.  round  bars  may  be  considered  secure  against  slipping. 
Stirrups  are  unnecessary  at  a  distance  from  support  equal  to 


0-  'i) 


1.80  ft. 


The  minimum  spacing  of  stirrups  (U-shape)  will  occur  at  the  supports,  or 

3    2(0.077)  (10,000)  (14) 


3.70  in. 


2  7650 

The  shear  diagram  for  one-half  the  beam  is  shown  in  Fig.  20.    For  a  4-in.  stirrup  spacing 


V 


2(0.077)  (10,000)  (7;/8)  (14) 


7090  lb. 


The  point  where  V  =  7090  lb.  is  easily  found  by  scaling  to  the  shear  diagram.  For  a5-in.  stirrup  spacing  V  =  Yo 
(7090)  =  5670  lb.  For  a  6-in.  spacing  V  =  (7090)  =  4730  lb.,  etc.  Time  can  be  saved  by  using  Diagram  I 
in  finding  values  of  V  directly. 


■R)in+  where  s+irnjp  spacing  (s)=  4ii 

•S'Stn. 
s  =  6in. 


Shear  Diagrami 


•■■-stirrups  not  required  be+ween 
this  point  and  center  of  bearr 


Fig.  20. 


Fig.  21. 


20.  Method  of  Placing  Stirrups  from  the  Moment  Diagram. — It  is  a  well-known  principle 
of  mechanics  that  the  difference  in  moment  between  any  two  points  along  a  beam  is  equal  to 
the  average  total  shear  over  the  distance  between  the  points  multiplied  by  that  distance.  Thus, 
from  Fig.  21, 

Vs  =  {Ma  -  Mc) 

or, 

V  =  (^-^  -  Mc)  ^) 
s 

For  loads  concentrated  at  points  along  a  beam  this  law  is  not  strictly  true,  unless  in  each 
case  the  concentration  occurs  at  a  point  midway  between  the  transverse  sections  chosen;  but 
in  the  case  of  concentrated  loadings,  by  beams  cast  against  girders  in  concrete  construction, 
and  even  by  loadings  on  slabs  transmitted  to  the  floor  beams,  the  concentration  may  not  be 
sharply  defined,  and  there  is  no  determinate  law  of  shear  variation  over  such  a  region.  More- 
over, as  this  discussion  will  show  later,  the  distance  s  is  relatively  small  where  shear  is  large. 


292 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-20 


Within  the  limits  of  actual  conditions  in  reinforced-concrete  construction,  therefore,  the 
above  statement  may  be  considered  very  approximate  to  the  truth,  for  the  beam  loaded  with 
concentrated  loads. 

Substituting  the  above  value  for  V  in  equation  (1)  on  page  285,  we  have 

(Ma  -  Mc)  ^  3  Asfsjd 
s  2  '  s 

whence 

Mi  =  (Ma  -  Mc)  =  1.5AJ,jd  (2) 

in  which  Mi  is  the  increment  of  moment  between  the  ends  of  the  portion  of  the  beam  to  be  re- 
inforced with  the  stirrup. 

If  the  stirrup  is  inclined  at  an  angle  d  with  the  horizontal,  then 

sm  d  ^  ^ 

When  e  =  45  deg.  (or,  accurately  enough,  any  angle  between  30  and  45  deg.) 

Mi  =  2.1  Asfsjd  (4) 

Consider  the  portion  of  the  beam  shown  in  Fig.  22a,  loaded  in  such  a  manner  as  to  pro- 
duce the  moment  curve  OP.  It  is  desired  to  reinforce  the  portion  shown  with  vertical  stirrups, 
keeping  in  mind  the  principles  just  laid  down.  A  certain  stirrup  has  been  adopted  which,  for 
this  particular  beam,  gives  the  value  of  Mi  from  equation  (2)  equal  to  the  vertical  distance 


0.4 


ii 

Cji_i 


1 


(6) 


Fig.  22. 


shown  in  Fig.  22a.  The  first  increment  intercepts  the  portion  Om  of  the  curve  OP;  the  second, 
mn,  and  so  on  Let  one  of  these  intercepts,  as  mn,  be  projected  on  the  beam,  thereby  defining 
the  area  ABDC  on  the  diagram  of  the  beam.  This  area  is  the  portion  of  the  beam  over  which 
the  adopted  stirrup  will  exactly  carry  the  shear.  The  length  of  the  portion  is  seen  to  vary  as 
the  shear  varies  along  the  beam.  Since  the  stirrup  is  required  to  carry  the  shear  for  this 
portion  of  the  beam,  it  should  be  placed  through  the  center  of  gravity  of  the  shear  area  for  this 
portion.  Likewise,  each  other  portion  of  the  beam  defined  by  the  projection  of  Mi  would 
have  a  stirrup  through  the  center  of  gravity  of  its  shear  area. 

To  eliminate  the  feature  of  having  to  locate  this  center  of  gravity,  the  following  method  is 
proposed:  Lay  off  as  the  first  value  }i  Mi  (Fig.  22&).  Let  all  other  spaces  be  equal  to  Mi  as 
before.  These  increments  have  m',  n',  etc.,  for  points  of  intersection  on  the  moment  curve. 
Let  these  points  be  projected  on  the  beam.  Each  projection  will  thus  determine  the  position 
of  a  stirrup.  This  scheme  gives  very  closely  the  same  results  as  before,  the  stirrup  being 
placed  slightly  nearer  the  support  than  when  placed  through  the  center  of  gravity  of  the  shear 
area  for  the  portion  of  the  beam;  this  error,  however,  is  well  inside  the  accuracy  of  placing  this 
part  of  the  reinforcing. 

Diagrams  IX  to  XII  inclusive  are  plotted  for  a  ready  solution  of  equations  (2)  and  (4) 
given  above.    Their  use  is  explained  in  an  illustrative  problem  on  page  295. 


Sec.  7-201 


BEAMS  AND  SLABS 


294  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  7-20 


spunod-i^sui  J.0  eptipsnom  ui  dnaaiis  joj.  lusLugjoui  4.u9luolu  Buipuag 


t  CO  fM  (\1 

(p)  ssqoui  ui  Luoaq  jo  qidap  aAi+Da^^g 


spunod-qDU!     spuDsnoqi  ui  dnjj.^s  aoj.  4.uauiaj3U!  4U8Luoai  Buipusg 


Sec.  7-201 


BEAMS  AND  SLABS 


295 


A  simple  method  of  constructing  the  parabola  or  moment  diagram  for  uniform  loading  is 
as  follows:  Let  AG,  Fig.  23,  represent  the  base  of  the  parabola,  with  a  middle  ordinate  of  4.5 
at  D.  Divide  the  base  into  any  desired  number  of  equal  parts,  as  for  instance,  six.  Number 
these  points  from  each  end  beginning  with  zero.    Divide  the  middle  ordinate  by  the  product 

4.5 

of  the  numbers  at  that  point,  as        g  =  0.5.    This  constant,  if  multiplied  by  the  product  of 

the  pair  numbers  at  any  point  gives  the  ordinate  at  that  point.  For  example,  the  ordinate  at 
(7  is  2  X  4  X  0.5  =  4.0.  If  an  ordinate  is  de- 
sired at  a  point  between  the  equal  divisions,  as 
A^,  the  fractional  part  of  the  division  may  be 
expressed  for  the  point  from  each  way.  At  X 
the  distance  from  A  is  2.6  units,  and  from  G, 
3.4  units.  The  ordinate  at  X  is  2.6  X  3.4  X 
0.5  =  4.42.  If  the  middle  ordinate  does  not 
fall  at  an  even  division,  as  would  be  the  case  if 

an  odd  number  of  units  were  used,  the  fractional  values  for  the  mid-point  would  be  used  the 
same  as  the  full  values  in  the  above  case. 

Illustrative  Problem. — Determine  the  size  and  spacing  of  vertical  stirrups  for  shear  reinforcement  in  a 
beam  loaded  as  shown  in  Fig.  24a. 

For  the  static  uniform  load  of  1000  lb.  per  ft.,  the  moment  at  the  center  is 


For  the  concentrated  loads 


ivl^  (1000)  (21)2  (12) 
^  =  -r  =  8 


M  =  (1000)  (7)  (12) 


=  662,000  in.-lb. 
840,000  in.-lb. 


which  moment  obtains  through  the  central  third  of  the  beam.    The  moment  curves  for  each  condition  are  plotted 

separately  and  the  ordinates  of  the  two  combined  to  form 
the  curve  of  total  moments,  shown  in  Fig.  24b. 

The  total  end  shear  is  (1000)  (21)  H  +  10,000  = 
20,500  lb.  Just  outside  the  third  point  the  shear  is  20,500 
-  (1000)  (7)  =  13,500  lb.  Just  inside  the  third  point  it  is 
13,500  -  10,000  =  3500  lb.  At  the  center  the  shear  is  zero. 
The  shear  diagram  is  shown  in  Fig.  24c. 

In  flexure  the  following  values  will  be  adopted:  fs  = 
16,000,  fc  =  650;  n  =  15.  It  is  found  that  for  equal 
strength  in  tension  and  compression  a  depth  {d)  of  26  in.  is 
required  when  6  =  20  in.    Also  j  =  0.875. 

The  allowable  shear  to  be  carried  by  the  concrete 
alone  will  be  taken  as  30  lb.  per  sq.  in.  The  concrete  will 
then  carry  (30)  (20)  (26)  =  15,600  1b.  This  value  is  plotted 
as  point  a  on  the  shear  diagram.  Fig.  24c;  and  the  distance 
from  the  support  to  point  a  is  the  distance  along  the  beam 
where  shear  reinforcement  is  required.  In  this  problem  the 
stirrups  will  be  hooked  at  the  ends  and  an  allowable  stress  of 
10,000  lb.  per  sq.  in.  will  be  assumed.  It  will  be  necessary 
to  select  a  size  of  stirrup  that  will  not  be  so  small  that 
the  spacing  will  be  too  small  for  convenient  construction, 
nor  yet  large  enough  to  cause  the  spacing  to  be  greater 
than  \<id,  a  limit  recommended  by  the  Joint  Committee. 
To  accomplish  this,  let  a  vertical  line  be  projected  from  a, 
Fig.  24c,  to  the  moment  curve,  as  at  h.  Assume  some  dis- 
tance along  the  moment  curve,  as  he,  whose  horizontal 
projection  is  approximately  Md,  and  note  the  value  of  its 
vertical  projection  (in  this  case  200,000  in.-lb.).  With  this 
value  for  vertical  stirrups,  enter  Diagram  IX  at  the  right  and 
move  to  the  left  until  the  value  of  ;  =  0.875  is  reached;  then 
horizontal  line  from  d  =  26  in.    This  point  is  found  to  give  a 


(c)  Shear  Diagrcim 


Fig.  24. 


vertically  until  an  intersection  is  made  with 
stirrup  area  equal  to  0.58  sq.  in. 

Four  Me-in.  round  rods  give  a  combined  area  of  0.601  sq.  in.,  and  by  entering  Diagram  IX  at  d  =  26  in., 
thenoe  horizontally  to  A,  =  0.60  sq.  in.,  thence  vertically  to;  =  0.875  and  finally  to  the  right,  M  =  205,000 in.- 
lb.  for  vertical  stirrups. 


206 


CONCRETE  ENGINEERS'  HANDBOOK 


[See.  7-21 


Beginning  as  in  Fig.  226,  (205,000)  is  laid  off  at  the  base  of  the  moment  curve,  as  de,  Fig.  246,  after 
which  equal  increments  of  205,000  are  laid  off  until  the  point  6  is  passed.  Through  the  points  thus  fixed,  hori- 
zontal lines  are  drawn  to  intersect  the  moment  curve.  From  each  intersection  a  vertical  line  projected  to  the 
beam  locates  a  stirrup. 

21.  Bent  Bars  and  Vertical  Stirrups  for  Web  Reinforcement. — The  ends  of  the  horizontal 
bars  in  a  reinforced-concrete  beam  may  usually  be  bent  up  to  assist  vertical  stirrups  in  pre- 
venting diagonal  tension  failure.  Although  in  some  cases  these  bars  may  be  found  theoretically 
to  take  all  the  diagonal  tensile  stresses  not  taken  by  the  concrete,  vertical  stirrups  are  always 
desirable,  as  shown  by  tests. 

Plain  rods  bent  up  to  provide  web  reinforcement  often  lack  sufficient  bond  strength  to 
render  them  fully  effective.  Where  bent  up  at  a  considerable  angle  they  should  be  turned  again 
horizontally  and  extend  some  distance  along  the  upper  part  of  the  beam,  as  shown  in  Fig.  25. 
In  heavy  construction  the  ends  of  all  bars  should  be  bent  into  a  hook.  The  most  convenient 
method  of  using  reinforcement  is  to  bend  up  two  rods  at  a  time  and  make  all  the  bars  inclined 
at  the  same  angle  with  the  horizontal.  The  bars  bent  should  theoretically  be  such  as  to  keep 
the  center  of  gravity  of  the  beam  cross-section  in  the  line  drawn  vertically  through  the  center 

of  the  section.  An  exception  occurs  to  the  bending  of 
two  rods  at  a  time,  in  the  case  of  an  odd  number  of 
horizontal  rods.  Here,  one  of  the  bends  may  consist 
of  either  one  or  three  rods. 

If  bent  rods  are  not  required  to  provide  for  di- 
agonal tension,  then  the  horizontal  rods  may  be  dis- 
pensed with  at  the  points,  beyond  which  they  are  not 
needed  to  provide  for  tension  due  to  bending.  This 
method  of  stopping  off  the  horizontal  rods  is  not  de- 
sirable, however,  as  the  bond  in  the  concrete  near  the 
middle  of  the  beam  is  not  as  good  as  would  be  the 
case  near  the  end  where  the  moments  are  smaller. 
Also,  when  a  bar  is  discontinued,  the  stress  in  those 
which  remain  is  immediately  increased  tending  still 
further  to  impair  the  bond  between  the  steel  and  the 
a  hook  is  employed  on  the  discontinued  rods.  With 
The  horizontal  components  of  the  upturned  bars  act 
with  the  bars  unbent  in  taking  the  tension  due  to  bending,  and  so  in  general  the  tension  in  the 
horizontal  rods  decreases  somewhat  more  gradually  toward  the  end  of  beam  as  it  should. 

At  the  bend  in  a  horizontal  rod,  the  unit  stress  in  the  concrete  may  become  excessive  if  the 
bend  is  too  abrupt.  Tests  indicate  that  the  strength  of  beams  with  bars  having  sharp  bends  is 
less  than  for  beams  with  bars  having  a  radius  of  bend  equal  to  about  12  diameters. 

The  bent  rods,  if  of  the  same  diameter,  should  be  so  arranged  that  each  rod  will  take  an 
equal  part  of  the  diagonal  tension — that  is,  if  they  can  be  bent  in  this  way  and  still  provide 
satisfactorily  for  the  horizontal  tension.  The  points  where  the  bent  rods  should  cross  the 
neutral  axis  of  the  beam  may  be  found  by  any  of  the  methods  given  for  determining  the  spacing 
of  vertical  stirrups,  remembering  that  a  rod  bent  at  45  deg.  (or,  as  tests  show,  at  any  angle  be- 
tween 30  and  45  deg.)^  is  q-^  =  1.43  times  as  effective  per  unit  area  as  a  vertical  stirrup.  If 

the  rods  cannot  be  bent  as  desired,  then  vertical  stirrups  must  be  used  to  provide  for  some  of  the 
diagonal  tension,  and  it  would  be  preferable  in  all  cases  to  use  stirrups  even  in  that  part  of  the 
beam  where  the  bars  are  bent  up. 

Consider  uniform  loading  and  let  ABCD  in  Fig.  25  be  the  diagonal  tension  area.  Assume 
that  four  rods  may  be  bent  near  the  end  of  beam  and  assume  also  that  the  first  two  bars  cannot 
be  bent  up  nearer  the  center  of  beam  than  the  point  K,  Fig.  25.    The  area  cdef  should  be  made 


>  CD 

\ 

i 
i 

i 
i 

■f 

a     1     d       ;t       e  D 

..-  ■2  Bars--.  ; 

"^"^N  '  k      \^  ' 

_  \  <^^_  "^-i^AV  |-N?ytr^lane3<  J 

^. — —  _  J 

Fia.  25. 

concrete.  This  is  true  whether  or  not 
bent  up  rods  a  better  condition  exists. 


1  See  p.  286. 


Sec.  7-22] 


BEAMS  AND  SLABS 


297 


equal  to  1.43  times  the  allowable  tensile  stress  in  the  two  No.  2  bars;  likewise  area  ahcd  should 
represent  1.43  times  the  allowable  tensile  stress  in  the  No.  1  bars.  (The  vertical  rt  should  theo- 
retically pass  through  the  center  of  gravity  of  the  area  and,  if  dt  is  made  ^2  and  te  J-f  2  of  de,  this 
will  be  practically  accomplished.  The  error  is  not  serious  if  dt  is  made  equal  to  te.)  If  the  No. 
1  bars  cannot  be  bent  up  so  that  the  areas  abed  and  edef  have  the  line  cd  in  common,  then  a  ver- 
tical stirrup,  or  stirrups,  will  be  needed  to  take  care  of  the  space  between  these  areas.  If  the  areas 
overlap,  the  No.  1  bars  may  be  bent  up  nearer  the  end  of  beam  if  no  other  condition  governs. 
In  any  case  the  distance  s  should  not  be  greater  than  ^id — that  is,  the  maximum  spacing  at 
which  inclined  web  reinforcement  can  be  considered  effective.  Stirrups  will  at  least  be  needed 
to  the  left  of  ab  and  to  the  right  of  ef.  The  area  taken  care  of  by  a  vertical  stirrup  is  equal  to 
its  tensile  value. 

The  Joint  Committee  recommends  that  bent  bars  be  considered  as  adding  to  diagonal 
tension  resistance  for  a  horizontal  distance  from  the  point  of  bending  equal  to  ^d.  The  Joint 
Committee  also  recommends  for  the  case  where  stirrups  are  needed  in  combination  with  bent- 
up  bars,  that  the  stresses  in  the  stirrups  be  determined  by  finding  the  amount  of  the  total  shear 
which  may  be  allowed  by  reason  of  the  bent-up  bars,  and  substracting  this  shear  from  the  total 
external  vertical  shear.  Two-thirds  of  the  remainder  is  recommended  as  the  shear  to  be  con- 
sidered as  carried  by  the  stirrups. 

The  bond  strength  of  inclined  bars  must  be  investigated.  This  strength  should  be  pro- 
vided in  the  upper  portion  of  the  beam.  As  with  vertical  stirrups,  it  is  arbitrarily  assumed  that 
no  stress  is  transmitted  from  the  steel  to  the  concrete  below  a  point  which  is  0.6d  below  the  upper 
surface  of  the  beam. 

Assume  that  the  stress  in  an  inclined  bar  is  its  working  stress.  This  gives  the  maximum 
condition.    Using  the  notation  of  page  270  and  I'  for  length 

Vou  =  Asfs 

and  for  round  or  square  bars, 


or 

/, 

V  =  ~-  diameters 

If  the  allowable  /«  =  10,000  lb.  per  sq.  in.  and  the  allowable  u  =  80  lb.  per  sq.  in.,  then  V 
(as  shown  at  No.  2  bars  in  Fig.  25)  should  equal  31  diameters  by  the  above  formula.  If  1'  = 
16,000  lb.  per  sq.  in.,  V  =  50  diameters. 

The  value  of  hooks,  on  the  ends  of  bars  is  discussed  on  page  268. 

See  illustrative  problem  on  page  298. 

22.  Points  Where  Horizontal  Reinforcement  May  be  Bent. — For  uniformly  loaded  beams 
the  bending-moment  curve  is  a  parabola  as  shown  in  Fig.  26. 
Let  a  =  area  of  bars  required  at  the  center  of  beam. 
02  =  area  of  bars  to  be  bent. 

P2  =  100  ^  =  %  of  total  steel  that  may  be  bent  up. 

M  =  maximum  moment  —— • 
<p 

X2  =  distance  from  support  to  point  where  bars  may  be  bent. 
Mx^  =  moment  at  distance  X2  from  support. 

Then 

M   ^  a 
Mx^     a  —  an 

Substituting  values  of  M  and  Mx^,  and  solving  for  Xi, 


298 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-22 


Fig.  26,'  based  on  the  above  formula,  indicates  the  points  at  which  rods  may  be  bent  up  for 
three  types  of  beams  with  the  maximum  bending  moments  specified.    To  illustrate  the  use  of 


the  diagram,  assume  that  a  beam  designed  for  M 


10 


requires  3.5  sq.  in.  of  steel  at  the 


center'.  To  find  the  point  where  40  %  of  the  steel  may  be  bent  up  and  still  leave  sufficient  steel 
to  carry  the  tension,  trace  horizontally  from  the  40%  mark  at  the  right  to  the  curve  M  = 


and  then  vertically  to  the  lower  margin  where  0.22Z  is  read. 


10 


100 


90 
80 
70 


e 

5  60 
i  50 


I 

t 

o 
u 

I- 


40 
30 
20 
10 


10  \ 
o 

SZ 

40+3 
60^ 


70 


80 


90 


100 


0.1  02  0.3  0.4 

Location  of  section  in  terms  of  span  length 


0.5 


Fig.  26. 


If  it  is  desired  to  bend  up  a  number  of  rods  two  or  more  at  a  time,  then  Xt  should  be  deter- 
mined for  each  bend.  After  this  is  done,  the  remaining  horizontal  bars  should  be  secure 
against  slipping. 

For  concentrated  and  unsymmetrical  loading,  the  maximum  moments  at  various  sections 
will  need  to  be  determined,  in  order  to  ascertain  the  points  where  the  horizontal  bars  may 

be  bent  up.  From  these  maximum  moments  obtain 
the  required  area  of  horizontal  rods  at  the  different 
points  (1,  2,  3,  and  4,  Fig.  27).  Plot  a  curve  to  scale, 
as  shown.  Thus,  ah  represents  the  area  required  at  the 
point  a.  On  the  center  ordinate  lay  off  the  required 
areas  of  the  rods,  and  draw  horizontals  as  shown.  The 
rods  may  be  bent  up  where  these  horizontals  cut  the 
curve  but  it  would  be  better,  however,  to  carry  them  a  short  distance  beyond  the  theoretical 
points. 

Illustrative  Problem. — Design  the  left  end  of  a  simply  supported  beam  to  span  15  ft.  and  to  support  the 
loads  shown  in  Fig.  28  with  equal  strength  in  tension  and  compression.  Allowable  Sc  =  650;  w  =  80;  »  =  40 
without  web  reinforcement  and  120  with  an  effective  web  reinforcement. 

1  Diagram  taken  from  an  article  in  Eng.  News,  Aug.  19,  1916,  by  Karl  D.  Schwendener. 


Fig.  27. 


Sec.  7-22] 


BEAMS  AND  SLABS 


299 


The  reactions  are  readily  found  and  are  given  in  the  sketch.  The  maximum  moment  occurs  at  the  center 
load  since  the  shear  passes  through  the  value  zero  at  this  point.  TVe  shall  assume  the  weight  of  beam  included  in 
the  uniform  load  of  1000  lb.  per  ft. 


M  =  (25,500)  (8)  (12)  -  (23,000)  (4)  (12) 
It  is  found  that  a  depth  (d)  of  28  in.  is  required  when  6  =  16  in. 
25,500 


1,344,000  in.-lb. 


_  V_  

~  bjd  ~  (16)(J^)(28)  ~ 

Thus  web  reinforcement  is  needed. 

As  =  (16)  (28)  (0.0077) 


65  lb.  per  sq.  in. 


3.45  sq.  in. 


We  shall  select  eight  %-in.  round  rods  =  3.53  sq.  in.  Bond  for  one  rod 
at  the  left  end  of  beam  is 


25,500 


443  lb.  per  sq.  in. 


(2.356)  (Ji)  (28) 

For  plain  rods,  the  number  which  must  extend  straight  to  the  left  end 
of  beam  is,  for  bond  conditions  especially  favorable  (see  page  284), 
443 


(1.5)  (80) 


=  4 


 8'"0*  -  -  > 

1 

1 

i 

Un'rfonn  \oad-\QO(? 
1 

<-  ^—  15- 

1 
1 

including  ^ 
weigh+  of  beam 

>'  -  > 

1 
1 
1 

tit  in 

Fig.  28. 


Thus,  at  this  end  of  beam  four  rods  may  be  bent  up. 

The  concrete  will  be  found  to  take  care  of  any  diagonal  tension  between  the  concentrated  loads  since  concrete 
will  take  (40)  (16)  =  640  lb.  per  lin.  in.    Horizontal  shear  (which  measures  diagonal  tension)  at  the  support  is 

V  25,500 

jd  =  Gi)(28)  =  ^0^0  P^"- 
and  to  the  left  of  the  adjacent  concentrated  load,  it  is 


2J^00 
(^/^)(28) 


880  lb.  per  lin. 


The  total  diagonal  tension  to  be  taken  by  the  web  re- 
inforcement is  represented  by  a  trapezoid  (Fig.  28), 
the  parallel  sides  of  which  are  (1040)  =  690  lb.  and 
%  (880)  =  590  lb.  and  the  length  4  ft.  Hence,  total 
stress  in  this  part  of  beam  to  be  taken  by  the  con- 
crete and  by  the  web  reinforcement  is 


690  +  590 


X  4  X  12 


30,720  lb. 


Fig.  29. 

is  required,  but  it  would  seem  advisable  in  a  design 
by  the  dotted  lines.    The  length  of  embedment  of  the 


Since  four  rods  are  to  be  bent,  their  compara- 
tive tensile  value  is 

(4)  (0.4418)  (16,000)  (1.43)  =  40,400  1b. 

Thus,  the  tensile  value  of  the  rods  is  in  excess  of  the 
stress  to  be  provided  for. 

An  investigation  must  now  be  made  to  see 
whether  the  tensile  stresses  in  the  bottom  of  the  beam 
will  permit  the  bending  of  the  bars.  Fig.  29  shows 
the  bending-moment  curve  plotted  to  scale,  and  the 
points  where  the  bars  may  be  bent  up  are  determined 
by  the  method  described  on  page  298.  It  is  clear 
that  the  bars  cannot  be  bent  up  as  desired  to  provide 
thoroughly  for  diagonal  tension.  The  points  where 
the  bars  are  actually  bent  up  are  about  2  in.  beyond 
the  theoretical  points  as  determined  by  moment. 

If  each  bent-up  bar  is  assumed  to  take  diago- 
nal tension  to  the  left  only  of  its  point  of  bending, 
then  the  area  bANc  remains  unprovided  for.  Stirrups 
will  be  provided  to  take  diagonal  tension  between 
the  point  t,  where  the  line  be  produced  meets  the 
neutral  line,  and  the  adjacent  load.  Only  one  stirrup 
of  this  kind  to  also  place  stirrups  at  the  positions  indicated 
inclined  bars  should  be  50  diameters,  or  37)^  in. 


300 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-23 


23.  Transverse  Spacing  of  Reinforcement. — The  shearing  stress  along  ab,  Fig.  30,  should 
equal  the  amount  of  stress  transmitted  by  bond  along  bed.    If  bond  and  shearing  strengths 

were  equal,  ab  should  equal  bed,  and  the  clear  space  between  bars  should  be  ^'^2^^  diameters 

=  1.57  diameters.  But  shearing  strength  here  employed  is  controlled  by  the  diagonal  tension. 
For  y  =  90  lb.  per  sq.  in.  and  u  =  80,  ab  should  be  at  least  1,40  diameters;  and  for  v  =  120  lb. 
per  sq.  in.  and  u  =  80,  ab  should  be  at  least  1.05  diameters.  There  is  likely  to  be  more  or  less 
tension  in  the  concrete  surrounding  the  bars,  and,  besides,  since  the  concrete  is  not  easily  placed 
between  the  rods,  it  may  have  a  lower  strength  in  that  vicinity.  A  clear  spacing  of  1^  to 
2  diameters  is  advisable  unless  it  is  determined  by  computation  that  the  bond  stress  is  very 
much  lower  than  the  allowable.  In  the  above  discussion  plain  bars  only  have  been  considered. 
Deformed  bars,  if  stressed  to  their  full  bond  value,  should  be  spaced  farther  apart  than  plain 
bars. 

The  Joint  Committee  recommends  that  the  lateral  spacing  of  parallel  bars  should  not  be  less 
than  3  diameters,  center  to  center,  and  that  the  distance  from  the  side  of  the  beam  to  the  center 
of  the  nearest  bar  should  not  be  less  than  2  diameters.  In  order  that  concrete 
may  be  readily  placed  between  bars  and  also  give  sufficient  concrete  on  the  sides  of 
the  beam  for  fire  protection,  it  is  also  advisable  to  require  that  the  spacing  of  rods 
be  not  less  than  1  in.  in  the  clear  (if  the  maximum  size  of  aggregate  does  not  ex- 
ceed 1  in.)  and  that  in.  in  the  clear  be  also  considered  the  minimum  distance 
Fig.  30.  of  the  rods  from  the  sides  of  the  beam.  Thus,  the  least  width  of  beam  should  be 
the  greater  of  the  two  values  determined  from  the  following  formulas: 

b  =  [3(n  -  1)  +  4]d, 

b  =  ag{n  —  1)  +  ndi  +  3 

in  which  b  =  least  width  of  beam  in  inches. 

di  =  thickness  of  the  rods  in  inches. 

n  =  maximum  number  of  rods  which  occurs  in  a  horizontal  layer. 
ag  =  maximum  size  of  aggregate  in  inches. 
For  an  aggregate  with  a  maximum  size  of  1  in.,  the  width  of  beam  for  all  rods  greater  than 
in.  in  diameter  will  ordinarily  be  governed  by  the  first  formula  and  for  ^^-in.  rods  and  less, 
by  the  second  formula. 

Where  two  or  more  layers  of  rods  are  used,  the  rods  should  be  so  placed  as  to  permit  the 
mortar  to  run  between  them.  The  Joint  Committee  specifies  a  limiting  clear  space  of  1  in.  and 
does  not  recommend  the  use  of  more  than  two  layers  ''unless  the  layers  are  tied  together  by 
adequate  metal  connections,  particularly  at  and  near  points  where  bars  are  bent  up  or  bent 
down."  The  Joint  Committee  also  advises  that  "where  more  than  one  layer  is  used,  at  least 
all  bars  above  the  lower  layer  should  be  bent  up  and  anchored  beyond  the  edge  of  the  support." 

24.  Depth  of  Concrete  Below  Rods. — Tests  show  that  a  2-in.  thickness  of  concrete  is 
necessary  to  thoroughly  protect  embedded  steel  from  the  direct  action  of  flames.  Flat  slabs 
are  found  to  be  affected  to  a  less  depth  than  projecting  members  such  as  beams  and 
columns.  The  Joint  Committee  suggests  that  ''the  metal  in  girders  and  columns  be  protected 
by  a  minimum  of  2  in.  of  concrete;  that  the  metal  in  beams  be  protected  by  a  minimum  of  1^ 
in.  of  concrete;  and  that  the  metal  in  floor  slabs  be  protected  by  a  minimum  of  1  in.  of 
concrete." 

The  following  depths  of  concrete  below  the  center  of  steel  may  ordinarily  be  employed 
except  where  conditions  are  unusually  severe. 

Slabs 

T-i        i     i.    wj\  Depth  below  center 

Depth  to  steel  (d)  ^  steel 

3^^  in.  and  under   in. 

Between  3^  in.  and  4^^  in   1  in. 

4^4  over.   1>^  in. 


Sec.  7-25]  BEAMS  AND  SLABS  301 

Beams  and  Girders 

Depth  to  steel  (d)  Depth  in  the  clear 

below  steol 

10  in.  and  under   1  in. 

Between  10  in.  and  20  in   1}^  in. 

20  in.  and  over   2  in. 


26.  Ratio  of  Length  to  Depth  of  Beam  for  Equal  Strength  in  Moment  and  Shear. — With 
given  working  stresses  in  concrete  and  steel,  there  is  a  definite  ratio  of  length  to  depth  of  beam 
which  will  give  equal  strength  in  moment  and  shear.  First,  consider  beams  simply  supported. 
For  a  single  concentrated  load  at  the  center  of  span 

I  ^  2f,p 
d  vi 

in  which  Vi  =  allowable  shearing  stress  and  fs  =  working  stress  in  steel.    For  a  uniformly- 


distributed  load 

d  Vi 

For  beams  loaded  with  equal  loads  at  the  third  points, 

I  ^  SfsP 
d  vi 

Taking  for  example,  vi  =  40  lb.  per  sq.  in.,  /,  =  16,000,  fc  =  650,  n  =  15,  and,  using  an 
average  value  of  ]4  for    we  have  the  following  ratios  for  ^• 

For  concentrated  load  at  center  of  span   J  =  6.16 

For  uniformly  distributed  load   J  =  12.32 

For  equal  loads  at  the  third  points   4  =  9.24 


It  should  be  clear  that  the  strength  of  beams  of  greater  relative  length  than  obtained  by  the 
formulas  will  be  determined  by  their  moment  of  resistance,  while  that  of  shorter  beams  by  their 
shearing  resistance. 

In  the  case  of  continuous  beams  the  above  formulas  will  apply  if  I  is  taken  as  the  length 
between  points  of  inflection.  It  is  often  convenient  to  know  the  extreme  limit  in  design.  The 
Joint  Committee  recommends  120  lb.  per  sq.  in.  for  the  shearing  strength  of  concrete  when 
adequately  reinforced  against  diagonal  tension.  This  is  a  low  figure  but  is  adopted  in  order  to 
prevent  any  likelihood  of  cracks  opening  up  in  the  concrete.    Suppose  then,  it  is  required  to 

know  the  minimum  value  of  ^  for  a  given  beam,  uniformly  loaded.    From  the  formula  for 

uniform  load,  using  the  working  stresses  given  above, 

l_  ^  (4)  (16,000)  (0.0077)  ^ 
d  120 

At  the  same  time  that  the  ratio  of  length  to  depth  is  being  investigated  for  moment  and 
shear,  there  are  other  conditions  which  must  be  considered.  For  instance,  the  ratio  of  length  to 
breadth  of  beam  should  not  exceed  a  value  of  about  25  if  the  beam  is  not  supported  laterally. 
The  reason  for  this  is  found  in  the  fact  that  the  upper  part  of  the  beam  is  a  column,  and  to 
prevent  additional  stress  due  to  side  bending  the  length  should  not  exceed  about  25  times  the 
width.  On  the  other  hand,  the  best-shaped  beam  is  one  in  which  h  lies  between  }4d  and  ^id. 
In  any  given  case,  to  satisfy  all  requirements  and  arrive  at  a  satisfactory  design,  two  or  three 
trials  may  be  required. 


302 


CONCfRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-26 


26.  Economical  Proportions  of  Rectangular  Beams. — Without  taking  the  cost  of  web 
reinforcement  into  consideration,  it  can  be  shown  mathematically  that  the  cost  of  a  rectangular 
reinforced-concrete  beam  to  resist  a  given  bending  moment  and  be  of  equal  strength  in  tension 
and  compression,  varies  inversely  with  the  depth,  directly  with  the  square  root  of  the  breadth, 
and  directly  with  the  cube  root  of  the  ratio  of  breadth  to  depth. 

The  breadth  and  depth  of  a  rectangular  beam  to  be  of  equal  strength  in  tension  and  com- 
pression may  be  found  by  means  of  the  formulas  (see  page  277) 

1+4 

nfc 

^  Jcl^J  PJsJ 

If  b  or  d,  or  the  ratio  ^  is  decided  upon,  the  proportions  and  steel  area  of  a  beam  to  resist  a 

given  bending  moment  are  definitely  determined.    Thus  for  a  fixed  breadth,  fixed  depth,  or 
fixed  ratio  of  breadth  to  depth,  the  cost  of  a  beam  will  vary  with  the  working  stresses  employed 
since  values  of  k,  j,  and  p  depend  wholly  on  values  of  fc,  fs,  and  n. 
Where  the  depth  is  fixed,  it  is  found  that,  if  the  ratio 

_     cost  of  steel  per  unit  volume 
cost  of  concrete  per  unit  volume 

does  not  exceed  a  value  of  60  to  80  (60  a  common  value),  no  economy  results  from  using/s  greater 
than  16,000  lb.  per  sq.  in.  when  fc  =  600  to  700  lb.  per  sq.  in.,  or  from  using  fs  greater  than 
12,000  lb.  per  sq.  in.  when  fc  =  400  to  500  lb.  per  sq.  in.  Somewhat  higher  values  than  these 
may  be  economically  used  for  /«  when  the  breadth  of  beam  is  fixed.  In  both  cases  cost  de- 
creases as  fc  increases.    When  the  ratio  ^  is  fixed,  no  economy  results  from  using  /«  greater 

than  16,000  to  18,000  when  fc  =  400  to  600,  or  from  using  fc  greater  than  14,000  when 
fe  =  700.    In  this  cag'e  cost  increases  as  fc  increases. 

In  the  case  where  the  cross-section  of  beam  is  determined  by  shear,  the  maximum  depth 
theoretically  permissible  is  that  for  which  bd  is  just  large  enough  to  carry  the  shear.  With  a 
beam  designed  for  moment  alone,  the  cost  decreases  as  the  depth  increases,  but  the  area  of  the 
cross-section  becomes  less.  A  point  must  be  reached  when  the  beam  will  be  of  just  the  required 
strength  in  moment  and  shear  (see  Art.  25).  The  question  which  now  arises  is  whether  or  not 
a  still  greater  depth  will  result  in  greater  economy.  The  quantity  bd  must  now  remain  constant 
for  the  greater  depths.  But  bd^,  on  the  other  hand,  is  increased  and  the  concrete  stress  (fc) 
decreased.  A  smaller  value  for  fc  permits  the  use  of  a  smaller  percentage  of  steel,  and  the  cost 
is  still  further  reduced.  Thus  it  should  be  clear  that  the  proportions  of  a  beam  will  not  be 
determined  by  shear  excepting  as  to  minimum  cross-section — an  increase  in  depth  always  result- 
ing in  a  gain  in  economy.  It  should  be  noted  in  this  connection,  however,  that  although  deep 
beams  are  economical  of  concrete,  the  wooden  forms  cost  more  than. they  do  for  shallow  beams. 

27.  Rectangular  Beams  with  Steel  in  Top  and  Bottom. — Compressive  stresses  are  usually 
carried  by  concrete  more  economically  than  by  steel.  It  is  sometimes  desirable,  however,  to 
place  steel  in  the  compression  as  well  as  in  the  tension  side  of  the  beam.  When  a  rectangular 
beam  is  limited  as  to  size,  double  reinforcement  is  sometimes  the  result,  and  in  such  cases  the 
value  of  the  steel  reinforcement  on  the  compressive  side  needs  to  be  known.  The  effectiveness 
of  steel  in  compression  has  sometimes  been  questioned,  but  the  results  of  tests  indicate  that 
the  steel  does  its  share  of  the  work. 

The  Joint  Committee  recommends  that  "the  reinforcing  bars  for  compression  in  beams 
should  be  straight  and  should  be  2  diameters  in  the  clear  from  the  surface  of  the  concrete.  For 
the  positive  bending  moment,  such  reinforcement  should  not  exceed  1%  of  the  area  of  the 
concrete." 


Sec.  7-27] 


BEAMS  AND  SLABS 


303 


The  formulas  which  are  used  in  the  design  of  double-reinforced  rectangular  beams  an^ 
derived  by  means  of  the  same  fundamental  principles  as  for  beams  with  single  reinforcement. 
In  deriving  the  following  formulas  the  compression  in  the  concrete  is  assumed  to  follow  the 
linear  law  and  the  tension  in  it  is  neglected ;  the  formulas  then  apply  to  working  conditions  only. 

Area  of  -..., 
compressive 
steel  =  A' 

Area  of  - 
tensile 
Steel  =  A, 

Cross- section         Stress  Diagram 
Fig.  31. 


Let  A'  =  cross-sectional  area  of  compressive  reinforcement  (Fig.  31). 

d'  =  distance  from  the  compressive  face  of  the  beam  to  the  center  of  the  compressive 
reinforcement. 

p'  =  ratio  of  cross-section  of  steel  in  compression  to  cross-section  of  beam  above  the 

1  A' 

tensile  steel  =  t~i  • 
bd 


/'s  =  compressive  unit  stress  in  steel. 


1  +^ 

nfc 


(1) 
(1-4) 

(2) 


•''      A,jd       pjbd^  ^  ' 

*/  _  fcujl  -  k)  '  .  (6) 

k 

Ms  =  bd%pj  CO 

'-m  ' 

The  cases  which  may  be  met  with  in  practice,  with  the  method  of  solution  in  each  instance 
indicated,  are  as  follows: 

1.  To  determine  fiber  stresses. 

Compute  p,  p',  and  ^• 

Solve  for  k  from  formula  (1)  and  j  from  formula  (2). 

Substitute  value  of  j  in  formula  (3)  and  value  of  A'  in  fornmlas  (4)  and  (5)., 
Solve  directly  for  fiber  stresses. 
2.  To  determine  moment  of  resistance. 

Compute  p,  p',  and  ^- 


304 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-27a 


Solve  for  k  and  j. 

Substitute  value  of  k  in  formula  (6)  and  find  value  of  /«  when  the  maximum  allowable 

value  of  fc  is  substituted. 
Solve  formula  (7)  for  Ms  using  either  the  value  of  fs  determined  from  formula  (6)  or 

the  allowable  value  of  fs,  whichever  is  the  lesser. 

3.  To  determine  d  for  a  given  b  and  given  values  of  As,  — „  fc,  and  /«. 

(Trial  method.    Best  shown  by  use  of  diagrams.    See  illustrative  problem,  page  347.) 

4.  To  determine  p  and  p',  or  only  p'  (see  Art.  27a). 

Formulas  for  shear,  bond,  and  web  reinforcement  are  the  same  for  double-reinforced  beams 
as  for  beams  with  tensile  steel  only.  When  using  formulas  for  shear  and  bond  stress  along 
horizontal  tension  rods  of  beams  double-reinforced,  an  average  value  of  j  =  0.85  may  be  taken. 

27a.  Formulas  for  Determining  Percentages  of  Steel  in  Double -reinforced 
Rectangular  Beams. ^ — The  formulas  given  below  are  based  on  the  fundamental  fact  that  for 
any  given  values  of  fc  and  fs,  k  has  exactly  the  same  value  regardless  of  the  shape  or  type  of 
beam.    This  single  value  for  all  beams  is  expressed  by  the  formula 

1 

k  =  - 


1  +  4 

nfc 


It  follows  from  this  that  if  steel  is  added  to  the  section  without  changing  the  extreme  fiber 
stresses,  this  added  tensional  and  compressive  steel  must  form  a  balanced  couple  whose  stresses 
conform  to  the  stresses  already  in  the  section. 

Let  pi  =  steel  ratio  for  the  beam  without  compressive  steel. 
P2  =  steel  ratio  for  the  added  tensional  steel. 

p  =  Pi  +  P2. 

p'  =  steel  ratio  for  compressive  steel. 
Ml  =  moment  of  the  beam  without  compressive  steel. 
M2  =  moment  of  the  added  steel  couple. 

M  =  Ml  +  M2. 


Then 


k=-^-j-  (1) 

I  7A 

(3) 


=  fsPi  (  1  -  I) 


M2  =  M  -  Ml  (4) 

p  =  Pl  +  P2  ^  (6) 

P'  =  P.-i^,    .  (7) 
(See  page  348  for  illustrative  problem.) 

28.  Deflection  of  Rectangular  Beams. — Fig.  32  gives  the  general  form  of  a  deflection  dia- 
gram for  a  reinforced-concrete  beam.  The  portion  AB  shows  the  deflection  before  the  con- 
crete has  begun  to  fail  in  tension  near  the  center  of  the  beam,  BC  shows  the  deflection  during 

1  From  thesis  by  Robert  S.  Beard  submitted  to  graduate  school  of  University  of  Kansas  in  partial  fulfill- 
ment of  the  requirements  for  the  Master's  Degree. 


Sec.  7-28a] 


BEAMS  AND  SLABS 


305 


a  second  or  readjusting  stage,  and  CD  the  deflection  with  the  steel  near  the  center  of  beam 
carrying  practically  all  the  tension. 

28a.  Maney's  Method. ^ — The  deflection  of  a  reinforced-concrete  beam  of  whatever 
shape  may  be  determined  by  the  formula 

D  =  c  ^  (ec  +  es) 

where 

D  =  maximum  deflection  (if  desired  in  inches,  the  units  specified  be- 
low should  be  used). 
I  =  span  (inches). 

d  =  depth  of  the  beam  to  the  center  of  the  steel  (inches). 

fc 

Be  =  unit  deformation  in  extreme  fiber  for  the  concrete  =  ^r'  a   

.  Deflection 
Cs  =  unit  deformation  in  extreme  fiber  for  the  steel  =  4-  Fig.  32. 

c  =  —  in  which 

Ci  =  the  numerical  coefficient  in  the  formula  for  deflection  of  homogeneous  beams, 

D  =  Ci  ~^Y^  depending  on  the  loading  and  on  how  the  ends  are  supported. 

C2  =  the  numerical  coefficient  in  the  formula  for  bending  moment,  M  =  C2wP, 

for  a  simple  beam  loaded  at  center,  c  =  3l2  or  0.0833 
uniformly  loaded,  c  =        or  0.1041 
loaded  at  the  third  points,  c  =  or  0.1065 

for  a  beam  with  fixed  ends,  loaded  at  center,  c  =        or  0.0416 
uniformly  loaded,  c  =  H2  or  0.0313 
loaded  at  the  third  points,  c  =  ^{44  or  0.0347 

28b.  Turneaureand  Maurer's  Method.- — Turneaureand  Maurer  recommend  that 
8  to  10  be  used  for  n  in  the  formulas  which  they  have  derived,  and  which  are  given  below.  They 
also  state  that  the  formulas  presented  are  the  result  of  modifying  the  deflection  formulas  for 
homogeneous  beams  in  accordance  with  the  following  assumptions : 

1.  The  representative  or  mean  section  has  a  depth  equal  to  the  distance  from  the  top  of 
the  beam  to  the  center  of  the  steel. 

2.  It  sustains  tension  as  well  as  compression,  both  following  the  linear  law. 

3.  The  proper  mean  modulus  of  elasticity  of  the  concrete  equals  the  average  or  secant 
modulus  up  to  the  working  compressive  stress. 

4.  The  allowance  for  steel  in  computing  the  moment  of  inertia  of  the  mean  section  should 
be  based  on  the  amount  of  steel  in  the  mid-sections,  since  stirrups  and  bent-up  rods  do  not 
affect  stiffness  materially  for  working  loads. 

The  following  are  the  deflection  formulas  for  rectangular  reinforced  concrete  beams: 

W73  ^  (1) 

a  =  }i[k^  +  (1  -  ky  +  Snpil  -  fc)2]  (2) 

k  =  141^  (3) 
2  +  2np 

From  equations  (2)  and  (3),  the  value  of  a  for  any  values  of  p  and  n  may  be  computed,  and  then 
the  deflection  from  equation  (1).    The  notation  employed  in  the  above  formulas  is  as  follows: 

1  See  paper  by  G.  A.  Maney,  presented  before  the  seventeenth  annual  meeting  of  the  American  Society  for 
Testing  Materials. 

2  "Principles  of  Reinforced  Concrete  Construction"  2d  Edition,  p.  116. 
20 


306 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-29 


D  =  maximum  deflection  (if  desired  in  inches,  the  units  specified  below  should  be  used). 
b  =  breadth  of  the  beam  (inches). 

d  =  depth  of  the  beam  to  the  center  of  the  steel  (inches). 
W  =  total  load  (pounds). 
I  =  span  (inches). 
p  =  steel  ratio. 

Es  =  modulus  of  elasticity  of  the  reinforcing  steel  (pounds  per  square  inch). 
n  =  ratio  of  the  moduli  of  elasticity  of  steel  and  concrete, 
a  =  a  numerical  coefficient  depending  on  p  and  n. 
k  =  proportionate  depth  of  the  neutral  axis. 

Ci  =  the  numerical  coefficient  in  the  formula  for  deflection  of  homogeneous  beams, 

Ci  -^jj  depending  on  the  loading  and  support.    For  example, 

for  a  cantilever  loaded  at  the  end,  Ci  =  }i 

for  a  cantilever  uniformly  loaded,  Ci  =  3^^ 

for  a  simple  beam  loaded  at  center,  Ci  =  }"^g 

for  a  simple  beam  uniformly  loaded,  Ci  =  ^is4 

for  a  beam  with  fixed  ends,  load  at  the  center,  Ci  =  '^{^2 

for  a  beam  with  fixed  ends,  uniformly  loaded,  Ci  =  ^84 

The  following  are  the  deflection  formulas  for  reinforced  concrete  T-beams  (referred  to  later): 
c  1      WP  n 
Es  '  biP  '  p 

ft  =  Vslk^  -  (  1  -       (fc  -      '  +     (1  -  ky  +  Spna  -k)^ 

«[r-r(r+©i' 


np  + 


,b'      b'/t\    ,  t 

in  which  /3  is  a  coefficient  depending  upon  the  steel  ratio  and  n,  and  other  symbols  as  before. 

29.  Slabs. — A  reinforced-concrete  slab  should  be  figured  in  the  same  manner  as  a  rectangu- 
lar beam,  the  bending  moment  being  usually  computed  for  a  width  of  slab  equal  to  1  ft.  The 
ratio  of  steel  in  a  slab  is  most  readily  found  by  dividing  the  cross-section  of  one  bar  by  the 
area  between  the  centers  of  two  adjacent  bars,  this  area  being  the  spacing  of  the  bars  multi- 
plied by  the  depth  of  steel  below  the  top  of  slab. 

Slab  bars  should  not  be  placed  too  far  apart  to  properly  take  stress  directly  nor  yet  should 
they  be  spaced  so  close  that  the  concrete  cannot  be  properly  placed  between  them.  The  main 
tensile  reinforcement  should  not  be  spaced  farther  apart  than  2}^  times  the  thickness  of  the  slab. 
The  minimum  limit  should  be  about  the  same  as  in  beams. 

Shearing  failures  are  not  usually  important  in  slabs,  but  in  special  cases  of  heavy  loading 
the  same  care  should  be  used  as  in  the  design  of  large  beams. ^ 

29o.  Moments  in  Continuous  Slabs. — For  uniformly  loaded  spans,  fully 
continuous  over  two  or  more  intermediate  supports,  a  moment  of  }i2U>l^  may  be  used  both  in  the 
centers  of  all  spans  and  over  all  supports,  for  both  dead  and  live  loads.  For  slabs  continuous 
for  two  spans  only,  with  ends  restrained,  the  bending  moment  both  at  the  center  support  and 

near  the  middle  of  span  should  be  taken  ^sj^'    For  very  unequal  spans  or  spans  of  unusual 

length,  the  moments  should  be  computed  more  accurately. 

295.  Provision  for  Negative  Moment  in  Continuous  Slabs. — Slabs  having 
spans  of  any  appreciable  length  should  be  reinforced  against  negative  moment.  This  may  be 
done  by  bending  up  a  part  of  the  rods  in  the  spans  on  each  side  of  a  support  and  extending  each 

1  See  p.  344  for  illustrative  problems  using  diagrams.   For  flat  slab  floors,  see  chapter  in  Sect.  11. 


Sec.  7-29c]* 


BEAMS  AND  SLABS 


307 


set  of  bent  rods  along  the  top  of  beam  into  the  adjoining  span.  The  bend  in  the  bars  should 
be  near  the  }i  points  in  the  span,  and  usually  at  an  angle  of  30  deg.  with  the  horizontal.  Too 
sharp  an  angle  may  tend  to  crack  the  slab. 

When  placing  slab  reinforcement  in  long  spans,  a  top  reinforcement  at  least  to  the  third 
point  will  be  desirable.  In  ordinary  sp.ans  the  steel  should  at  least  be  lapped  a  sufficient  dis- 
tance over  supports  to  provide  adequate  bond  strength,  and  the  steel  should  be  bent  up  far 
enough  from  the  support  to  provide  properly  for  negative  moment. 

29c.  Floor  Slabs  Supported  Along  Fom  Sides. — When  a  floor  panel  is  square, 
or  nearly  so,  the  slab  may  advantageously  be  reinforced  in  both  directions.  Exact  analysis 
of  stresses  in  such  a  case  is  impossible,  but  some  important  facts  have  been  brought  out  by  ap- 
proximate solutions  for  uniform  loading.  The  theory  applied  in  such  an  analysis  depends  upon 
the  fact  that  the  load  at  any  point  on  the  slab  is  distributed  to  the  two  systems  of  reinforcing 
bars  at  that  point,  in  proportion  to  the  stiffness  of  the  beam  elements  lying  in  those  directions. 

The  following  recommendations  are  from  the  report  of  the  Joint  Committee: 

Floor  slabs  having  the  supports  extending  along  the  four  sides  should  be  designed  and  reinforced  as  con- 
tinuous over  the  supports.  If  the  length  of  the  slab  exceeds  times  its  width,  the  entire  load  should  be  carried  by 
transverse  reinforcement. 

For  uniformly  distributed  loads  on  square  slabs,  one-half  the  live  and  dead  load  may  be  used  in  the  cal- 
culations of  moment  to  be  resisted  in  each  direction.  For  oblong  slabs,  the  length  of  which  is  not  greater  than  I'/i 
times  their  width,  the  moment  to  be  resisted  by  the  transverse  reinforcement  may  be  found  by  using  a  proportion  of 
the  live  and  dead  load  equal  to  that  given  by  the  formula 

I 

r  =      -  0.5 

b 

where  I  =  length  and  b  =  breadth  of  slab.  The  longitudinal  reinforcement  should  then  be  proportioned  to  carry 
the  remainder  of  the  load. 

In  placing  reinforcement  in  such  slabs  account  may  well  be  taken  of  the  fact  that  the  bending  moment  is 
greater  near  the  center  of  the  slab  than  near  the  edges.  For  this  purpose  two-thirds  of  the  previously  calculated 
moments  may  be  assumed  as  carried  by  the  center  half  of  the  slab  and  one-third  by  the  outside  quarters. 

29(i.  Cross-reinforcement  in  Slabs. — When  the  length  of  a  floor  panel  is  large 
compared  to  its  breadth,  the  longitudinal  reinforcement  (that  is,  reinforcement  parallel  with 
the  length)  is  of  little  value  in  carrying  loads,  but  a  small  amount  is  nevertheless  generally 
desirable  in  preventing  shrinkage  and  temperature  cracks  and  in  binding  the  entire  structure 
together.  It  is  more  important  for  wide  beam  spacing  than  when  the  beams  are  closely  spaced. 
The  amount  of  steel  to  use  is  usually  selected  somewhat  arbitrarily,  and  Y^-\^.  or  Y^-va.  rods 
spaced  18  to  24  in.  apart  is  common  practice.  The  top  of  the  slab  over  a  girder  should  be  re- 
inforced transversely  not  only  for  stiffening  the  girder,  but  also  to  provide  for  the  negative 
bending  moment  produced  with  the  bending  of  the  slab  at  right  angles  to  the  direction  of  the 
principal  slab  steel. 

T-BEAMS 

30.  T-Beams  in  Floor  Construction. — When  a  slab  and  beam  (or  girder)  are  built  at  the  same 
time  and  thoroughly  tied  together  by  means  of  stirrups,  bent-up  rods,  and  cross-slab  reinforce- 
ment, a  part  of  the  slab  may  be  considered  to  act  with  the  upper  part  of  the  beam  in  compression. 
This  form  of  beam  is  called  a  T-beam,  and  the  extra  amount  of  concrete  in  the  compressive 
part  of  such  a  beam  makes  possible  a  considerable  saving  over  the  rectangular  form.  The 
thickness  of  the  flange  is  fixed  by  the  thickness  of  slab  required  to  support  its  load,  but  the 
width  of  slab  which  can  be  taken  as  effective  flange  width  must  be  selected  somewhat  arbitrarily. 

31.  Tests  of  T-beams.— T-beams  are  found  to  fail  under  essentially  the  same  condi-. 
tions  as  rectangular  beams,  and  the  same  general  principles  apply.    Tests  show  that  the  maxi- 
mum load  carried  can  be  materially  increased  by  placing  cross  bars  in  the  top  of  slab  and 
by  adding  fillets  between  the  flange  and  the  beam.    Cross  bars  are  found  to  be  actually  needed 
to  insure  T-beam  action  but  fillets  are  not  required  in  ordinary  cases. 


308 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-32 


T-beams  with  projections  of  flange  on  each  side  of  web  of  10.5  times  the  thickness  of  the 
slab  have  been  found  to  carry  a  load  only  5%  larger  than  beams  with  projections  of  6.8  times 
the  thickness  of  the  slab.  No  appreciable  difference  was  found  in  the  latter  beams  between  the 
deformations  at  the  edge  of  flange  and  the  deformations  in  the  flange  at  the  web. 

32.  Flange  Width. — The  Joint  Committee  has  recommended  the  following  rules  for  deter- 
mining flange  width : 

(a)  It  shall  not  exceed  one-fourth  of  the  span  length  of  the  beam. 

(6)  Its  overhanging  width  on  either  side  of  the  web  shall  not  exceed  6  times  the  thickness  of  the  slab. 

Beams  in  which  the  T-form  is  used  only  for  the  purpose  of  providing  additional  compression  area  of  concrete 
should  preferably  have  a  width  of  flange  not  more  than  3  times  the  width  of  the  stem  and  a  thickness  of  flange 
not  less  than  one-third  of  the  depth  of  the  beam. 

33.  Bonding  of  Web  and  Flange. — The  web  and  flange  of  a  T-beam  can  be  considered  well 
tied  together  when  slab  reinforcement  crosses  the  beam  and  when  the  web  reinforcement  extends 
well  up  into  the  slab.  The  bonding  should  be  especially  well  looked  after  near  the  end  of  beam, 
and  this  is  generally  accomplished  by  means  of  the  bent  rods  and  stirrups  brought  up  as  high 
as  possible,  in  addition  to  the  slab  reinforcement  (as  mentioned)  acting  at  right  angles  to  the 

length  of  the  beam.  Along  the  center  of  the 
beam  the  differential  stresses  between  the 
beam  and  slab  are  not  large,  but  it  is  better 
to  insert  vertical  stirrups  extending  up  into 
the  slab  at  occasional  intervals  since  shrinkage 
of  the  concrete  is  apt  to  part  the  slab  from  the 
beam  if  there  is  not  some  means  to  hold  the 
two  together  mechanically.  The  thinner  the 
sections,  the  more  thorough  should  be  the 
bonding. 

34.  Flexure  Formulas. — With  a  T-beam 
it  is  necessary  to  distinguish  two  cases;  namely,  (1)  the  neutral  axis  in  the  flange,  and  (2) 
the  neutral  axis  in  the  web. 

Case  I.  The  Neutral  Axis  in  the  Flange. — All  formulas  for  "moment  calculations"  of 
rectangular  beams  apply  to  this  case.    It  should  be  remembered,  however,  that  h  of  the  for- 

A  A 

mulas  denotes  flange  width,  not  web  width,  and  p  (the  steel  ratio)  is      not  ^     (Fig.  33). 

Case  IL  The  Neutral  Axis  in  the  Weh. — The  amount  of  compression  in  the  web  {aaaa, 
Fig.  33)  is  commonly  small  compared  with  that  in  the  flange,  and  is  generally  neglected.  The 
formulas  to  use,  assuming  a  straight-line  variation  of  stress  and  neglecting  the  compression  in 
the  web,  are: 

1 


<• -^c >j 

\ 

■t  rol  plane  ^ 

■i  i 

Stress  DiQ9ram 


Fig.  33. 


M  = 


k  = 


jd  = 


1  +-4- 
nfc 

2ndK  +  ht^ 
2nA,  +  2bt 


+ 


(a 


(1) 
(2) 

(3) 

(4) 
(5) 

(6) 


Sec.  7-34a] 


BEAMS  AND  SLABS 


309 


"  A;) 

/.=^^,-^'  (9) 
M,  =  S,A,id  (10) 

Approximate  formulas  can  also  be  obtained.  From  the  stress  diagram,  Fig.  33,  it  is  clear 
that  the  arm  of  the  resisting  couple  is  never  as  small  as  —  3^f,  and  that  the  average  unit 
compressive  stress  is  never  as  small  as  ^/c,  except  when  the  neutral  axis  is  at  the  top  of  the 
web.    Using  these  limiting  values  as  approximations  for  the  true  ones, 

Mo  =  y2fcht{d  -  y2t)  (a) 

M 

M.  =  A.f.{d  -  Ht),  or  A,  =  (j^-^^^  _  y^^^  (6) 

The  errors  involved  in  these  approximations  are  on  the  side  of  safety. 

Formulas  which  take  into  account  the  compression  in  the  stem  are  recommended  where  the 
flange  is  small  compared  to  the  stem.  Such  formulas  may  be  found  in  the  report  of  the  Joint 
Committee,  and  are  as  follows: 


kd 


z 


^2ndAs  +  (b  -  b')t''  ^  ^As  +  (b  -  b')t\j  ^ 

(kdt'  -  HP)h  +  [{kd  -  ty  {t  +  H^kd  -  i))W 
t{2kd  -  t)b  +  {kd  -  tyb' 
jd  =  d  —  z 

Asjd 

2Mkd 


nAs  +  (6  -  b')t 


[{2kd  -  t)bt  +  {kd  -  tyb']jd 

34a.  Case  II  Formulas  for  Determining  Dimensions  and  Steel  Ratio  for 
Given  Working  Stresses.^ — The  following  formulas  are  sometimes  useful  in  the  design  of  T- 
beams  when  the  neutral  axis  is  in  the  web : 

t  -  VR2'  -  12fcRi 

d  =  2r;   ^^^^ 

in  which 

Ri=Ic+^- 
n 


and 

©©-©■(!:) 

(Formula  (12)  should  be  solved  by  exact  methods  as  the  slide  rule  does  not  give  satisfactory 
results.) 

If  the  depth  of  beam  is  fixed  by  the  headroom  available,  formula  (13)  gives  directly  the 
proper  percentage  of  steel  for  given  working  stresses. 

1  From  thesis  by  Robert  S.  Beard  submitted  to  graduate  school  of  University  of  Kansas  in  partial  fulfillment 
of  the  requirements  for  the  Master's  Degree. 


310 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-36 


35.  Designing  for  Shear. — Since  a  T-beam  will  usually  have  ample  strength  in  compression 
for  any  ordinary  depth  of  beam  likely  to  be  selected,  the  design  of  the  stem  of  the  T,  or  the  beam 
below  the  slab,  is  largely  a  question  of  providing  sufficient  concrete  to  take  care  of  the  shearing 
stresses  and  to  give  a  good  layout  of  the  tension  rods.  The  manner  of  providing  reinforce- 
ment for  shearing  stresses  in  T-beams  is  similar  to  that  described  for  rectangular  beams.  In 
T-beams,  however,  the  reinforcement  for  shear  should  run  well  up  into  the  slab  in  order  to  tie 
the  beam  and  slab  together.  The  shearing  strength  of  a  T-beam  is  about  the  same  as  that  of  a 
rectangular  beam  of  the  same  depth  and  a  width  equal  to  the  width  of  the  stem  of  the  T. 

36.  General  Proportions  of  T-beams. — T-beams  should  not  be  made  too  deep  in  propor- 
tion to  the  width  of  stem  as  such  forms  are  relatively  weak  at  the  junction  of  stem  and  flange. 
The  width  should  preferably  be  from  one-third  to  one-half  the  depth  in  ordinary  cases.  For 
large  beams  the  width  may  be  made  from  one-third  to  one-fourth  the  depth. 

All  re-entrant  angles  in  concrete  are  points  of  weakness  and  such  angles  should,  therefore, 
be  avoided. 

37.  Economical  Considerations. — When  a  floor  slab  forms  the  flange  of  a  T-beam,  it  is 
possible  to  determine  economical  proportions  for  the  stem. 

Consider  a  portion  of  a  rectangular  beam  one  unit  in  length. 

Let  c  =  cost  of  concrete  per  unit  volume. 

r  =  ratio  of  cost  of  steel  to  cost  of  concrete  per  unit  volume. 
•  C  =  cost  of  beam  per  unit  length. 
d  =  depth  of  beam  below  slab. 

Then 

using  the  approximate  formula  (5)  on  page  309. 

When  d'  is  fixed  by  the  headroom  available,  the  cost  will  be  a  minimum  when  b'  is  made  as 
small  as  possible,  and  its  value  will  then  be  determined  by  the  shearing  stress  or  by  the  space 
required  for  the  rods.  The  expression  also  shows  that  the  cost  will  decrease  with  increased 
values  of  fs,  and  that  with  a  fixed  value  of  b'd'  the  cost  decreases  with  increase  in  depth.  If  the 
value  of  b'  is  assumed  as  fixed,  then  there  is  a  definite  value  of  d  which  will  give  minimum  cost. 
The  following  expression  has  been  deduced  from  the  preceding  equation  and  will  give  the  value 
of  d  for  minimum  cost  when  the  value  of  6'  is  fixed : 

From  this  expression  the  best  depths  for  various  assumed  widths  may  readily  be  determined  and 
the  desirable  proportions  finally  selected. 

The  following  table  is  convenient  in  determining  values  of  r: 

38.  Conditions  Met  with  in  De- 
sign of  T-beams. — In  practice  the  de- 
sign of  T-beams  will  take  one  of  the 
following  forms  with  method  to  be 
followed  in  each  case  indicated: 

1.  To  find  moment  of  resistance 
or  fiber  stresses. 
The  values  of  k  and  j  may  be 
found  from  equations  (3)  and 
(6),  or  from  equations  (2),  (4) 
and  (5),  on  page  308,  and  then 
the  values  of  the  fiber  stresses 
from  equations  (7)  and  (8),  or 
the  moment  of  resistance  from 


Cost  of 

Cost  of  concrete,  dollars  per  cubic  yard 

steel, 

cts.  per  lb. 

5 

G 

7 

8 

■  9 

10 

11 

12 

1 

26 

22 

19 

16 

IK 

40 

33 

28 

25 

22 

2 

63 

44 

38 

33 

29 

26 

66 

66 

47 

41 

37 

33 

30 

3 

80 

66 

67 

60 

44 

40 

36 

33 

92 

78 

66 

68 

61 

46 

42 

38 

4 

88 

76 

66 

69 

63 

48 

44 

Sec.  7-39] 


BEAMS  AND  SLABS 


311 


equations  (9)  and  (10),  When  the  moment  of  resistance  depends  upon  the  concrete, 
equation  (9)  is  useful  in  determining  the  value  of to  use  in  equation  (10).  To  obtain 
this  value,  the  maximum  allowable  value  of  fc  should  be  inserted  in  equation  (9).  (If 

the  value  of  k  is  found  to  be  less  than  ^,  then  the  problem  falls  under  Case  I  and  the 

formulas  for  rectangular  beams  apply.) 

2.  To  design  a  T-beam  in  which  the  flange  forms  a  portion  of  a  floor  slab. 

Depth  and  width  of  stem  of  beam  should  be  selected  with  reference  to  shearing  strength, 
space  for  necessary  rods,  and  other  considerations.  The  depth  hashing  been  selected, 
the  amount  of  steel  may  be  approximately  determined  by  equation  (6).  The  amount 
of  steel  being  known,  the  value  of  j  may  be  determined  by  equation  (6).  The  value 
of  k  should  also  be  found  from  equation  (2)  or  (3)  in  order  to  ascertain  if  the  beam 
falls  under  Case  I  or  Case  II.  The  stress  in  the  concrete,  corresponding  to  the  allow- 
able working  stress  in  the  steel,  is  then  found  from  equation  (8). 

3.  To  find  the  minimum  depth  for  a  single-reinforced  T-beam. 

The  value  of  ^,  or  d,  may  be  found  from  equation  (12)  for  given  working  stresses,  and 

the  amount  of  steel  from  equation  (13).  The  width  of  stem  should  then  be  selected 
with  reference  to  shearing  strength,  etc. 

4.  To  design  a  T-beam  not  connected  with  a  floor  system. 
First  method : 

First,  select  suitable  proportions  for  the  web.    A  flange  thickness  is  then  assumed 

such  as  to  give  satisfactory  proportions  between  t  and  d.    The  value  of  ^  is  then 

known  and  k  and  j  can  be  determined  from  equations  (1),  (4),  and  (5).  The 
area  of  steel  and  the  breadth  of  flange  are  then  found  from  equations  (10)  and 
(11)  respectively. 
Second  method: 

For  any  assumed  thickness  and  width  of  flange,  the  depth  of  beam  may  be  de- 
termined by  equation  (12)  and  the  percentage  of  steel  from  equation  (13).  The 
width  of  stem  should  then  be  selected  with  reference  to  shearing  strength,  etc. 
(When  making  approximate  computations  for  shear  or  bond  stress  along  the  horizontal 
tension  rods,  an  average  value  of  j  =      may  be  assumed,  as  for  rectangular  beams.) 

39.  Design  of  a  Continuous  T-beam  at  the  Supports. — Negative  bending  moment  exists 
at  the  supports  of  continuous  beams  and  tensile  steel  must  be  placed  in  the  top  of  beams  over 
supports  to  prevent  cracks  opening  up  at  these  points.  For  the  usual  case  of  equal  spans  and 
indefinite  live  load,  the  common  method  of  providing  for  this  negative  moment  is  by  bending 
up  one-half  of  the  rods  on  each  side  and  extending  each  set  over  the  supports  into  the  adjoin- 
ing span.  The  remaining  lower  horizontal  rods  in  each  span  are  carried  horizontally  through 
the  supporting  columns. 

In  a  design  of  continuous  T-beams  at  the  supports  it  should  be  noted  that  the  flange  is 
under  tension,  that  the  stress  in  the  concrete  is  negligible  above  the  neutral  axis  and  that 
a  rectangular  section  may  be  considered  at  such  points.  The  method  of  design  is  thus  similar 
to  the  design  of  a  double-reinforced  rectangular  beam  at  the  center  of  span  with  the  exception 
that  the  compressive  and  tensile  stresses  about  the  neutral  axis  are  inverted  (see  page  302). 

Since  a  T-beam  in  the  center  of  span  becomes  a  rectangular  beam  over  supports,  the  stress 
in  the  tensile  steel  at  the  support  will  generally  be  greater  in  ordinary  designing  than  the  corre- 
sponding stress  at  the  center  of  beam;  that  is,  this  stress- will  be  greater  if  half  the  rods  are  bent 
up  on  each  side  and  lap  over  the  support.  For  this  reason,  then,  when  selecting  the  steel  at 
the  center  of  span,  a  little  more  than  the  required  amount  at  that  point  should  be  chosen.  It 
should  be  noticed,  however,  that  the  column  has  some  strengthening  action  at  the  support 
and  it  will  not  be  necessary  to  keep  t'^o  closely  to  the  allowable  stress. 


312 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-39 


A  higher  compressive  stress  may  be  allowed  in  the  concrete  at  the  supports  than  at  the 
middle  of  span,  because  of  the  fact  that  the  negative  moment  decreases  very  rapidly  and  only 
a  short  section  is  under  maximum  stress.  Also,  a  slight  excess  of  stress  at  this  point  does  not 
in  any  way  endanger  the  structure  but  merely  increases  somewhat  the  positive  moment  on  the 
beam. 

There  are  three  methods  of  reducing  the  compressive  stress  in  the  concrete  at  the  bottom 
of  the  beam  over  supports:  (1)  by  increasing  the  amount  of  compressive  steel  in  the  bottom 
of  the  beam;  (2)  by  increasing  the  area  of  compressive  concrete,  which  may  or  may  not  require  a 
flat  haunch  depending  upon  the  width  of  the  support;  and  (3)  by  increasing  the  areas  of  both 
steel  and  concrete. 

The  bond  stress  along  the  horizontal  rods  at  the  top  of  a  continuous  beam  over  supports 
may  be  found  by  the  same  formula  as  is  employed  for  the  tension  rods  at  the  end  of  a  simply 
supported  beam.  However,  if  bent  up  rods  are  employed  for  web  reinforcement  and  if  these 
same  rods  are  employed  to  take  the  tension  over  supports,  the  beam  is  greatly  stiffened  and  the 
bond  stress  along  the  top  rods  is  undoubtedly  reduced  appreciably  below  that  given  by  the 
theoretical  formula.  This  bond  stress  is  affected  by  the  amount  of  web  reinforcement  used  in  a 
somewhat  similar  manner  to  the  way  the  bond  stress  is  affected  along  the  rods  at  the  end  of  a 
simply  supported  beam  (see  page  284). 

In  beams  considered  uniformly  loaded,  the  rods  which  are  bent  should  extend  beyond  the 
center  of  support  to  about  the  fourth  point,  or  in  beams  of  very  definite  live  load  to  the  third 
point  (point  of  zero  moment  varies  for  different  loadings),  to  provide  thoroughly  for  negative 
moment,  and  this  length  should  be  increased  if  it  is  not  sufficient  to  transfer  to  the  concrete 
through  bond,  the  greatest  allowable  tensile  stress  in  the  rods. 

If  half  of  the  rods  from  each  span  are  used  over  the  support,  then  half  of  the  total  number 
will  extend  to  about  the  fourth  point  where  the  tension  due  to  negative  moment  becomes  zero. 
At  this  point  the  shear  is  only  one-half  of  what  it  is  at  the  end  of  span,  if  the  beam  is  considered 
uniformly  loaded.  Since  bond  stress  due  to  increment  (or  decrement)  tension  varies  as  shear, 
a  sufficient  number  of  rods  are  thus  run  out  to  the  fourth  point,  and  with  the  bent  rods  being 
added  gradually  to  this  number  until  all  the  rods  are  acting  in  this  manner  at  the  support,  it 
is  clear  that  this  method  of  design  is  satisfactory  even  when  the  bond  stress  at  the  support 
is  the  maximum  allowable. 

Rods  should  be  bent  in  a  position  to  take  as  much  diagonal  tension  as  possible,  usually 
at  an  angle  between  30  and  .45  deg.,  and  the  points  where  the  rods  are  no  longer  needed  at  the 
bottom  of  beam  to  resist  tension  may  be  found  as  explained  on  page  297.  It  is  also  necessary 
to  determine  where  the  rods  over  supports  may  be  bent  down.  It  will  be  on  the  safe  side, 
and  sufficiently  accurate,  to  consider  the  curve  for  negative  moment  as  a  straight  line  between 
the  support  and  the  point  of  zero  moment  at  the  fourth  point.  (For  a  very  definite  live  load, 
zero  moment  should  be  assumed  at  the  third  point.)  With  this  variation  of  the  moment  in 
mind,  it  is  an  easy  matter  to  find  where  the  rods  may  be  bent  down  at  the  top  of  the  beam. 
The  designer  must  use  his  judgment  in  the  matter,  but  this  much  may  be  said:  if  a  bend 
cannot  be  made  in  a  rod,  as  proposed,  due  to  the  controlling  points  for  bending  at  the  top 
and  bottom,  a  greater  number  of  rods  may  be  employed  at  the  center  of  span  in  order  to 
make  this  bending  possible,  and  the  design  governed  accordingly.  It  is  evident  from  the 
above  that  it  will  not  always  be  possible  to  place  the  rods  so  as  to  take  all  the  diagonal  ten- 
sion, in  which  case  both  stirrups  and  bent  rods  must  be  used. 

Another  point  to  be  noted  in  the  design  of  a  continuous  beam  at  the  supports  is  the  bond 
stress  of  the  compressive  reinforcement.  It  can  be  shown  that  the  bond  stress  per  square  inch 
for  the  tension  and  compression  rods  will  be  proportional  to  the  product  of  the  diameters  by 
their  distances  from  the  neutral  axis.  Since  the  compressive  steel  will  generally  be  nearer  the 
neutral  axis  than  the  tensile  steel,  it  follows  that,  if  the  compression  bars  are  no  larger  in  di- 
ameter than  the  tension  bars,  the  bond  stress  per  square  inch  will  always  be  less  than  that  of 
the  tension  bars.    It  is  sufficient  to  consider  simply  the  compressive  stress  in  the  steel  and 


Sec.  7-40]  BEAMS  AND  SLABS  313 

provide  a  sufficient  length  from  this  point  to  the  end  of  the  bar  to  transmit  this  stress.  The 
working  strength  of  the  steel  in  compression  cannot  be  reached  without  exceeding  the  com- 
pressive strength  of  the  concrete  in  which  it  is  embedded.  Consequently,  in  common  design 
it  will  be  satisfactory  to  provide  a  lap  beyond  the  support  sufficient  to  take  care  of  compress- 
ive stress  in  the  steel  equal  to  the  maximum  as  determined  by  the  concrete. 

40.  T-beams  with  Steel  in  Top  and  Bottom. — The  following  formulas  correspond  to  those 

for  rectangular  beams  given  on  page  303.    ^  =  ^' 


A(2k  -  A)  -      (2k  -  2A)  +  2p'n  (k  -       (l  - 
A(2k  -  A)  +2p'n(^k-~^ 


(1) 


(2) 


Asjd  pjbd^ 

=  r^k 

_  fcfijl  -  k)  ,  . 

Ms  =  bd'fspj  (7) 


t 

T-beams.^  A  = 


40a.  Formulas  for  Determining  Percentages  of  Steel  in  Double -reinforced 

i  • 

d 

1 


1  +  ^- 


6-6A+2A^  +  A3(^) 


J  = 


(2) 


(3) 


6  -  3A 

Ml  =  fsp^jbd^  (4) 
M2  =  M  -  Ml  '  (5) 

M2 


P2  = 


bd^ 


(6) 


P  =  Pi  +  P2  ■  (7) 

1  -  k 

P  (8) 


d 

41.  Deflection  of  T-beams. — Formulas  are  given  in  Art.  28 


1  From  thesis  by  Robert  S.  Beard  submitted  to  graduate  school  of  University  of  Kansas  in  partial  fulfillment 
of  the  requirements  for  the  Master's  Degree.    See  p.  304  for  notation,  etc. 


314 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-42 


SPECIAL  BEAMS 


42-  Wedge-shaped  Beams. ^ — The  analysis  of  wedge-shaped  beams  is  useful  chiefly  in 
the  design  of  counterforts  and  buttresses,  and  in  the  design  of  cantilever  beams  for  overhanging 
sidewalks  or  roadways  on  deck  bridges.    Formulas  follow  for  the  general  case  shown  in  Fig.  34: 


k  = 


V2pn  cos      ,    p^n^  cos^  /3t 
cos2  /3«  cos*  /3c 


pn  cos  |3< 

cos  2  /3; 


1  + 


+  1 


Mc  = 


fc  U/< 

Hfckj  (bd^)  cos2  /3c,  or  bd^  = 


^  fck  /cos^  fic\ 
2f,  \cos  ^t) 


^COS  Pt. 

2M 


Mc  =  pfsj  (bd^)  COS  ^t,  or  bd'^ 


 M  

p/J(cos  /SO 
COS  /3i 


_  2/.P/COS 
A;  \cos=^^c/ 


0' 
,  or/s 


or/c  = 


nfc 


2M 


M 


Asjd  (cos  /St) 


^cos2  /3c/      n(l  -  /c) 

When  the  compression  side  of  the  beam  is  horizontal,  cos  /3c  becomes  equal  to  unity. 

Likewise,  when  the  tension  side  of  the  beam  is 
horizontal,  cos  /3t  =  1.  With  both  top  and  bot- 
tom faces  of  the  beam  horizontal,  the  above 
formulas  reduce  to  those  for  a  rectangular  beam 
given  in  Art.  9.  The  above  formulas  should  not 
be  applied  to  beams  having  /3c  greater  than  45 
deg.  on  account  of  approximations  in  the  theory 
which  depart  more  and  mare  from  accuracy  as 
/3c  increases. 

Let  Vi  represent  the  total  shear  to  be  taken 
by  concrete  and  web  reinforcement,  and  let  V 


Fig.  34. 


represent  total  shear  on  section  computed  as  for  a  rectangular  beam.  Then 

M 


(tan  /3c  +  tan  /Sj 


jSc  and  /3 1  are  to  be  taken  as  positive  when  they  bear  the  same  relation  to  the  direction  of  V  as 
shown  in  Fig.  34,  and  are  to  be  taken  as  negative  when  they  bear  the  reverse  relation.  The 
formulas  for  shear,  bond,  stirrup  spacing,  etc.  in  rectangular  beams  apply  to  wedge-shaped 
beams  if  V  in  formulas  is  replaced  by  Vi. 

43.  Beams  of  Any  Complex  or  Irregular  Section. 

43a.  Analytical  Method. ^ — Long  and  cumbersome  formulas  for  the  analysis 
of  complex  sections  can  be  avoided  by  a  simple  application  of  general  methods  of  solution  to 
the  homogeneous  transformed  section.  Such  a  general  solution  is  here  presented,  based  upon 
the  standard  notation  and  using  the  homogeneous  section  easily  obtained  by  multiplying  the 
steel  areas  by  n,  the  ratio  of  the  moduli  of  elasticity  of  steel  and  concrete.  Thus  an  equivalent 
concrete  section  is  obtained,  to  which  the  ordinary  principles  of  analysis  for  homogeneous 
beams  are  applied.    An  equivalent  steel  section  could  as  well  be  used  if  desired. 

Adopting  the  usual  fundamental  assumptions  for  the  analysis  of  reinforjped-concrete 


1  See  Appendix  I  of  "Earth  Pressure,  Retaining  Walls  and  Bins' 
"Bridge  Engineering"  by  J.  A.  L.  Waddell. 

2  Method  as  given  by  J.  H.  Cissel  in  Eng.  Rec,  March  24,  1917. 


by  William  Cain.    See  also  vol. 


of 


Sec.  7-43a] 


BEAMS  AND  SLABS 


315 


beams,  based  upon  the  straight-line  theory,  it  can  easily  be  shown  that  an  equivalent  homo- 
geneous concrete  section  will  be  obtained  by  multiplying  the  steel  area  by  n.  The  neutral 
axis  can  then  be  located  at  the  centroid,  or  center  of  gravity,  of  the  transformed  section.  This 
is  done  most  conveniently  by  equating  the  statical  moment  of  the  equivalent  area  on  one  side 
to  the  statical  moment  of  that  on  the  other  side. 

Knowing  the  position  of  the  neutral  axis,  the  moment  of  inertia  of  the  transformed  section 

fl 

with  respect  to  this  axis  may  be  calculated,  and  the  well-known  fundamental  formula  M 

y 

used  to  find  the  resisting  moments  for  a  given  section,  or  the  fiber  stresses  produced  by  a  given 
bending  moment. 

Fig.  35  gives  the  dimensions  and  notation  used  for  the  exact  analysis  of  a  reinforced-concrete  T-beam,  in- 
cluding the  effect  of  the  compression  in  the  concrete  of  the  stem  above  the  neutral  axis.  To  compute  the  safe 
resisting  moment  for  this  beam  when  As  =  4  sq.  in.,  n  =  15,  /,  =  16,000  and  fc  =  650,  the  compressive  area  is 
divided,  for  convenience,  into  the  parts  shown  in  the  figure.  Equating  the  statical  moments  with  respect  to  the 
neutral  axis  of  the  transformed  steel  and  the  concrete, 

(32  X  4)(?/  -  2)+  ^=  60(24  -  y) 

Solving, 

y  =  7.31  and  d  -  y  =  16.69 
The  moment  of  inertia  about  this  axis  can  then  be  computed  as  follows: 
n/s  =  15  X  4  X  (16.69)2  = 

1, 


Ic  =  (44  X  7.313  X  H)  -  (32  X  3.31^ 
I  =  Ic  =  nis  = 


16,713 
5,342 


22,055 


Fig.  35. 


Fig.  36. 


The  resisting  moments  are  therefore: 

fj 

y 

n(d  —  y) 


=  M„  = 


Ms 


650  X  22,055 
7.31 

16,000  X  22,055 


=  1,960,000  in.-lb. 
=  1,410,000  in.-lb. 


15  X  16.69 

The  safe  resisting  moment  is  thus  1,410,000 — given  by  the  steel. 

Given  the  rectangular  beam  shown  in  Fig.  36  subjected  to  a  positive  bending  moment  of  760,000  in.-lb 
with  n  =  15,  As  =  2.25  sq.  in.,  and  A'  =  1.69  sq.  in.,  to  compute  the  fiber  stresses  in  the  steel  and  concrete,  proceed 
as  follows: 

The  transformed  area  of  compressive  steel  =  15  X  1.69  =  25.4 
The  transformed  area  of  tensile  steel     '      =  15  X  2.25  =  33.8 
Equating  statical  moments  of  tensile  and  compressive  areas  about  the  neutral  axis  (using  transformed  section) : 
^  +  25.4(2/  -  2)  =  33.8(22  -  y) 
Solving,  y  =  7.58  in.  and  d  —  y  =  14.42  in. 

Then  the  moment  of  inertia  will  be: 

nl's  =  15  X  1.69  X  (5.58)2    =  789 
nIs  =  15  X  2.25  X  (14.42)2  =  70I8 
Zc  =  12  X  (7.58)3  X  }i  =1742 
'l  =  Ic  +  nIs  +  nfs  =  9549 


Therefore  the  fiber  stresses  are:- 


fc  =  -r 


My  _ 

T  ~ 

nM(y 


760,000  X  7.58 


=  605 


2) 


nM(22  -  y) 


9549 

760.000  X  5.58  X  15 
9549 

760,000  X  14.42  X  1 
9549 


6680 


=  17,300 


316 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-436 


436.  Graphical  Method.^ — Application  of  graphical  methods  to  the  location 
of  the  neutral  axis  and  the  determination  of  effective  depth  and  resisting  moment  of  reinforced- 
concrete  beams  is  here  proposed  for  cases  of  complex  sections  where  the  steel  is  distributed 
as  in  beams  reinforced  for  compression  or  where  several  layers  of  rods  are  used.  It  is  assumed 
that  graphical  methods  are  famiHar  to  the  reader,  and  these  methods  will  be  illustrated  both 
for  investigating  a  given  section  and  for  designing  a  section  to  resist  a  given  bending  moment. 


67,^OOX  17.3= 1.161600 -M.  \ 


/ 


/ 


mi  / 


/ 


(h) 

Fig.  37. 


 ^     j  30^ 


To  Find  the  Neutral  Axis. — Consider  the  problem  of  finding  the  neutral  axis  and  resisting  moment 
of  a  given  reinforced-concrete  beam,  reinforced  on  the  compression  side,  as  in  Fig.  37a.  Applying  the 
usual  method  of  finding  the  centroid  of  an  area,  the  compression  side  of  the  beam  is  divided  into  thin 
slices,  taken  small  in  order  to  avoid  large  errors,  and  each  slice  is  represented  by  a  force  Ai,  A2,  etc.  In 
order  to  obtain  a  homogeneous  section,  the  area  of  the  steelis  multiplied  hy  n  =  15.    The  force  diagram  for 

these  "area  forces"  is  then  drawn.  Fig.  376,  beginning  with  nAs  at  one 
end,  Ai  next,  etc.,  as  shown. 

The  funicular  polygon  for  locating  the  resultant  of  these  forces  is 
then  drawn,  Fig.  37c,  and  the  intersection  O  of  the  line  NO,  with  the  lines 
parallel  to  the  rays  for  the  compressive  areas,  gives  the  position  of  this 
resultant,  or  the  centroid  of  the  section,  and  hence  locates  the  neutral  axis. 
Note  that  none  of  the  area  below  O  is  used,  according  to  the  usual  assump- 
tion that  tension  in  concrete  is  neglected. 

To  Find  the  Resisting  Moment. — Now  in  Fig.  37e  the  point  P  is  on 
the  neutral  axis  just  found,  RS  is  drawn  to  convenient  scale  to  represent  the 
allowable  stress  in  the  concrete,  700  lb.  per  sq.  in.,  and  the  straight  line  PS 
is  drawn  to  represent  the  variation  of  stress  across  the  section.  By  scaling  the  ordinates  to  this  line  at  centers 
of  the  slices  considered,  and  multiplying  by  their  areas,  the  values  of  the  resisting  forces  were  obtained,  after  noting 
that  the  steel  stress  in  tension  is  UV  X  15,  or  13,400  lb.,  which  is  less  than  the  allowable  value,  showing  that  the 
concrete  governs.  If  the  steel  stress  were  found  to  exceed  the  allowable  value,  the  line  UV  should  be  made 
16,000/n  to  locate  the  stress  line  PS,  and  the  steel  would  govern.  The  compressive  forces  are  plotted  in  the 
force  polygon,  Fig.  37d,  in  order  to  locate  their  resultant  by  the  polygon,  Fig.  37/  at  X. 

Knowing  the  magnitude  of  the  compressive  forces,  by  summation,  to  be  67,200  lb.  the  effective  depth  is 
scaled  off  as  17.3  in.  and  the  resisting  moment  is  then  67,200  X  17.3  =  1,162,600  in.-lb.  This  has  been  checked 
closely  by  the  usual  formulas. 


Fig.  38. 


»  Method  as  given  by  W.  S.  Wolfe  in  Eng.  Rec.  March  24,  1917,  and  June  27,  1917. 


Sec.  7-436] 


BEAMS  AND  SLABS 


317 


Application  to  complex  sections,  as  Fig.  38a,  can  be  made  as  shown  by  Figs.  386  and  38c,  locating  the 
neutral  axis. 

Designing  Double-reinforced  Beams. — To  design  a  double-reinforced  beam  for  a  given  bending  moment,  first 
assume  the  position  of  the  steel  and  the  allowable  total  depth,  and  assume  a  convenient  width  of,  say,  10  in.  and 


Given  :  ^^6S0  i%=/6,000 
<■■  Assume  Jb=lO  5 


M=I,OCO,000 


Assume  d'=  01 
or  A' =1.75°" 

A,  -  : 


Allowable  depfh  over  all  20" 

—  T580—  8700 

 \455_          /  15.700 

'  3,550 


Required  b-- 10  %^;ooo  ^ ^^-^  ^ay  eo" 
A'=/a9  X  17.5  X.OI  =3.43°" 
A=19.9  X /75  A. 01/8 =4.10°" 


Fig.  39. 


a  proper  value  for  the  compression  steel  ratio  p'.  The  stress  line  US  is  then  drawn  in  Fig.  39</  by  making  RS 
equal  to  the  allowable  compressive  stress  in  the  concrete  (650)  and  UV  equal  to  the  allowable  stress  in  the  steel  in 
tension  (16,000)  divided  by  n  (15),  or  1066.    The  intersection  P  then  locates  the  neutral  axis. 


y=az5-/>\ 
i  (d)/ 

I        /  I=H^H>'Y 
I     /  ^I00(l0)(9f5) 
I    /        1  =  9^50  in* 

1/ 


/   5:  I  \     \\  \ 
/     ;  n    \\\.   -  . 
/      i  I  \  \\\\\\\ 


Fig.  40. 


1 


The  compression  side  is  divided  into  a  number  of  slices  as  shown,  and  the  areas,  A\,  A2,  etc.,  computed, 
knowing  the  value  of  A2,  because  the  compressive  steel  area  is  known  from  the  given  ratio  p'.  To  find  the  area  of 
tension  steel  required,  the  value  of  nAs  is  obtained  from  the  polygon.  Fig.  39b,  and  the  force  diagram  Fig.  39c, 


318 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-44 


using  the  closing  line  NO.  nAg  is  then  scaled  off  (31)  and  divided  by  n  (15),  giving  2.06  sq.  in.  for  the  area  desired. 
The  steel  ratio  p  is  then  easily  computed.  The  resisting  moment  is  obtained  as  before,  using  the  diagrams,  Figs. 
39d,  39e,  and  39/,  by  which  a  resisting  moment  of  502,000  in. -lb.  is  obtained,  as  shown. 

Now,  if  the  width  is  increased  and  the  steel  ratios  are  kept  constant,  the  resisting  moment  will  increase 
directly  as  the  increase  in  width.  Therefore,  if  the  assumed  width  be  multiplied  by  the  ratio  of  the  required  moment 
to  the  moment  obtained  for  this  width,  the  required  width  is  found.  This  computation,  given  on  the  diagram, 
shows  that  a  20-in.  width  is  necessary.  The  required  areas  of  steel  in  compression  and  tension  can  then  be  com- 
puted as  given,  knowing  the  values  of  the  steel  ratios  p  and  p'. 

Moment  of  Inertia  of  Complex  Beam  Sections. — Fig.  40a  shows  the  cross-section  of  a  double-reinforced 
concrete  beam,  the  moment  of  inertia  of  which  is  desired.  The  compression  side  of  the  beam  is  divided  into  small 
slices,  the  area  of  the  steel  being  multiplied  by  15,  and  the  areas  of  these  slices  are  laid  off  in  the  force  polygon. 
Fig.  40b,  together  with  nAs,  or  15  times  the  area  of  the  tension  steel.  For  convenience  the  pole  p  is  taken 
with  the  pole  distance  H  equal  to  100  sq.  in.  to  the  scale  at  which  the  areas  were  laid  out  in  the  force  polygon. 
From  Fig.  406  the  funicular  polygon  Fig.  40c  is  drawn  locating  the  neutral  axis  by  the  intersection  O.  It  will 
be  noted  that  all  the  strings  in  this  funicular  polygon  are  extended  until  they  intersect  the  neutral  axis,  the  axis 
about  which  /  is  desired,  at  points  1,  2,  3,  etc.  Now  for  convenience  the  pole  p'  is  taken  so  that  the  pole  distance 
//'  equals  10  in.  to  the  scale  at  which  the  section  of  the  beam  was  drawn,  and  p'  is  connected  with  points  1,  2,  3, 
etc.  Now,  parallel  to  these  rays  the  corresponding  strings  in  the  funicular  polygon.  Fig.  40d,  are  drawn,  thus 
following  Culmann's  approximate  method  for  finding  the  moment  of  inertia  graphically.  From  this  construction 
we  get  I  =  H  X  H'  X  V  =  100  X  10  X  9.25  =  9250  in.*,  from  which  fc  and  /«  can  easily  be  obtained  for  any 
given  bending  moment  by  using  the  formulas 


SHEAR  AND  MOMENT  IN  RESTRAINED  AND  CONTINUOUS  BEAMS 

44.  Span  Length  for  Beams  and  Slabs. — The  Joint  Committee  recommends  the  following: 

The  span  length  for  beams  and  slabs  simply  supported  should  be  taken  as  the  distance  from  center  to  center 
of  supports,  but  need  not  be  taken  to  exceed  the  clear  span  plus  the  depth  of  beam  or  slab.  For  continuous  or 
restrained  beams  built  monolithically  into  supports,  the  span  length  may  be  taken  as  the  clear  distance  between 
the  faces  of  supports.  Brackets  should  not  be  considered  as  reducing  the  clear  span  in  the  sense  here  intended, 
except  that  when  brackets  which  make  an  angle  of  45  deg.  or  more  with  the  axis  of  a  restrained  beam  are  built 
monolithically  with  the  beam,  the  span  may  be  measured  from  the  section  where  the  combined  depth  of  beam 
and  bracket  is  at  least  one-third  more  than  the  depth  of  the  beam.  Maximum  negative  moments  are  to  be  con- 
sidered as  existing  at  the  end  of  the  span  as  here  defined. 

When  the  depth  of  a  restrained  beam  is  greater  at  its  ends  than  at  mid-span  and  the  slope  of  the  bottom 
of  the  beam  at  its  ends  makes  an  angle  of  not  more  than  15  deg.  with  the  direction  of  the  axis  of  the  beam  at 
mid-span,  the  span  length  may  be  measured  from  face  to  face  of  supports. 

45.  Recommendations  of  Joint  Committee  as  to  Positive  and  Negative  Moments. — In 

computing  the  positive  and  negative  moments  in  beams  and  slabs  continuous  over  several 
supports,  due  to  uniformly  distributed  loads,  the  Joint  Committee  recommends  the  following 
rules : 

wl- 

(a)  For  floor  slabs,  the  bending  moments  at  center  and  at  support  should  be  taken  at  for  both  dead  and 
live  loads,  where  w  represents  the  load  per  linear  unit  and  I  the  span  length. 

(6)  For  beams,  the  bending  moment  at  center  and  at  support  for  interior  spans  should  be  taken  at  ^-^  and 

for  end  spans  it  should  be  taken  at  ~^  for  center  and  interior  support,  for  both  dead  and  live  loads. 

(c)  In  the  case  of  beams  and  slabs  continuous  for  two  spans  only,  with  their  ends  restrained,  the  bending 
moment  both  at  the  central  support  and  near  the  middle  of  the  span  should  be  taken  as  . 

(d)  At  the  ends  of  continuous  beams,  the  amount  of  negative  moment  which  will  be  developed  in  the  beam 
will  depend  on  the  condition  of  restraint  or  fixedness,  and  this  will  depend  on  the  form  of  construction  used.  In 
the  ordinary  cases  a  moment  of  jg-  may  be  taken;  for  small  beams  running  into  heavy  columns  this  should  be 

wl- 

increased,  but  not  to  exceed  —  • 

For  spans  of  unusual  length,  or  for  spans  of  materially  unequal  length,  more  exact  calculations  should  be 
made.    Special  consideration  is  also  required  in  the  case  of  concentrated  loads. 

Even  if  the  center  of  the  span  is  designed  for  a  greater  bending  moment  than  is  called  for  by  (o)  or  (6),  the 
negative  m  'ment  at  the  support  should  not  be  taken  as  less  than  the  values  there  given. 


46.  Theorem  of  Three  Moments. — By  means  of  the  theorem  of  three  moments,  the  moments 


I 


(15) 


Sec.  7-46] 


BEAMS  AND  SLABS 


319 


at  the  supports  of  a  continuous  beam  may  be  deduced.  The  theorem,  assuming  level  supports, 
is  in  its  general  form  as  follows  (Fig.  40 A)^: 

M^kh  +  2M3  (^2/3  +  ^3/2)  +  M4  ^3/2  =  -  P2  h'h  (ko-k^')  -  P3  ^3-12  m,-'Sk,^W)  (1) 

1  Derivation  of  the  theorer,:  of  three  moments  is  as  follows: 

Let  the  origin  of  coordinates  be  B  (Fig.  A),  with  x  measured  positively  toward  the  left.  Considering  only 
the  deformation  due  to  the  bending  moment,  and  neglecting  the  deformation  due  to  shearing  forces,  the  equation 
of  the  elastic  curve  is  given  by 

d^y  M 

dx2  ~  EI 

in  which  M  is  the  bending  moment  at  any  point  x,  y.  If  this  expression  is  integrated  once,  there  results  an  ex- 
pression of       the  slope  of  the  tangent  to  the  elastic  curve  at  any  point  x,  y.    Thus  the  slope  of  the  tangent  at 

P  is 


P  Mdx 
EI 


and  for  the  whole  member  the  change  in  slope  of  the  tangent  becomes 

Mdx 
A  EI 


(a) 


Fig.  a. 


In  Fig.  B  is  shown  a  beam  resting  on  several  supports,  all  on 
the  same  level.  Let  us  consider  the  portion  of  the  beam  between  .4. 
and  B,  by  cutting  it  out  close  to  the  support  by  the  planes  m  and  n. 

The  part  of  the  beam  cut  out  is  shown  in  Fig.  C.  Each  end  has  the  same  shear  and  moment  acting  upon  it  as  it 
did  in  its  original  position,  thus  causing  stresses  throughout  the  portion  AB  identical  with  those  acting  before  the 
beam  was  cut.    The  moment  at  any  point  L,  to  the  left  of  the  load  P,  is 


Ml  =  A/2  +  Vox 

\       I  1 

H — 

A 

[        t  ti 

9                 C  D 

Fig.  B. 


r 

•jr 

Fig.  C. 


> 


The  moment  at  any  point  R  to  the  right  of  the  load  is 

Mr  =  M2  +  V-ix"  -  Pix"  -  kl) 
By  taking  moments  first  about  .4,  and  then  about  B,  the  values  of        and  V3  are  found  to  be 

Ml  -  Ms  +  Pkl 


Mz  -  M2  +  P(l  -  kl) 


1   t^^^.__. 


:) 


(c) 
id) 


It  is  apparent  that  the  moment  at  any  point  in  the  beam  may  be  found  if  the  moment  at  the  reaction  can 
be  found.  We  will,  therefore,  proceed  with  the  solution  of  a  general  case  of  a  continuous  girder  with  concentrated 
loads. 

Consider  now  a  beam  resting  on  several  supports  on  the  same  level,  and  loaded  as  shown  in  Fig.  D.  The 
slope  of  the  tangent  to  the  deflection  curve  at  B,  considering  the  portion  of  the  beam  to  the  left  of  B,  is  ^2;  and 
that  for  the  tangent  to  the  deflection  curve  at  B,  considering  the  portion  to  the  right  of  B,  is  08.  Since  the  de- 
flection curve  of  a  beam  must  necessarily  be  continuous,  MN  is  a  straight  line,  and 


<l>2  =  —  <l>3 


(/) 


320 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec,  7-46 


This  is  the  general  equation  of  three  moments  for  one  concentrated  load  in  each  span. 
When  there  is  more  than  one  concentrated  load  in  each  span,  the  loading  may  be  broken  up  into 
a  series  of  cases  similar  to  the  above.  For  each  set  of  loads  the  right-hand  portion  of  equation 
(1)  is  solved,  and  the  results  finally  combined,  and  placed  equal  to  the  left-hand  portion  of 
equation  (1). 

The  theorem  may  be  applied  to  a  beam  with  uniform  loads.  For  the  loading  shown  in 
Fig.  41  the  theorem  has  the  form 


M2l2h  +  2Mz(l2h 

■Mr 


3/2)  +  M,IJ 


4 


^3, 


Ms, 


(2) 


Fig.  40A. 


For  a  constant  moment  of  inertia  and  all  spans  equal,  equation  (1)  reduces  to 

M2  +  4Af3  +  iif4  =  -  P2Z(fc2  -  W)  -  PsK^ks  -  3/C32  +  /C33) 

When  k2  =  kz  =  0.5  this  equation  reduces  to 

M2  +  4ikr3  +  M4  =  -  O.375P2Z  -  0.375P3Z 

When  in  equation  (2)  the  moment  of  inertia  is  a  constant  and  all  spans  carry  the  same  uniform 
load 


M2I2  +  2M3(72  +  h)  +  M,h 


and  when  h  =  h, 


2 


M2  +  4ilf3  -h  M4  = 

1000  lb.  per  ff: 


Fig.  41. 


800  lb.  per  ft 


■ZO'- 


1000  lb.  per  H 


■I8'- 


Fig.  42. 


When  using  any  of  the  foregoing  formulas  for  continuous  girders,  it  should  be  borne  in 
mind  that  the  supports  are  assumed  to  be  on  the  same  level  throughout  the  process  of  loading. 

Illustrative  Problem. — Compute  the  moments  at  the  supports  and  the  magnitude  of  the  reactions  for 
the  beam  shown  in  Fig.  42.  Assume  a  constant  section  throughout,  whence  Ii  =  I2  =  I3.  Consider  first  the 
two  spans  between  Ri  and  Rs.    From  equation  (2) 

I6M.  +  2M.(16  +  20)  +  20M.  =  -  - 


If  the  values  of  M  in  equations  (6)  and  (c)  are  substituted  into  equation  (a),  and  the  latter  integrated  from  A  to 
P2,  and  from  P2  to  B,  and  finally  the  values  of  V2  and  F3  as  given  in  equations  (d)  and  (e)  are  incerted,  there  re- 
sults for  4>2  the  value 

M2Z22  +  23/i?22  +  P2h3(k2  -  k2^) 

In  a  similar  manner  the  values  of  ^3  may  be  found  by  considering  C  as  the  origin  of  x,  and  integrating  toward  the 
left,  whence 

^4^32  +  2MiU^  +  PzhK2k3  -  3^32  +  ks^) 
^3  _____ 

Inserting  these  values  into  equation  (/)  there  results 

M2hl3  4-  2^3(^2/3  +  Z3/2)  +  ikf4Z3/2  =  -  P2l2^l3{k2  -  A;2»)  -  Pzh''l2{2kz  -  Zkz^  +  kz^)  ig) 
A  development  precisely  similar  to  the  foregoing  may  be  applied  to  a  beam  with  uniform  loads. 


Sec.  7-46 J 


BEAMS  AND  SLABS 


321 


20M>  +  2M3(20  +  18)  +  I8A/4  =  - 


whence 

IMi  +  iHMi  +  oMi  =  -  UoO.OOO 
Applying  equation  {2)  to  the  two  spans  between  Ri  and  Ra,  and  noting  the  change  in  subscripts  accordingly,  we 
obtain 

(80U)(2U)-i  _  (100())(18)3 
4  4 
whence 

IOM2  +  38^3  +  9M4  =  -  1,529,000  {h) 
Since  all  supports  are  free,  Mi  =  Mi  =  0.    Noting  this,  and  solving  (a)  and  {b)  simultaneously, 

90ilf2  +  25M3  =  -  3,280,000 
90 M2  +  34 Ms  =  -  3,761,000 
317M3  =  -  10,481,000 
Afs  =  -  33,100  ft.-lb. 


^2 


M4 


M2 


M3 


M4 


(a) 


1    1  • 

yyjperfA 

(b) 


W2  perft\ 

A 

2 

M4 

\W2perft 


per  ft 


M3 


M4 


> 

per  ft 

rn 

— 1  perff. 

<•■  •■> 

V-./p-i-  ..>| 


iVj  per  ft 
~  (f) 


Mb 


> 

^>2>  per  ft 

<  4  ■ 

M3 


M4 


■r/y|  1  iVjperft 

A/^  /l/j  /^^ 


Mz 


M4 


> 

Wz  per  ft. 

k^Z 

k/h\ 

["!■ 

perft\ 

<..  ^z  -  > 

M3  M4 
Fig.  43. 


(j) 


Substituting  this  into  (6)  we  find 

We  may  now  find  the  reactions. 

16Z?i 


M2 


-  -  45,600 


45,000  ft.-lb. 


16/2i  =  128,000  -  45,600  =  82,400 
Ri  =  5150  lb. 

(5150)  (36)  -  (1000)  (16)  (28)  +  2^Ri 


(800)  (20)-' 
2 


=  -  33,100 


20i?2  =  -  33,100  -  185,400  +  448,000  +  160,000  =  389,500 
222  =  19,470  lb. 
(1000)  (18)2 


18«4 


33,100 


21 


Rk  =  7,160  lb. 


322 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-46 


(7160)  (38)  -  (1000)  (18)  (29)  +  20R, 


(800) (20) 2 


45,600 


20/23 


45,600  -  272,000  +  552,000  +  160,000 
Rs  =  18,220  lb. 


As  a  check, 


Ri  +  Ri  +  R3  +  Ri 


total  load  =  50,000  lb. 


Very  often  a  continuous  girder  may  have  a  uniform  load  over  one  or  more  spans.  Fig.  43 
will  be  found  to  give  the  possible  cases,  and  the  corresponding  formulas  follow.  Should  no 
load  be  on  one  of  the  spans,  w  for  that  span  becomes  zero,  and  the  term  containing  it  will  drop 
out.    Only  the  right-hand  side  of  the  general  equation  is  affected  by  the  loading. 

Let  M 2/2  +  2M3  {h  +  Z3)  +  Mih  be  denoted  by  r. 


Then  (a)  r 

(b)  r 

(c)  r 

(d)  r 

(e)  r 


W3I3 


[2  4.)  4: 

U  .  2  ^  4  /     4  • 


ki'  + 


ki'^ 


I 


w=  2000 lb.  per  n 
J<--/<5'---5|^  18'--^  /<?'-->i 


Fig.  44. 

(/)  r  = 
(.9)  r  = 
(h)  r  = 
{i)  r  = 
U)  r  = 


w=  2000  lb.  per  ft 

»  16'  >|<  18'-  ■>}<  18'-  > 

Fig.  45. 


2Po?/(A:  -       -  w;3Z3-^(^  -  fci^  +  k^^  -  • 


Spans  similarly  located  and  similarly  loaded  have  the  same  representative  term.  Cases 
{%)  and  (jf)  are  given  to  show  how  concentrated  loads  may  be  considered  with  uniform  loads. 

When  a  beam  has  fixed  ends — ^that  is,  when  the  slope  of  the  tangent  to  the  elastic  curve  at 
the  end  is  constant  for  all  loading — ^the  theorem  of  three  moments  may  readily  be  applied.  This 
is  accomplished  by  supplying  a  span  of  zero  length  at  each  fixed  end,  and  then  by  proceeding  as 
before.    This  satisfies  the  requirement  made  in  the  above  definition  for  fixed  ends. 

Illustrative  Problem. — Determine  the  moments  at  the  supports  and  the  magnitude  of  the  reactions  for 
the  beam  shown  in  Fig.  44.    In  Fig.  45  the  fixed  ends  have  been  removed  and  the  spans  /„  and  V  put  in  their  places. 
The  equations  now  become,  remembering  that  Ro  =  R'  =  0,  and  Mi  =  M2  =  0, 

2 Ml  +  M2  =  -  \wl2 


All  +  4M2  +  M3 


Sec.  7-47] 


BEAMS  AND  SLABS 


323 


M2  +  4A/3  +  Mi  =  -  ~wli 


If  these  equations  are  solved  simultaneously,  there  results 


Ml  =  M2  =  M 
Ri  =        =  18,000  lb 
Rz  =  Rs  =  36,000  lb 


54,000  ft.-lb. 


-./06  ^ 

_  -  077,  

--<-C77 

NT 

2 

3 

4 

5 

Fig.  46. — Moments  in  continuous  beams;  supported  ends;  uniform  load  on  all  spans;  spans  all  equal. 

Coefficients  of  {wl-). 


of7 

6 


10 


6\S 
JO 


S\6 

/a 


4\o 

10 


1  2 

3  4 

0  t// 

I7\ /S  /3\l3 

//to 

28 

28  28 

2d 

28 

1 

2  3 

A 

5 

23\20 
38 


/8  I  /9 
38 


A  S3 


63  \' 


49]  S/ 


^0 


ofse 

d4Z 


86^75      67'\70  72~T7/ 


7S\86 


MZ  J42  J42  i42         i42  142  i42 

kFiG.  47. — Shears  in  continuous  beams;  supported  ends;  uniform  load  on  all  spans;  spans  all  equal. 
Coefficients  of  {wV). 

47.  Uniform  Load  Over  All  Spans. — In  Fig.  46  are  given  the  moments  in  continuous  beams 
for  a  uniform  load  over  all  spans.  Supported  ends  and  equal  spans  are  assumed.  Positive 
moments  are  plotted  above  the  beam.  The  shears  on  each  side  of  the  supports  are  given  in 
Fig.  47.    The  reaction  at  any  given  support  is  the  sum  of  the  two  shears  at  that  support. 

The  maximum  moments  at  (or  near)  the  center  of  many  of  the  interior  spans  are  not  given, 
as  they  are  small  and  do  not  vary  greatly  from  those  given  for  the  continuous  beam  of  four 
spans.    Maximum  positive  moment  occurs  for  zero  shear  as  in  simple  beams. 

In  continuous  beams  with  fixed  ends,  and  with  uniform  load  and  equal  spans  (the  same  as 


324 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-48 


above),  the  iriaximum  positive  moment  occurs  at  the  center  of  each  span  and  its  value  in  every 
case  is  The  negative  moment  over  each  support  equals  ^2     Shears  close  to  the  supports 

are  all  equal  with  a  value  of  3-2^'^- 

The  maximum  positive  moment  on  a  beam  of  one  span,  with  one  end  fixed  and  the  other 
end  free,  and  uniformly  loaded  is  ^{23'^^^  and  the  negative  moment  at  the  fixed  end  is  }^iwl^. 

48.  Fixed  and  Moving  Concentrated  Loads. — Continuous  beams  of  one,  two,  and  three 
equal  spans  and  any  span  length  may  be  figured  for  fixed  and  moving  concentrated  loads  by 
means  of  the  influence  lines  of  Figs.  48  to  52  inclusive. 

48a.  Influence  Lines. — As  a  load  moves  over  a  beam,  the  shear  and  moment  at 
a  given  section  will  vary.  If  the  value  of  moment  at  any  point  A  is  plotted  as  an  ordinate  at 
the  point  where  the  load  is  applied,  and  this  process  repeated  for  each  position  of  the  load,  the 
result  is  called  an  influence  diagra7n  for  the  moment  at  point  A ;  and  the  curve  generated  by  the 
extremities  of  all  ordinates  is  called  an  influence  line  for  the  moment  at  point  A.  Similar  lines 
may  be  drawn  for  shear  and  for  deflections.  In  structures,  influence  lines  may  also  be  drawn 
for  stress  intensities  at  a  given  point.    The  curve  gets  its  name  because  of  the  fact  that  for  any 


chosen  point,  it  gives  the  influence  on  a  certain  function  at  that  point,  for  varied  positions  of  the 
load. 

It  should  be  noted  that  the  influence  line  for  moment — for  a  simple  beam,  for  instance — • 
differs  from  the  moment  diagram  for  that  beam.  The  moment  diagram  gives  the  moment  at 
any  point  for  one  position  of  the  load ;  while  the  influence  hne  for  moment  gives  the  moment  at 
one  point  for  any  position  of  the  load.  For  each  point  in  the  beam  there  may  be  drawn  an  in- 
fluence line,  but  each  influence  line  is  descriptive  of  but  one  point.    In  Fig.  53  there  is  drawn  an 

influence  line  for  moment  at  A.    The  moment  at  ^  is  -  ^  '  and  that  is  the  value  of  the  ordinate 

Pah  X 

at  A.    The  ordinate  at  B  is  —f-  •  -  and  is  the  moment  at  A  when  the  load  P  is  at  B. 

I  a 

Suppose  the  beam  to  have  a  load  of  1  lb,  moving  across  it.    The  ordinate  at  A  is  then-^  ' 

Usually  influence  lines  are  drawn  for  unit  loads.  The  ordinate  at  B  is  then  the  moment  at  .1 
when  a  unit  load  is  placed  at  B.  If  the  load  at  B  is  not  unity,  then  the  moment  at  A  will  be 
equal  to  the  load  times  the  ordinate  at  B  for  the  1-lb.  load. 

If  the  beam  is  loaded  with  a  uniform  load,  the  moment  at  A  is  equal  to  the  load  per  foot 


Sec.  7-4Sol 


BEAMS  AND  SLABS 


325 


Moment  over 
Center  Support 


End  Reaction 
and  End  Shear  | 


Center 
Reaction 


Shear  at 
Center  Support 


oooo'ocio  od^oociddoooo 


Fig.  49. — Influence  lines  for  two  equal  spans,  supported  ends. 


Moment  over 
End  Support 


o 

000 


Moment  at"M' 


Moment  over 
Center  Support 


End  Reaction 
and 
End  Shear 


Center 
Reaction 


Shear  at 
Center  Support 


000000000 


ciooooddoo 


to  §1 
o  o 


o  o  o  o  o 


OOOOOuOOO 


Fig.  50.— Influence  lines  for  two  equal  spans,  fixed  ends.     (Spans,  10  ft.  Load, 


unity.) 


326 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-48a 


Fig.  51. — Influence  lines  for  three  equal  spans,  supported  ends.    (Spans,  10  ft.    Load,  unity.) 


Fig.  52. — Influence  lines  for  three  equal  spans,  fixed  ends.    (Spans,  10  ft.    Load,  unity.) 


Sec.  7-48a] 


BEAMS  AND  SLABS 


327 


times  the  area  of  the  influence  diagram  for  the  moment  at  A.    In  Fig.  53  this  is  \  w  --y  'l'2j 

w 

or  ^  •  ab,  which  is  readily  recognized  as  the  moment  at  A  for  a  uniform  load.    For  a  partial 

uniform  loading,  the  load  per  foot  multiplied  by  the  area  of  the  influence  diagram  for  the  loaded 
portion  will  give  the  moment  at  A. 


<  X  

<  a  •■■ 

Fig.  53. 

Influence  lines  have  been  constructed  in  Figs.  48  to  52  inclusive  for  continuous  beams  of 
equal  spans,  each  of  10  units  in  length,  with  the  outer  ends  either  fixed  or  simply  supported. 
If  the  influence  lines  are  desired  for  equal  spans  other  than  10  ft,  in  length,  they  may  be  con- 


Hz 


w  ib.per  Jin.ft 


■e 


Mz 


Ms 


3 


Moment 


.096  wl 


063 y/t^ 


Shear 


le 


wi 


Supported  Ends 


Rj  =  -i 


Moment 


Shear 


.0S4 


..021 


Fixed  Ends 

Fig.  54. — Moving  uniform  load,  two  equal  spans. 


structed  by  regarding  one  unit  of  length  as  one-tenth  the  span.  The  ordinates  will  be  the  same 
as  those  plotted  here.    The  ordinates  for  positive  moment  are  plotted  above  the  line. 


328 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-48a 


For  two  equal  spans  with  ends  either  supported  or  fixed,  it  is  readily  seen  that  the  greatest 
positive  moment  at  any  point  M  will  be  obtained  when  the  load  covers  only  the  span  in  which 


uj  lb.  perl  in  ft. 

My 

UJ  lb.  per  lin.  ft 

—  > 

<■ 

<  /  > 

^4 


,-.101w-t^ 


Moment 


Shear 


Supported  Ends 


MoTTient 


Shear 


-.059 u/^^ 


Fixed  Ends 

Fi(i.  ^>^^. — Moving  uniform  load,  three  equal  spans. 


^  w Ib.perlin.ft 


Moment 


Shear 


20, 


-.028  W 


Supported  Ends 
iZ  ....069  rri^ 


Moment 


Shear 


.  -.OS 8  w^^ 

P2=pj-  2  we 


Fixed  Ends 

Fig,  56. — Moving  uniform  load,  three  equal  spans. 

M  occurs,  since  the  area  for  that  span  is  positive.  The  greatest  end  reaction  and  end  shear  will 
also  be  obtained  when  the  load  is  over  one  span.    The  greatest  center  reaction,  negative  mo- 


Sec.  7-48a] 


BEAMS  AND  SLABS 


329 


ment  (over  center  support),  and  shear  at  center  support,  will  be  obtained  by  fully  loading  both 
spans. 

For  three  equal  spans,  the  uniform  live  load  should  cover  alternate  spans  to  give  the 
greatest  positive  moment  in  any  span,  and  to  give  the  greatest  end  reaction  and  end  shear.  P'or 


w  lb  per  I  in.  ft 


^2 


>K-  --  -e 


.073  wi' 


.053  we' 


Moment 


Shear 


60 

^4  =  -jW 


Supported  Ends 


.039  wi' 


056  yvi"- 


.022  wi' 


Moment 


Shear 


.  ■32  we 


Mo 


.045  w^^ 


ISO 


■81  we 

180 


Fixed  Ends 

Fig.  57. — Moving  uniform  load,  three  equal  spans.  j 

intermediate  reactions  and  negative  moment  over  intermediate  reactions,  the  spans  adjacent; 
to  the  reaction  in  question  should  be  fully  loaded, 

49.  Moving  Uniform  Loads. — If  a  uniform  load  is  considered,  influence  lines  indicate  the 
spans  which  should  be  loaded  in  order  to  obtain  the  maximum  values  of  the  given  functions. 


Mb 

Afc 

\ 

Fig.  58. 


Fig.  54  represents  the  variation  in  moment  and  shear  for  a  uniform  load  on  one  span  of  a  beam 
of  two  equal  spans,  both  fixed  and  supported  ends.  Figs.  55,  56  and  57  give  values  for  various 
loadings  with  three  equal  spans. 


330 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-50 


To  illustTate  the  effect  of  loads  on  various  spans  upon  the  bending  moments,  influence  hnes 
have  been  drawn  for  six  equal  spans  (Fig.  58),  for  moments  at  the  centers  of  span  1-2  and  3-4, 
and  at  supports  2  and  4.  A  maximum  moment  at  the  center  of  a  span  requires  each  alter- 
nate span  to  be  loaded,  and  a  maximum  moment  at  the  support  requires  the  two  adjacent 
spans  to  be  loaded  and  then  each  alternate  span.  The  effect  of  loads  on  remote  spans  is 
seen  to  be  small.  Influence  lines  are  not  drawn  for  shears  since,  in  a  large  number  of  spans, 
the  shears  do  not  differ  greatly  from  those  in  simple  beams. 

50.  Maximum  Moments  from  Uniform  Loads. — The  following  table  gives  the  values  of 
maximum  negative  and  positive  moments  for  girders  of  equal  spans.  Each  column  headed 
Fixed  load"  gives  the  maximum  moment  at  the  point  under  consideration  for  a  uniform  load 
covering  the  entire  length.  The  columns  headed  ''Moving  load"  give  the  maximum  moment 
at  the  point  under  consideration  when  the  uniform  load  is  placed  on  certain  spans  to  cause  the 
maximum  moment. 

Maximum  Moments  in  Continuous  Beams;  Supported  Ends;  Uniform  Fixed  and  Moving 

Loads 
Coefficients  of  (wP) 


No.  of  spans 

Intermediate  spans 

End  spans 

Fixed  load 

Moving  load 

Fixed 

load 

Moving  load 

At 
center 
+ 

At 
support 
(-) 

At 
center 
+ 

At 
support 
(-) 

At 
center 
+ 

At  2d 
support 
(-) 

At 
center 
+ 

At  2d 
support 
(-) 

Two  

0.070 
0.080 

0. 125 
0.100 

0.096 
0.101 

0.125 
0.117 

Three  

0.025 

0.075 

0.036 

0.071 

0.081 

0.107 

0.077 

0.107 

0.098 

0.120 

(0.115)1 

Five  

0.046 

0.079 

0.086 

0.111 

0.078 

0.105 

0.099 

0.120 

(0.106)1 

(0.116)1 

Six....  

0.043 

0.086 

0.084 

0.116 

0.078 

0.106 

0.099 

0.120 

(0.106)1 

(0.116)1 

0.044 

0.085 

0.084 

0.114 

0.078 

0.106 

0.099 

0.120 

(0.106)1 

(0.116)1 

1  Where  two  adjacent  spans  only  are  loaded. 

The  fixed-load  coefficients  will  apply  to  the  dead  load  when  finding  the  maximum  coefficients 
due  to  a  moving  uniform  load — the  case  ordinarily  encountered  in  building  construction.  In- 
asmuch as  the  theoretical 
maximum  moments  in  con- 
tinuous beams  of  five  or  more 
spans  would  involve  unreason- 
able assumptions  as  to  posi- 
tion of  the  live  loads,  the 
values  of  moment  coefficients 
in  small  table  may  be  taken. 

Combining  the  dead  and 
live  loads  into  a  single  unit 
for  the  purpose  of  determin- 
ing general  moment  coefficients  which  will  apply  to  all  ordinary  cases,  we  obtain  the  values 
given  in  table  on  page  331. 


Nature  of  load 

Intermediate  spans 

End  spans 

At 
center 

At 
support 

At 
center 

At  2d 
support 

0.046 

0.086 

0.080 
(0.070) 

0.101 
(0.096) 

0.107 

(0.125) 
0.117 

(0.125) 

0.086 

0.107 

Sec.  7-51] 


BEAMS  AND  SLABS 


331 


In  continuous-beam  com- 
putations, the  beam  is  as- 
sumed as  freely  supported  at 
the  interior  supports  and  the 
assumption  is  made  that  the 
supports  are  of  no  appreci- 
able width.  For  beams  in 
concrete  construction,  there- 
fore, the  coefficients  in  the 
third  column  of  the  table 
should  be  reduced,  and  could 
very  well  be  taken  equal  to 
those  in  the  second  column. 
The  live  load  will  generally 
range  from  two  to  five  times 
the  dead  load,  but  the  ratio  of  10: 1 
is  given  to  show  the  slight  varia- 
tion in  moment  coefficients  for  ra- 
tios above  5:1. 

From  a  study  of  the  table,  re- 
ducing the  bcnding-moment  coeffi- 
cients at  the  interior  supports  as 
above  proposed,  it  is  seen  that  the 
bending  moment  at  the  center  and 
at  the  support  for  interior  spans 


Ratio  of  live  to  dead 

Intermediate  spans 

End  spans 

At 
center 

At 
support 

At 
center 

At  2d 
support 

Three  or  more  spans 
2:1 
5:1 
10:1 

0. 073 
u .  u/  y 
0.082 

0. 100 
n  1  r\A 

U .  iU't 

0.105 

0.094 

U  .  yJvo 

0.099 

0.114 

U  .  1  i  O 

0.116 

Two  spans 
2:1 
5:1 
10:1 

0.087 
0.092 
0.093 

0.125 
0.125 
0.125 

may  be  taken  as  (0,083 


and  "for  end  spans  it  may  be  taken 
as  Jq-  for  center  and  adjoining  sup- 
port, where  w  includes  both  dead 
and  live  loads.  In  the  case  of  two 
spans  only,  the  bending  moment  at 
the  center  support  may  be  taken 

as  -TT,  and  near  the  middle  of  the 


span  as 


10 


Where  the  ends  of 


a  two-span  beam  are  restrained, 
the  bending  moment  may  well  be 

taken  as  jj^,  both  at  the  center 

support  and  near  the  middle  of  the 
span. 

The  shear  at  each  support  of 
continuous  beams  with  fixed  ends 
may  be  taken  as  one-half  the  span 
load.  If  the  ends  are  simply  sup- 
ported, the  shear  in  the  end  spans 
near  the  second  support  will  be 
approximately  O.Qwl. 

51.  Beam  Concentrations. — 
Floor  systems  of  beam-and-girder 


Loads  at  Middle  Fbmts 


■.67 


p  / 

\i  / 

/// 

Loads  at  Th.rd  Points 

.1.97  .267 


1 40  .'SO  /SQ 

Loads  at  Middle  and  Quarter  Points 
Fig.  59. — Moments  and  shears  in  continuous  beams;  supported 
ends;  spans  all  equal;  concentrated  loads  as  shown.    Coefficients  of 
(PI)  for  moment.    Coefficients  of  (P)  for  shear. 


332 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-51 


construction  impose  concentrated  loads  on  the  girders  at  the  ends  of  the  floor  beams. 
There  may  be  one  or  more  floor  beams  built  into  each  girder,  depending  upon  the  shape  of 

the  panels. 

Figs.  59  and  62  inclusive  give  the  shears  and  moments 
caused  by  beam  concentrations  on  continuous  girders.  The 
girder  spans  are  assumed  equal  and  the  ends  of  the  girders 
as  simply  supported.  In  girders  with  fixed  ends  and  with 
full  loading  as  shown  in  Fig.  59,  the  maximum  positive  mo- 
ment for  loads  at  the  middle  points  is  the  same  as  the  maxi- 
mum negative  moment  and  equals  0.125P/  in  every  case. 
For  loads  at  the  third  points,  the  maximum  positive  moment 
is  0.110  PI  and  the  maximum  negative  moment  is  exactly 
twice  this  value.  For  loads  at  the  middle  and  quarter 
points,  the  maximum  positive  moment  is  0.187PZ  and  the 
maximum  negative  is  0.313PZ.  The  maximum  shears  in  all 
cases  are  the  same  as  in  simple  beams. 

In  the  following  table  are  given  the  maximum  positive 
and  negative  moments  due  to  beam  concentrations.  Ends 
of  beams  are  assumed  as  simply  supported. 

It  is  quite  evident  that  the  variation  of  moment  co- 
efficients is  very  nearly  the  same  as  shown  in  the  table  pre- 
viously given  for  uniform  loads. 


Maximum  Moments  in  Continuous  Girders  Due  to  Beam  Concentrations; 

Supported  Ends 
Coefficients  of  (PI) 


No.  of  spans 

Intermediate  spans 

End  spans 

Fixed  load 

Moving  load 

Fixed  load 

Moving  load 

At 
center 
+ 

At 
support 
(-) 

At 
center 
+ 

At 
support 
(-) 

At 

center 
+ 

At  2d 
support 
(-) 

At 
center 
+ 

At  2d 
support 

(-) 

Loads  at 
middle  points 
Two  

0.156 
0.175 
0.171 

0.187 
0. 150 
0.158 

0.203 
0.213 
0.211 

0.187 
0.175 
0.1741 

0.100 
0.130 

0.175 
0.191 

Five  

0.119 

0.156^ 

Loads  at 
third  points 
Two  

0.222 
0.244 
0.240 

0.333 
0.267 
0.281 

0.278 
0.289 
0.286 

0.333 
0.311 
0.3091 

0  .066  . 
0.122 

0.200 
0.228 

Five  

0.211 

0.2761 

Loads  at 
middle  and 
quarter  points 
Two  

0.267 
0.314 
0.303 

0.465 
0.372 
0.394 

0.383 
0.406 
0.401 

0.465 
0.438 
0.4351 

0.128 
0.204 

0.312 
0.352 

Five  

0 . 296 

0.3891 

1  Two  adjacent  spans  only  are  loaded. 


Fig.  60. — Concentrated  loads  as 
shown;  loads  at  middle  points;  two 
and  three  equal  spans;  supported  ends. 
Coefficients  of  (PI)  for  moment.  Co- 
efficients of  (P)  for  shear. 


Sec.  7-51 


BEAMS  AND  SLABS 


333 


By  similar  reasoning  to  that  employed  in  deriving  mom(nit  coefficients  for  uniform  loads, 
we  obtain  the  following  values :  p  p 


Intermediate  spans 


Nature  of  load 


At  center 


Loads  at  middle  points 
Dead  load  

(two  spans)  

Live  load  

(two  spans)  


Loads  at  third 
Dead  load  

(two  spans).. . 
Live  load  

(two  spans).. . 


pomis 


Loads  at  middle  and 

quarter  points 
Dead  load  

(two  spans)  

Live  load  

(two  spans)  


0.130 
0.191 


0.122 
0.228 


0.204 
0.352 


At 
support 


0.119 
0.156 


0.211 
0 . 276 


0.296 
0.389 


End  spans 


At  center 


0.175 
(0.156) 

0.213 
(0.203) 


0.244 
(0.222) 

0.289 
(0.278) 


0.314 
(0.267) 
0.406 

(0.383) 


At  2d 
support 


0.158 
(0.187) 

0.175 
(0.187) 


0.281 
(0.333) 

0.311 
(0.333) 


0.394 
(0.465) 

0.438 
(0.465) 


■  87 


Fig.  61. — Concentrated  loads  as 
shown;  loads  at  third  points;  two  and 
three  equal  spans;  supported  ends. 
Coefficients  of  (P)  for  shear. 


Combining  the  dead  and 
live  loads  into  a  single  unit  for 
the  purpose  of  determining 
general  moment  coefficients, 
we  obtain  the  following: 


.38J 


.438  — 
/.94 

Fig.  62. — Concentrated  loads  as 
shown;  loads  at  third  points;  two  and 
three  equal  spans;  supported  ends. 
CoeflScients  of  {PI)  for  moment.  Co- 
efficients of  {P)  for  shear. 


Ratio  of  live  to  dead 


Loads  at  middle  points 
2:1 
5:1 
(Two  spans) 
2:1 
5:1 


Loads  at  third  points 
2:1 
5:1 
(Two  spans) 
2:1 
5:1 


Loads  at  middle  and 
quarter  points 
2:1 
5:1 
(Two  spans) 
2:1 
5:1 


Intermediate  spans 


At  center 


0.171 
0.181 


At 
support 


0.143 
0.150 


0.193 
0.210 


0.303 
0.327 


End  spans 


At  center 


0.200 
0.207 

0.187 
0.195 


At  2d 
support 


0.169 
0.172 

0.187 
0.187 


0.254 
0.265 


0.274 
0.281 

0.259 
0.269 


0.301 
0.306 

0.333 
0.333 


0.358 
0.374 


0.375 
0.391 

0.344 
0.364 


0.423 
0.431 

0.465 
0.465 


334 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-52 


The  following  table  shows  that  a  floor  girder  carrying  one  or  more  beams  and  subjected 
to  an  indefinite  live  load  may  be  computed  with  sufficient  accuracy  by  considering  it  simply 
supported  and  then  reducing  the  maximum  moment  so  found  (and  an  equal  negative  moment) 
by  the  same  ratio  of  reduction  used  with  uniform  loading.  For  example,  suppose  the  maximum 
moment  due  to  given  concentrated  loads  is  K  (considering  the  beam  supported),  then  if 
}^i2^l^  is  used  for  uniform  loading  instead  of  /-sivP,  ^{2  of  K,  or  %K,  may  be  used  for  the  con- 
centrated loads.  The  table  gives  moment  coefficients  according  to  this  rule.  These  coeffi- 
cients should  be  compared  with  those  in  the  preceding  table. 


No.  of  spans 

Intermediate 
spans 

End  span  and 
adjoining 
support 

Loads  at  middle  points 

Three  or  more  spans  

Two  spans  

0.167 

0.208 

0.208 
0.250 

Loads  at  third  points 
Two  spans  

0.222 
0.278 

0.278 
0.333 

Loads  at  middle  and 
quarter  points 

0.333 
0.417 

0.417 
0 . 500 

In  a  beam  loaded  at  the  middle  points  we  find  that  the  moment  at  the  center  of  intermediate 
spans  may  have  a  value  about  8%  greater  than  the  recommended  value  for  use  in  design. 
(This,  however,  is  considering  the  beam  as  freely  supported  at  the  interior  supports,  and  the 
supports  of  no  appreciable  width.)  All  other  values  for  this  loading  are  somewhat  less  than 
those  recommended.  In  fact,  the  specified  moment  coefficient  for  the  center  support  of  a  two- 
span  beam  may  be  reduced  and  made  the  same  as  for  the  center  of  span.  In  beams  of  three  or 
more  spans  and  for  the  same  loading  as  just  mentioned,  the  moment  coefficient  for  the  inner 
supports  of  end  spans  may  be  reduced  so  as  to  have  the  same  value  as  specified  for  the  interior 
spans. 

The  moment  at  interior  supports  in  beams  loaded  at  the  third  points  may  have  a  value 
about  19%  greater  than  that  specified,  but  the  width  and  monolithic  character  of  the  supports 
will  offset  this  to  a  considerable  extent.  It  is  preferable,  however,  to  make  some  allowance 
for  this  in  design  although  for  simplicity  this  has  not  been  done  in  this  handbook.  The  same 
is  true  for  the  inner  supports  of  the  end  spans  although  the  increase  in  moment  over  that  speci- 
fied is  about  10%. 

The  reader  may  draw  his  own  conclusions  in  regard  to  moment  coefficients  in  beams  loaded 
at  the  middle  and  quarter  points. 

The  recommendations  for  shear  given  for  uniform  loads  will  apply  in  the  case  of  beam  con- 
centrations. 

52.  Negative  Moment  at  the  Ends  of  Continuous  Beams. — The  amount  of  negative  mo- 
ment at  the  ends  of  continuous  beams  depends  upon  the  manner  in  which  the  ends  are  restrained. 
A  beam  cannot  be  entirely  fixed  unless  the  restraint  is  sufficient  to  cause  the  neutral  surface  at 
the  ends  to  be  horizontal.  The  moment  coefficient  must  be  left  to  the  judgment  of  the  designer, 
but  the  shear  and  moment  diagrams  shown  in  Figs.  54  to  57  inclusive  (for  beams  with  fixed 
ends)  and  in  Figs.  70  and  72  will  prove  useful  in  this  connection  (see  also  recommendations 
Qf  Joint  Committee  on  page  318). 


Sec.  7-53] 


BEAMS  AND  SLABS 


335 


63.  Bending  Up  of  Bars  and  Provision  for  Negative  Moment.— In  Figs.  63  to  65  inclusive 

are  given  bending-moment  curves  which  apply  to  continuous  beams,  supported  ends,  for  uni- 
form loads  (both  live  and  dead)  on  two,  three,  and  four  equal  spans.  The  dead-load  curves 
are  the  same  as  shown  in  Fig.  46  for  uniform  load  over  all  spans.  In  plotting  the  live-load 
curves,  the  loadings  were  considered  which  give  maximum  and  minimum  values  at  each  of  the 


Fig.  63. — Moment  curves  for  uniform  load;  two  spans;  supported  ends. 


one-tenth  division  sections.  Thus,  these  curves  do  not  represent  any  one  condition  of  loading, 
but  may  be  used  to  determine  the  extreme  values  of  the  live-load  moment  at  any  given  point 
in  the  span. 

It  should  be  noted  that  some  portions  of  the  live-load  curves  are  quite  different  from  those 
shown  in  Figs.  46  to  57  inclusive.  For  example,  the  part  of  the  maximum  live-load  curve  close 
to  the  center  support  in  the  beam  of  two  spans  (Fig.  63)  is  quite  different  from  a  similar  portion 


0.12  

0.14  I  I  I  [  \  L_J  I  I  \  \  I  \  \  \  

0        0.2       a4.       0,6       0.8        l.O        1.2  1.4 
Fig.  64. — Moment  curves  for  uniform  load;  three  spans;  left-hand  half;  supported  ends. 

in  any  of  the  curves  shown  in  Figs.  46  and  54.  This  is  due  to  the  fact  that  for  these  sections 
maximum  and  minimum  moments  are  caused  by  only  partial  loading,  and  not  by  having  either 
one  or  both  spans  fully  loaded.  If  influence  lines  were  plotted  for  these  sections,  this  point 
would  be  clearly  brought  out. 

In  the  two-span  beam  shown  in  Fig.  66,  maximum  and  minimum  bending-moment  curves 


336 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-53 


are  given  for  a  3  : 1  ratio  of  live  to  dead  load.  To  obtain  these  curves  from  Fig.  63,  points  should 
be  determined  for  each  one-tenth  of  the  span.    The  following  notation  will  be  employed: 

tVd  =  dead  load  per  unit  of  length. 

wi  =  live  load  per  unit  of  length. 

Wt  =  Wd  +  wi  =  total  load  per  unit  of  length. 


I^Ki-  6r). — Moment  curves  for  uniform  load;  four  spans;  left-liand  half;  supported  ends. 

Consider  a  point  in  either  span  of  a  two-span  })eam  (Fig.  63)  at  a  distance  0.21  from  the  center 
support.    The  moment  will  vary  between 

-  Omwdl"^  +  omwii^ 

and 


0.12 


0.14  I  1  i  1  1  \  \  1  1  1  1  1  1  1  I  1  1  \  \  1  1 

O  02  0.4  06  0.8  t.O  1.2  U  (.6  1.8  ZO 

Fig.  66. — Moment  curves  for  continuous  beams  of  two  spans;  supported  ends.     Ratio  of  live  load  to  dead  load  3  :  1. 

Assuming  wi  =  Swa,  the  moment  varies  from  +  0.07wdP  to  -  0.17iVdP;  that  is  (since  Wd  = 
Huh)  from  +  0.0175ty«Fto  +  0m25wtl'. 

Curves  such  as  shown  in  Fig.  66  show  what  positive  and  negative  moments  should  be  pro- 
vided for  at  any  point  in  the  span.  They  also  indicate  in  what  manner  the  steel  may  safely 
be  bent  up  from  the  lower  side  of  the  beam.    The  curves  in  Fig.  66  show  that  a  negative  moment 


Sec.  7-53] 


BEAMS  AND  SLABS 


337 


is  likely  to  occur  over  one-half  of  each  span  of  a  two-span  beam.  Any  fixing  of  the  ends,  how- 
ever, will  reduce  this  length. 

Referring  to  Figs.  66,  67  and  68,  it  is  clear  that  negative  moment  may,  under  extreme 
conditions,  occur  entirely  across  the  beam.    For  ordinary  cases,  then,  it  would  seem  that  top 


0.12 

0.10 

%  0.08 

*5  0.06 
in 

^  0.04 
^  O02 

.E  0 

4- 

S  002 
O  004. 
<^  0.06 
ift  008 


0) 


3  0.10 
^  0.1  E 
0.14 


V — 

+ 

0.2 


0.4 


0.6 


0.8 


I.O 


Pig   f,7 — Moment  ourves  for  continuous  beams  of  three  spans;  left-hand  half;  supported  ends.    Ratio  of  live  load 
*  to  dead  load  3:1. 

reinforcement  should  extend  to  at  least  the  fourth  point.  In  special  cases,  however,  it  may 
be  desirable  to  provide  for  negative-tension  reinforcement  over  the  entire  span.  If  reinforcing 
frames  are  used,  the  top  rods  employed  for  handling  and  for  fastening  the  stirrups  into  a  unit 
will  aid  materially  in  taking  care  of  any  tensile  stresses  which  may  occur  in  the  top  of  the  beam. 


0      0.2     04     0,6     0.8      1.0     l.E      1-4-     16      "0  20 
Fig.  68. — Moment  curves  for  continuous  beams  of  four  spans;  left-hand  half;  supported  ends. 

to  dead  load  3:1. 


Ratio  of  live  load 


It  is  also  true  that  in  monolithic  floor  construction,  the  adjoining  slab  will  help  considerably  in 
preventing  top  tensile  stresses  at  the  center  of  the  span. 

In  view  of  the  above  considerations,  it  would  seem  that  rods  may  be  bent  up  with  sufficient 
accuracy  (for  ordinary  cases  where  uniform  live  load  is  somewhat  indefinite),  by  applying  the 
method  of  Art.  22.    For  special  cases,  curves  should  be  drawn  similar  to  those  shown  in  Figs. 
66  to  68  inclusive. 
22 


338 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-53 


Maximum  and  minimum  moment  curves  for  concentrated  loads  are  shown  in  Figs.  69  to 
73  inclusive.  Three-span  beams  only  are  considered  and  curves  are  given  for  both  supported 
and  fixed  ends.  From  a  study  of  these  curves  and  in  view  of  the  considerations  presented 
previously  in  this  article,  it  would  seem  (assuming  the  usual  indefinite  live  load)  that  rods  in 
girders  loaded  at  the  third  points  may  safely  be  bent  up  as  explained  in  the  floor-bay  design  of 
Art.  11,  Sect.  11.    The  curves  are  given  for  a  4  :1  ratio  of  live  to  dead  load.    The  moment 


Co. 

Eh- 

•si 

CD  1- 


0.16 
O.08 
0. 
O.08 
0.16 


/- 

/ 

H 

■ 

h 

\:: 

\ — 

7  - 

0' 

0 

2 

OA 

\  0. 

Q»  t.O 

15 

Fig.  69. — IVIoment  curves  for  continuous 
beams  of  three  spans;  supported  ends;  loads  at 
middle  points.  Ratio  of  live  load  to  dead  load 
4  :  1. 


Fig.  70. — Moment  curves  for  continuous 
beams  of  three  spans;  fixed  ends;  loads  at 
middle  points.  Ratio  of  live  load  to  dead 
load  4  :  1. 


due  to  dead  weight  of  girder  stem  has  little  effect  in  considerations  regarding  the  bending  up  of 
rods. 

The  formulas  given  below  may  be  of  use  when  considering  the  variation  of  moment  in 
beams  of  many  equal  spans  for  different  kinds  of  loading.  In  deriving  the  formulas  for  maxi- 
mum positive  moment,  alternate  spans  were  considered  as  covered  with  live  load.  This  gives 
the  worst  condition  of  loading  for  positive  moment.  Likewise  in  deriving  the  formulas  for 
maximum  negative  moment,  the  worst  condition  of  loading  for  negative  moment  was  assumed 

0.32 


0.24 
0. 16 


.e  0.08 

o  O.06 

%  016 

§  0.2^ 


i 

. 

+ 

M 

P 

i 

\ 

l- 

\ 

/ 

<u  a- 


0.2  0.4  0.6  0.8    I.O  I.2_U 


024 

0.16 
0.08 
0 
0.08 
0.16 
0.24 
0.32 


55 


^2 


02  0.4  0.6  08   1.0   1.2  1.4 


Fig.  71. — Moment  curves  for  continuous 
beams  of  three  spans;  supported  ends;  loads  at 
third  points.    Ratio  of  live  load  to  dead  load  4  :  1 


Fig.  72. — Moment  curves  for  continuous  beams  of 
three  spans;  fixed  ends;  loads  at  third  points.  Ratio 
of  live  load  to  dead  load  4:1. 


— that  is,  two  adjacent  spans  were  assumed  as  fully  loaded  alternating  with  one  span  unloaded. 
For  the  same  load  on  each  span,  the  formulas  reduce  to  simple  terms,  and  give  the  moments  on 
continuous  beams  with  fixed  ends  and  with  any  number  of  spans. 
The  following  notation  will  be  employed: 

maximum  positive  moment  at  center  of  span, 
minimum  positive  moment  (or  maximum  negative  moment)  at 
center  of  span. 

maximum  negative  moment  at  the  support. 


M  max. 
M,nin. 

M  max. 


Sec.  7-54] 


BEAMS  AND  SLABS 


339 


Uniform  loads: 


Loads  at  middle  points: 


Mr, 


M, 


Mr, 


Mr 


Mr 


Mr 


24 


{2wt  -  Wd) 


12 

-3g(4^. 


(3P, 

J_ 
16 
_| 
24 


(4P, 


Loads  at  third  points: 

Mmax. 
Mmin. 
M  max- 


(2P,  -  Pd) 


(Pt  -  2Pd) 


Pd) 


Triangular  distribution  of  load : 
51 


Mr 


Mr 


=      (2.2TF.  -  Wd) 


2.2Tr,) 

-  Wd) 


Pa) 

0.40 

0.E4 
£0.16 
^  0.08 
0 

4- 

£0.08 
E 

J  0.16 

in 
a> 

^^0.40 


-r 

vl  

r- 

-/ 

B 

/: 

f 

-  d-i 



r 

0  0.2  0.4  0.6  08  1.0   1.2  1.4 

Fig.  73. — Moment  curves  for  con- 
tinuous beams  of  three  spans;  supported 
ends;  loads  at  middle  and  quarter  points. 
Ratio  of  live  load  to  dead  load  4  :  1. 


64.  Continuous  Beams  with  Varying  Moment  of 
Inertia. — It  is  the  practice  of  some  designers  to  place 
more  steel  between  the  supports  of  continuous  beams 
than  the  amount  just  sufficient  to  resist  the  bending 
moment  specified  by  the  Joint  Committee.  They  consider  that  by  doing  this  the  stresses 
over  the  supports  are  reduced  and  the  design  is  more  economical.  They  maintain,  also,  that 
this  method  of  procedure  is  advisable  in  order  to  provide  for  imperfect  continuity  of  the 
beam  and  to  take  care  of  unknown  stresses  caused  by  unequal  settlements  of  the  supports. 
It  is  important,  therefore,  to  determine  the  actual  moments  which  occur  at  the  center  and 
supports  in  such  cases. 

A  study  of  this  kind,  assuming  uniform  loads,  has  been  made  by  R.  E.  Spaulding^  for  beams 
with  fixed  ends  and  for  beams  with  one  end  fixed  and  one  end  free.  The  curves  shown  in  Fig. 
74  are  the  result  of  his  investigations  and  apply  to  either  rectangular  or  T-beams.  Mr.  Spauld- 
ing  assumed  a  uniform  moment  of  inertia  for  that  portion  of  the  beam  over  the  support  in  which 
negative  moments  exist,  and  another  moment  of  inertia  for  the  central  portion  of  the  span — 
that  is,  between  points  of  inflection. 

The  condition  of  fixed  ends  is  obtained  for  full  loading  on  the  lower  floors  of  a  building  hav- 
ing very  heavy  columns.  The  case  of  one  end  fixed  and  one  end  free  is  found  in  either  span  of  a 
two-span  beam  with  the  same  uniform  load  on  both  spans. 

Referring  to  the  curves  of  Fig.  74  it  is  clear  that  with  both  ends  fixed  and  with  the  same 

moment  of  inertia  throughout,  the  moment  at  the  center  is  0.042ii'Z2  =  —  and  at  the  end  is 

1  Eng.  News,  Jan.  13,  1910. 


340 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-54 


12' 


as  is  well  known.    If,  as  is  sometimes  done,  a  small  amount  of  steel  is  placed 


It 


over  the  supports,  such  that  j  =  0.20,  and  the  full  bending  moment      is  provided  for  at 

55  %  of  -g- j  and  at 

the  support  will  be  O.OSGtt'Z^.  Such  a  condition  stresses  the  steel  at  the  support  to  a  value  2.2 
times  the  working  stress,  since  provision  is  made  at  the  support  for  a  moment  of  only  (0.20) 
mwP)  =  Howl^  =  0.025wP — that  is,  of  course,  assuming  the  amount  of  steel  used  to  be  pro- 
portional to  the  moments  of  inertia.  Again,  suppose  the  amount  of  steel  at  the  support  of  a 
beam  with  fixed  ends  to  be  made  one-half  that  at  the  center  and  that  the  center  be  designed 
for  XowP-  The  actual  moment  at  the  center  will  be  0.053  wP  and  the  end  bending  moment  will 
be  0.07SwP.    Thus,  with  this  distribution  of  the  reinforcement,  the  steel  at  the  support  will 

0073 

be  overstressed  to  an  amount  ^  ^^^  =  1.5  times  the  assumed  working  stress.    It  may  be  seen 

from  the  curves  of  Fig.  74  (for  beams  with  fixed  ends)  that  if  a  beam  is  figured  as  simply  sup- 
ported, then  about  0.6  of  the  amount  of  steel 
that  is  employed  in  the  middle  of  the  beam 
should  be  placed  over  supports  in  order  to 
make  as  economical  a  design  as  possible  under 
the  conditions.  For  example,  with  this  dis- 
tribution of  steel,  provision  is  made  at  the  sup- 
port for  a  moment  of 


O.ISO 


0.075u;Z2 


0.5  1.0 

Values  of  1^ 
I 

"Mf  denotes  Max.  Moment  at  Support 

M      "         »       "     iDef^veen  Supports 

If    moment  of  inertia  at  support 

J  =      "      "      "       y  center  of  spari 

Fig.  74. — Curves  of  maximum  bending  moments  in 
beams  with  different  moments  of  inertia  at  end  and 
centers. 


and  this  is  exactly  the  actual  moment  caused 
by  such  an  arrangement.  The  assumption 
which  is  made  that  the  moments  of  inertia  are 
proportional  to  the  amount  of  steel  used  makes 
practically  no  difference  in  these  comparative 
results. 

In  the  above  discussion  no  compressive 
steel  has  been  considered  at  the  supports.  In 
rectangular  beams,  of  course,  there  is  none 
needed  but  in  T-beams  the  section  becomes 
rectangular  at  the  supports  and  the  stress  in 
the  concrete  needs  attention.  Referring  to  Table  2,  page  355,  for  n  =  15,  it  may  be  seen  that  for 
an  allowable  compressive  stress  in  the  concrete  at  the  support  of  750  lb.  per  sq.  in.  and  16,000 
lb.  in  the  steel,  the  required  percentage  of  tensile  steel  is  practically  1%.  It  is  thus  possible 
to  get  along  without  any  additional  strengthening  of  the  compressive  part  of  the  beam  at 
the  support  only  when  the  beam  is  reinforced  at  the  center  of  span  with  less  than  1%  -r- 
0.6  =  1.7%  of  the  area  of  the  stem  (including  the  portion  of  the  slab  directly  above  it), 

voP 

whether  or  not  1.7%  is  less  than  the  amount  determined  for  the  full  bending  moment  of 

The  question  naturally  arises  whether  it  is  more  economical  to  design  for  the  full  bending 

voP 

moment  of  -g-  and  provide  steel  over  supports  equal  in  amount  to  0.6  of  the  steel  at  the  middle 

wP 

of  beam,  or,  as  recommended  by  the  Joint  Committee,  to  design  for  -  ^  both  at  the  center  of 

span  and  over  supports.  Consider  a  given  case  where  a  continuous  beam  designed  as  simply 
supported  requires  3  sq.  in.  of  steel  at  the  center  of  span.  Of  this  amount  (0.6)  (3)  =  1.8  sq. 
in.  should  be  bent  up  and  carried  over  the  top  of  the  support  (disregarding  amount  of  steel 
required  for  bond),  the  rest  of  the  rods  being  horizontal  in  the  bottom  of  the  beam.  The 


Sec.  7-55] 


BEAMS  AND  SLABS 


341 


approximate  volume  of  this  steel  may  be  taken  as  the  area  of  the  steel  in  the  middle  times  the 
span  in  inches,  or  3  sq.  in,  X  I  =  SI  cu.  in.  The  same  beam  designed  according  to  the  Joint 
Committee's  recommendations  would  require  2  sq.  in.  of  steel  at  the  center  of  span  and  2  sq.  in. 
over  the  top  at  the  support,  and  the  volume  of  steel  may  be  taken  as  the  volume  of  the  long 
rods,  the  area  of  which  amounts  to  2  sq.  in.,  plus  the  volume  of  steel  carried  over  from  the 
adjoining  spans  and  extending  to  say  the  one-fourth  point  of  the  span,  or  approximately  (2  sq. 
in.)(Z)  +  (2)(3^/)  =  cu.  in.  The  reader  should  notice  in  the  above  comparison  that  the 
first  design  is  favored  to  the  extent  that  no  top  steel  is  assumed  to  extend  beyond  the  center 
of  the  support.  Assume  this  steel. to  extend  to  only  the  one-fifth  point  of  the  span,  then  the 
volume  of  steel  in  the  first  case  becomes  equal  to  31  +  (1.8)  (3-^0  =  3.4Zcu.  in.  Thus  it  is  clearly 

seen  that  a  beam  designed  for  a  moment  -g-  in  the  center  of  span  requires  approximately  25% 

more  steel  than  the  beam  designed  with        for  both  positive  and  negative  moments. 

Mr.  Spaulding  in  his  study  of  continuous  beams  (referred  to  above)  assumed  that  the 
moment  of  inertia  is  constant  between  the  points  of  inflection,  and  there  changes  abruptly  to 
another  value  which  is  constant  for  the  ends  of  the  beam.  This  assumption  neglects  in  all 
cases  the  value  of  concrete  below  the  neutral  axis  because  it  is  in  tension  and  is  liable  to  crack. 
This  is  true,  however,  only  for  sections  subjected  to  the  maximum  bending  moments.  In  fact, 
the  variation  of  the  moment  of  inertia  throughout  the  beam  may  be  represented  by  a  curve 
with  maximums  at  the  points  of  inflection  and  minimums  at  the  middle  of  the  beam  and  at 
the  supports.  Sanford  E.  Thompson  in  an  article  published  in  the  issue  of  Engineering  News 
of  Jan.  13,  1910,  under  the  title  "Continuity  in  Reinforced-concrete  Beams,"  states  that  exten- 
sive studies  made  in  his  office,  considering  the  moment  of  inertia  to  vary  in  this  way,  gave  results 
which  substantially  agree  with  those  obtained  by  Mr.  Spaulding  and  prove  the  latter's  assertion 
that  the  assumption  of  constant  moment  of  inertia  between  points  of  inflection  is  sufficiently 
accurate  for  all  practical  purposes. 

On  page  340  it  is  shown  that  a  beam  reinforced  for  the  full  bending  moment  of  -g-  at 

the  center  of  span  will  induce  a  bending  moment  (if  properly  designed)  of  approximately 

O.OTSifZ^  over  supports.    This  is  only  about  10%  less  than  the  moment  of  recommended 

by  the  Joint  Committee. 


DESIGNING  TABLES  AND  DIAGRAMS  FOR  BEAMS  AND  SLABS 

55.  Illustrative  Problems. — The  use  of  designing  tables  and  diagrams  can  best  be  explained 
by  giving  the  solutions  of  typical  designing  problems.  The  following  working  stresses  will 
be  assumed  throughout: 

fc  =  650.    fs  =  16,000.    n  =  15.    v  =  40  without  web  reinforcement 
and  120  when  thorough  web  reinforcement  is  provided. 

Bond  stress  will  not  be  considered  here. 

.  Design  a  rectangular  beam  to  span  4:0  ft.  and  to  support  a  load  of  600  lb.  per  ft.  {including 
weight  of  beam) .    Beam  is  assumed  to  be  simply  supported. 
Solution  using  Tables. 

From  Table  2,  for  n  =  15,  /.  =  16,000  and      =  650 
K  =  107.4 

^       ^  (600X40^2)  ^      4  ,0 
8  8  '  ' 


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[Sec.  7-55 


Assume  d  =  1.56.  Then  Table  4  shows  that  6  =  18  in.  and  d  =  27^  in.  will  be  satisfactory. 
Area  of  cross-section,  bd  =  (18)  (27.5)  =  495  sq.  in. 

As  =  (495)  (0.0077)  =  3.81  sq.  in. 

We  shall  select  four  l^^-in.  round  rods  =  3.98  sq.  in.  (see  Table  1  or  Table  5). 

V  12,000 

'^bfd^  (18) (^) (2-7:5)  =  2^  P^^.^^- 

Web  reinforcement  is  not  theoretically  needed. 
The  beam  may  be  reviewed  as  follows: 

P  =  T->^^  =  0.0080 
bd  495 

From  Table  3,  for  this  value  of  p, 

k  =  0.384   j  =  0.872 

Then, 

1,440,000   irmniK 

=  (3:98)(a^)T2^  ^  '^''^^ 
.       (2)  (15,100)  (0.0080) 

fc  =   Qgg^   =  630  lb.  per  sq.  in. 

Solution  Using  Diagrams. — In  Diagram  2,^  the  intersection  of  the  curves  fc  =  650  and 
fs  =  16,000  is  first  found.    Tracing  down,  p  is  found  to  be  0.0077,  and  tracing  horizontally 

is  found  to  be  107.3.    The  solution  then  follows  as  in  the  use  of  tables  given  above. 

Diagrams  1  and  2  may  also  be  employed  to  determine  the  safe  resisting  moment  of  a  given 
beam  and  the  greatest  unit  stresses  in  the  steel  and  concrete  due  to  a  given  bending  moment. 

To  determine  the  safe  resisting  moment  of  a  given  beam,  the  value  of  p  should  be  computed. 
After  finding  this  value  on  the  lower  margin,  trace  vertically,  stopping  at  the  first  of  the  two 
curves /c  =  650  and/s  =  16,000  (assuming  these  the  allowable  stresses).  Now  trace  horizon- 
tally to  either  side  margin  and  the  value  of  K  is  found.  Then,  M  =  Kbd"^.  Consider  a  beam 
of  the  above  dimensions  to  have  1  %  of  steel.  Tracing  vertically  from  this  value  on  the  lower 
margin  of  Diagram  2,  the  650  curve  is  the  first  curve  to  be  reached  and  at  a  value  of  K  =  117.0. 
ThenM  =  (117)(18)(27.5)2  =  1,593,000  in.-lb. 

To  determine  the  greatest  unit  stresses  in  the  steel  and  concrete  of  a  given  beam  due  to  a 
given  bending  moment,  the  value  of  p  should  be  computed  as  before.    Also,  K  should  be  com- 

M 

puted  from  the  formula  K  =  With  these  values  of  p  and  X,  find  the  intersection  of  the 

vertical  and  horizontal  lines  through  these  values  respectively,  and  from  the  adjacent  steel  and 
concrete  curves  the  values  of /c  and/  may  be  estimated.  Consider  a  beam  of  the  above  dimen- 
sions and  with  0.7%  of  steel,  to  be  subjected  to  a  bending  moment  of  1,200,000  in.-lb.  or 

K  =  ^Qy2  ~  88.2.    The  intersection  of  the  vertical  and  horizontal  lines  through  these 

values  respectively  in  Diagram  2  gives  fc  =  550  and  fs  =  14,400.  This  procedure  is  followed 
in  reviewing  beam  design. 

Diagrams  1  and  2  may  also  be  employed  to  find  minimum  allowable  depth  of  beam  for 
a  given  percentage  of  steel  and  various  assumed  widths,  also  to  find  the  amount  of  steel  for 
a  beam  with  given  loading. 

To  find  the  depth  of  beam  for  a  given  percentage  of  steel  and  given  allowable  stresses, 
select  the  lower  value  of  K  determined  by  the  intersection  of  the  allowable  stress  curves  with 


1  Diagram  first  given  by  Arthur  W.  French,  Trans.  Am.  Soc.  C.  E.,  vol.  56,  1906,  p.  362. 


Sec.  7-55] 


BEAMS  AND  SLABS 


343 


the  vertical  line  representing  the  given  steel  percentage.    This  value  of  K  substituted  in  formula 

M  =  Kbd^,  ord  = 

\  oK. 

gives  the  smallest  permissible  depth  for  various  assumed  widths. 

To  find  the  percentage  of  steel  for  a  given  beam,  compute  the  value  of  K  from  formula 
M 

K  =  Locate  this  value  at  the  left  of  the  diagram.    Trace  horizontally  to  the  right  until 

the  proper  allowable  stress  curve  is  reached.  Thus,  ii  K  =  80,  the  curve  of  fc  =  650  intersects 
the  horizontal  through  the  given  value  of  K  at  a  value  for  p  of  0.003,  but  fs  for  this  percentage 
is  seen  to  be  over  22,000.  The  desired  percentage  is  0.0056,  determined  by  the  intersection  of 
the  curve  fs  =  16,000  with  the  horizontal  in  question. 

2.  A  beam  of  16-m.  width,  having  its  compression  face  inclined  at  an  angle  of  30  deg.  and 
its  tension  face  at  an  angle  of  20  deg.,  is  to  be  designed  for  a  moment  of  3,000,000  in.-lb.  What 
depth  and  percentage  of  reinforcement  are  necessary? 

Diagram  2  gives  K  =  107.3  and  p  =  0.0077  (see  preceding  problem). 

COS^  jSc 

These  values  should  be  multiplied  by  cos^jSc  and  respectively.    The  products  may 

cos  P( 

be  obtained  directly  from  Diagram  3. 

Entering  the  diagram  with  a  value  of  10.73  (resetting  the  decimal  in  X  =  107.3)  on  the 
lower  margin,  trace  vertically  to  inclined  line  for  =  30  deg.  and  then  horizontally  to  the  left- 
hand  margin  where  a  value  of  10.73  cos^  (30  deg.)  =  8.05  is  found.  Pointing  off  properly,  the 
proper  value  of  K  to  use  is  80.5.  Then 


3,000,000  ,  . 


To  find  0.0077  enter  the  diagrams  with  a  value  of  7.7  on  the  lower  margin,  trace 

vertically  to  inclined  line  for  I3c  =  30  deg.,  then  horizontally  to  inclined  line  for  /3f  =  20  deg., 
and  then  vertically  upward  to  the  upper  margin  where  a  value  of  6.1  is  found.  The  proper 
value  of  p  to  use  is  0.0061. 

Diagram  3  may  be  employed  when  either  /3c  =  0  or  )3(  =  0.  The  procedure  would  be 
the  same  as  above. 

3.  A  beam  with  ?>  =  16  in.,  d  =  45  in.,  and  p  =  0.007  is  subjected  to  a  moment  of  2,500,000 
in.-lb.  Assuming  the  compression  face  inclined  at  an  angle  of  20  deg.  and  the  tension  face  at  25  deg., 
what  are  the  unit  stresses  fc  and  fsf 

^  2,500,000  ^ 
.  (16)  (45)2  ''-^ 

Before  using  Diagram  2,  the  values  of  K  and  p  should  be  multiplied  by  — and  ^^^^ 

cos   Pc  cos  Pc 

respectively.    These  products  may  be  obtained  directly  from  Diagram  3. 

Entering  the  diagram  with  a  value  of  7.72  on  the  left-hand  margin,  trace  horizontally  to 
inclined  line  for  jSc  =  20  deg.  and  then  vertically  downward  to  the  lower  margin  where  a  value 
7  72 

of  (.os2(20  deg  )  ^  ^'"^^  found.  Pointing  off  properly,  the  proper  value  of  K  to  use  in  Diagram 
2  is  87.5. 

To  find  7.00  ,  enter  the  diagram  with  a  value  of  7.00  on  the  upper  margin,  trace 

cos  Pc 

vertically  downward  to  inclined  line  for  j8j  =  25  deg.,  then  horizontally  to  inclined  line  for 
/3c  =  20  deg.,  and  then  vertically  downward  to  the  lower  margin  where  a  value  of  7.25  is  found. 
.  The  proper  value  of  p  to  use  in  Diagram  2  is  0.0072. 

Using  K  =  87.5  and  p  =  0.0072  in  Diagram  2  gives /c  =  540  and/..  =  13,700. 

Diagram  3  may  be  employed  when  either  /3c  =  0  or  /3j  =  0.  The  procedure  would  be  the 
same  as  above. 


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[Sec.  7-55 


4.  Determine  the  approximate  weight  of  a  rectangular  beam  24  in.  wide,  with  a  clear  span  of 
25  ft.  and  carrying  a  load  of  5000  lb.  per  ft. 

The  load  per  foot  length  per  inch  width  will  be  : 

wl^ 

From  Diagram  4^  we  obtain  c  =  0.885.    If  we  take  M  =  —  ,  then  the  weight  of  the  beam  per 

o 

foot  length  will  be: 

iv'  =  [0.885  +  (25) (0.003)]^^^^^-^-?  =  1200  1b:  per  ft. 

5.  What  safe  load  per  square  foot  {including  dead  weight)  can  be  supported  by  a  slab  6  in. 
deep  {d  =  4^^  in.)  and  lO-ft.  span  reinforced  with  ^i-'m.  round  rods  placed  8  in.  apart?  The 
slab  is  simply  supported  and  reinforced  in  only  one  direction. 

0.1963 
=  (8X4.75)  ^^-^^^^ 

Referring  to  Diagram  6,  Part  2,  and  tracing  vertically  from  this  value  of  p  on  the  lower 
margin  to  an  intersection  with  the  curve  of  d  =  4:-^-i  in.,  and  then  tracing  horizontally  to  the 
left-hand  margin,  a  l)ending  moment  of  20,100  in. -lb.  is  found. 

Select  this  value  of  the  bending  moment  on  the  left-hand  margin  of  Diagram  5  and  trace 
horizontally  to  the  right  to  an  intersection  with  a  vertical  line  through  10,  denoting  span 

wl^ 

length.  The  safe  load,  based  on  M  =  can  now  be  estimated  directly  by  means  of  the 
curved  lines  and  is  found  to  be  168  lb.  per  sq.  ft. 

♦ 

(168)  (0.80)  =  1343^  lb.  per  sq.  ft.,  safe  load  for  slab  simply  supported. 

6.  Design  a  slab  to  span  6  ft.  and  to  carry  a  live  load  of  250  lb.  per  sq.  ft.  Slab  is  to  be  fully 
continuous  and  reinforced  in  only  one  direction. 

Assume  the  weight  of  slab  at  50  lb.  per  sq.  ft.    Total  load  for  slab  is  thus  300  lb.  per  sq.  ft. 
From  Diagram  5  for  this  span  length  and  load  per  square  foot,  a  bending  moment  of  11,000 
wl^ 

in. -lb.  is  found,  based  on  y^'    Diagram  6,  Part  1,  shows  that  a  depth  (d)  of  3  in.  will  be  ample 

— total  depth  3^^  in.    Also,  As  =  0.275  sq.  in. 

From  Table  6,  we  may  use  ^-^-in.  round  rods  spaced  4%  in.  on  centers. 

The  assumed  and  actual  dead  weights  are  close  enough,  and  the  slab  need  not  be  redesigned. 
The  slab  should  be  reinforced  against  negative  moment  at  the  supports.  The  slab  should  also 
be  reinforced  transversely  in  order  to  prevent  shrinkage  and  temperature  cracks.  Shear  at 
ends  of  slab  in  direction  of  reinforcement  is  (300)  (3)  =  900  lb.  per  ft.  of  breadth.  Allowable 
shear  =  (12)(3)(40)  =  1440.  Thus  no  web  reinforcement  is  needed,  as  is  usually  the  case 
except  for  excessive  loading. 

7.  Design  a  slab  for  a  10  by  lO-ft.  panel  to  carry  a  live  load  of  250  lb.  per  sq.  ft.  Slab  is  to 
be  fully  continuous  and  reinforced  in  both  directions. 

The  dead  load  will  be  assumed  at  60  lb.  per  sq.  ft.  Total  moment  to  be  resisted  in  each 
direction  according  to  recommendations  of  the  Joint  Committee  (Art.  29c,  page  307)  is 

wl"^  ...  ^ 

(Diagram  5  may  be  used,  assuming  M  =  j^"?        dividing  result  by  2.) 

Using  Diagram  6,  Part  1,  the  slab  is  seen  to  be  of  very  nearly  equal  strength  in  tension 
and  compression  when  d  =  S}'2  in.  and  As  =  0.32  sq.  in.    The  required  spacing  for  center  half 

1  DiaRram  and  formulas  taken  from  article  by  M.  J.  Lorente  in  Eng.  News,  March  20,  1913. 


Sec.  7-55] 


BEAMS  AND  SLABS 


345 


of  slab,  then,  is  4  in.  on  centers  for  ^^-in.  round  bars.  The  bars  should  be  spaced  the  same 
throughout  the  center  half  of  slab  and  then  the  spacing  gradually  increased  to  the  edge  of  the 
slab,  using  one-half  as  many  bars  in  the  outside  quarters.  The  slab  should  be  reinforced  against 
negative  moment  at  the  supports. 

The  depth  of  the  slab  should  be  made  5  in.  in  order  to  have  the  upper  reinforcing  system 
at  the  minimum  distance  33-^  in.  from  the  surface  of  the  slab.  The  lower  system  will  then  be 
slightly  stronger  than  necessary.  The  dead  weight  is  approximately  that  assumed.  For 
safety  in  construction,  it  is  preferable  to  require  the  two  systems  of  reinforcement  to  be  fastened 
together  at  frequent  intervals.    Web  reinforcement  is  not  necessary. 

8.  Design  the  center  cross-section  of  a  T-beam  in  a  floor  system;  the  beam  is  to  have  a  snan 
of  12  ft.  and  be  fully  continuous.  Maximum  shear  {live  plus  dead)  is  closely  equal  to  12,200  lb. 
Maximum  moment  {live  plus  dead)  =  356,300  in.-lb.    Supported  slab  is  Q-in.  thick. 

The  only  purpose  of  the  concrete  below  the  neutral  axis  is  to  bind  together  the  tension  and 
compression  flanges,  and  consequently  its  section  is  determined  by  the  shearing  stresses  in- 
volved and  space  for  the  necessary  bars.  The  shearing  stress  v  should  not  be  greater  than  120. 
The  area  b'd  (unless  the  value  of  j  should  turn  out  to  be  less  than  '^-^^ 

12,200  . 

=  116  sq.  m. 


(%)(120) 

The  following  formula  of  Art.  37,  gives  the  most  economical  depths  for  various  assumed 
web  widths: 

fsb'  2 
Assuming  r  as  60,  then 

for  b'  =    9  in.      d  =  15.2 

for  //  =  10  in.      d  =  14.6,  etc. 

Some  rough  calculations  show  that  if  four  bars  are  to  be  used  and  all  in  one  row,  the  breadth 
of  stem  necessary  for  the  bars  controls.  A  breadth  b'  of  10  in.  and  a  depth  d  of  15  in. (total 
depth  17  in.)  will  be  tried. 

Diagrams  7  and  8  cannot  be  employed  to  solve  for  the  resisting  moment  of  a  given  beam 
but  are  useful  in  designing.    Formula  (11),  Art.  34,  may  be  put  in  the  following  form 


M 

bd^ 


(  ^      2kd}  d 


k  and  j  in  this  equation  are  functions  of  fc  and  fs,  and  hence  the  variables  are  /c,  and  the  ratio 
^-    The  curves  at  the  left  in  Diagrams  7  and  8  are  plotted  from  this  equation  with  a  fixed  value 

M  t 

of /s  =  16,000  lb.  per  sq.  in.    Values  of  fc  may  be  determined  for  various  values  of  ^  and  -^j  or 

M  t 
values  of       may  be  determined  for  various  values  of  fc  and        It  must  not  be  overlooked, 

however,  that  these  diagrams  will  apply  only  when  the  amount  of  steel  is  such  that/s  =  16,000 
lb.  per  sq.  in.    This  amount  of  steel  may  be  easily  determined  when  the  corresponding  j  is 

M  t 

found  from  the  curves  at  the  right  of  the  diagram.    Suppose  ^^^2  j  ^ 

intersection  of  horizontal  and  vertical  lines  through  these  values  respectively  in  Diagram  8 
shows /c  to  equal  600,  and  then  tracing  from  this  intersection  horizontally  to  the  right  until  the 
vertical  line  is  reached  indicating  fc  =  600  (at  the  right-hand  side  of  the  diagram),  we  find  j 

equal  to  0.91.    Finally,  As  =  j^,  in  which  j  =  0.91,  /.  =  16,000,  and  M  and  d  are  known. 

Diagram  8  will  now  be  employed  in  working  out  the  problem  stated  at  the  beginning  of  this 
discussion. 


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[Sec.  7-55 


The  breadth  of  the  flange  is  controlled  by  one-fourth  the  span,^  or  36  in.  Assuming  a 
depth  (d)  of  15  in.  . 

M  356,300 


bd^     (36)  (15)2 


=  44 


For  this  value  of  ^  and  for  ^  =         =  0.40,  we  find  from  the  diagram  that  this  beam  falls 

under  Case  I;  that  is,  the  neutral  axis  is  in  the  flange. 

Diagrams  1  and  2  may  be  used  for  T-beams  under  Case  I.  In  the  problem  at  hand,  a 
horizontal  line  through  the  value  44  for  K,  in  Diagram  2,  intersects  the  oblique  line  fs  =  16,000 
at  a  value  of  fc  =  370.  The  value  of  p  corresponding  is  0.003.  Then  As  =  pbd  =  (0.003)  (36) 
(15)  =  1.62  sq.  in.    Table  5  shows  that  four  M-in.  round  bars  will  give  the  required  steel  area. 

9.  The  flange  of  a  T-beam  is  24  in.  wide  and  4  in.  thick.  The  beam  is  to  sustain  a  bending 
moment  of  480,000  in.-lb.    What  depth  of  beam,  and  amount  of  steel  are  necessary? 

We  will  try  d  ^  IS  in. 

M  480,000 


bd^     (24)(18)2  ^^-^ 


I 


M  t  4 

For  this  value  of  ^  and  for  ^  =  =  0.222,  we  find  from  Diagram  8,  fc  =  485  lb.  per  sq.  in. 
and  j  =  0.910.  Then 

A   -  480,000  _ 

~  (16,000) (0.910) (18)  ~  ^-^^  sq- 

The  stress  in  the  concrete  of  485  is  permissible  and  the  beam  as  designed  will  be  considered 
satisfactory.  (Formula  (12)  in  Art.  34a  may  be  used  to  find  minimum  depth  for  a  given  flange 
width  without  trial.) 

Suppose  2.0  sq.  in.  of  steel  were  inserted  in  a  beam  of  the  above  dimensions,  and  suppose 
that  the  safe  resisting  moment  is  desired.    Diagram  10  must  be  used  for  this  case. 

^  =  0.222  as  before.    Tracing  vertically  from  this  value  on  the  lower  margin  of  the  left  diagram 

to  a  value  of  p  =  0.0046  and  then  tracing  horizontally  to  the  left  margin,  we  find  a  value  of  k 
=  0.32.    In  a  similar  manner  we  find  j  equal  to  0.91 

Ms  =f.Asjd  =  (16,000) (2.0) (0.91) (18)  =  525,000  in.-lb. 

_  fsk  _  (16,000)  (0.32)  _ 
~  nil  -  k)  -  (15)(1  -0.32)  - 

or,  from  Table  8,  ■ 

fc  =  (0.0314)  (16,000)  =  502  lb. 

Since  fc  is  less  than  650,  the  resisting  moment  depends  upon  the  steel,  or  Ms  =  525,000  in.-lb. 

10.  A  continuous  T-beam,  uniformly  loaded,  has  a  bending  moment  at  the  center  of  each  span 
of  356,300  in.-lb.    Negative  bendi7ig  moment  at  the  supports  and  the  positive  bending  moment  at 

wl^ 

the  ceriter  of  span  are  figured  by  the  formula,  M  =  -^^^  tensile  steel  at  the  center  of  span 

consists  of  four  %^-in.  round  bars,    h'  =  10  in.    d  =  15  in.    Design  the  supports. 

At  the  supports  the  flange  of  the  T-beam,  being  in  tension,  is  negligible  and  the  T-beam 
changes  into  a  rectangular  beam  with  steel  in  top  and  bottom.  Two  of  the  tension  bars  on 
each  side  of  the  supports  will  be  bent  up  and  made  to  lap  over  the  top  of  the  supports,  while  the 
other  two  bars  on  each  side  will  be  continued  straight  and  lapped  over  supports  at  the  bottom 
of  beam. 

The  ratios  of  steel  in  tension  and  compression  are  the  same,  and  are  respectively: 

1  See  recommendations  of  the  Joint  Committee,  Art.  32. 


Sec.  7-551  BEAMS  AND  SLABS  347 


(1.77  in  above  equation  taken  from  Table  5.) 

=  A 
d  15 

From  Diagram  12,  knowing      =  p,  we  obtain 


0.133 


Thus, 


^     d'  _             \k  ^  0.361 

For  ^  =0.10....  j.  ^^ggg 

^     d'  _  ^  ^         I     =  0.377 

For      =  0.15  \   .  „ 

I  J  =  0.866 

^     d'  „             f  /c  =  0.372 

For  =  0.133...]  .^^_g^3 


(It  is  usually  well  within  the  precision  of  the  actual  work,  and  on  the  safe  side,  to  use  the  curves 
for  the  value  of  ^  next  larger  than  the  actual  value.    Thus  in  this  problem  the  values  of  k  and 

j  for  ^  =0.15  could  be  used  with  sufficient  accuracy.) 
Then 

,        M  356,300  i^.nmK 

^'  =  Ajd='  (1.77)  (0.873)  (15)  =  ^^'^^^ 

and,  using  Table  9, 

Jc  =        ^  =  (0.0394)  (15,400)  =  607  lb.  per  sq.  in. 

The  stresses  in  the  concrete  and  steel  are  within  the  allowable  and  no  haunch  or  additional 
steel  are  necessary. 

The  moment  of  resistance  at  the  supports  may  be  found  as  follows: 

.      fMl  -  k)  650 

=   ^          =  0;039^  =  16,500  lb.  per  sq.  m. 

Thus  the  moment  of  resistance  depends  on  the  steel  and 

Ms  =  bd^fspj  =  (10)  (15)2  (16,000)  (0.0118)  (0.873)  =  371,000  in. -lb. 

11.  At  the  support  of  a  continuous  T-beam  the  following  values  are  known:  b  =  12  in., 
p  =  p',  As  =  3.0  s^.  in.,  M  =  750,000  in. -lb.,  fc  =  750  and  fs  =  16,000.  Find  the  required  depth 
of  beam. 

Assume  i-  =  0.10 

d 

From  formula  on  Diagram  12, 

/.  =- 

Assume  j  =  0.87.    Then  d  =  17.95 

Adopting  d  =  18  in.  p  =  ^^^HIS)  ^  ^'^^^^ 

Diagram  12  for  ^  =0.10  and  p  =      =  0.0139  shows  j  =  0.886 
Assume  j  =  0.886.     Then  d  =  17.6  in. 
Adopting  d=  17M  in.    p  =  jYfyifJK)  =  ^"^^^^ 


.  _    M  M  75,000  _ 

-  Asjd  Asfs  ~  (3)  (16,000)  -  ^^-^ 


348 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-56 


Diagram  12  shows  j  ~  0.886 

d' 

Thus  d  =  17§^  in  is  satisfactory  provided  ^  is  approximately  0.10, 

12.  In  a  double-reinforced  rectangular  beam  b  =  12  m.,  d!  =  18  in.,      =  0.10,  M  =  750,000, 

fc  —  650  and  fs  =  16,000.    Determine  the  required  percentages  of  tensile  and  compressive  steel. 
Following  the  method  outlined  in  Art.  27a,  we  have,  using  Table  2, 

k  =  0.378,  Pi  =  0.0077,  and  K  =  107.4 
Ml  =  107.4  (12) (18)2  =  418,000  in.-lb. 
M2  =  750,000  -  418,000  =  332,000  in.-lb. 

332,000  nnnr^n 

=  16,000  (0.9)(12)(18)2  =  ^-^^'^ 
P  =  Pi  +  P's  =  0.0136 


7>' 


=  (0-0059)  (oW'^)  = 


56.  Leffler*s  Comprehensive  Beam  Chart. ^  Simple  Rectangular  Beams. — The  procedure 
to  design  a  beam  simply  reinforced  to  carry  a  certain  bending  moment  M  with  certain  allowable 
stresses  is  as  follows:    Divide  the  allowable  fs  by  the  allowable  fc  thus  obtaining  the  value  of 

fs         .  .  .  fs- 

T'    Find  this  value  on  the  chart  (Diagram  13)  on  the  curve  .  •    From  it  move  vertically  to  the 

Jc  Jc 

p'  =  0  curve.  This  point  on  the  p'  =  0  curve  lies  where  some  p  curve  intersects  the  p'  =  0 
curve.    The  value  of  this  p  curve  gives  the  p  to  use.    The  abscissa  of  this  point  on  the  p' 

M 

=  0  curve  gives  the  value  of  L.,  to  be  used  in  Ls  =  Equation  (I)  given  on  the  diagram 

can  then  be  solved  for  bd"^  which  completes  the  solution  for  moment.  To  b  and  d  such  values 
can  then  be  assigned  as  shear  requirements  may  demand.  If  shear  requirements  are  so  large 
as  to  govern  the  dimensions  of  the  beam,  the  design  for  moment  is  accomplished  by  solving  (I) 
for  Ls,  fs  being  used  at  its  allowable  value.  The  p  to  use  is  that  of  the  p  curve  which  intersects 
the      =  0  curve  at  the  point  whose  abscissa  is  Ls. 

Doubly  Reinforced  Rectangular  Beams. — Suppose  the  dimensions  b  and  of  a  beam  to 
carry  a  certain  M,  with  certain  allowable  stresses,  are  arbitrarily  fixed  by  such  limitations  as 
headroom,  clearance,  architectural  effects,  shear  requirements,  etc.,  the  procedure  would  then 
be  as  follows:  Solve  equations  (I)  and  (II)  for  Ls  and  Lc.  Using  Ls  as  an  abscissa  and  Lc  as 
an  ordinate,  plot  a  point  on  the  chart.  If  the  point  falls  below  or  on  the  p'  =  0  curve,  the  beam 
can  be  designed  as  a  simple  beam;  the  value  of  p  to  use  being  that  of  the  p  curve  which  intersects 
the  p'  =  0  curve  at  the  point  whose  abscissa  is  Ls.  If  the  point  falls  well  above  the  p^  =  0  curve, 
the  beam  must  be  a  doubly  reinforced  one.  The  values  of  p  and  p'  to  use  are  those  of  the  p 
and  p'  curves  on  which  the  point  falls.  If  the  point  falls  above  the  p'  =  0  curve  and  beyond  the 
scope  of  the  chart,  the  beam  is  probably  impossible  as  a  reinforced  concrete  beam  and  recourse 
must  be  had  to  structural  steel. 

If  the  point  falls  but  a  short  distance  above  the  p'  =  0  curve,  it  is  possible  to  design  the 
beam  as  a  simply  reinforced  one.  The  procedure  is  as  follows:  Proceed  horizontally  from  the 
point  until  the  p'  =  0  curve  is  intersected.  The  value  of  the  p  carve  that  meets  the  p'  =  0 
curve  at  this  point  of  intersection  gives  the  value  of  p  to  use  for  designing  the  beam  with  ten- 
sile reinforcement  only.  The  actual  fc  will  be  the  same  as  the  allowable  fc,  but  the  actual/., 
will  be  less  than  the  allowable  fs.  Carefully  made  cost  figures  are  the  only  means  of  determining 
whether  this  simply  reinforced  beam  will  be  cheaper  than  a  doubly  reinforced  one. 

To  find  M  when  p,  p',  b,  d,  the  allowable  fs,  and  the  allowable  fc  are  given,  proceed  as 
follows:    Read  off  the  abscissa  Ls  of  the  intersection  of  the  p  and  p'  curves,  then  evaluate  equa- 

1  By  Ralph  R.  Lepft>er,  Chicaeo,  111. 


Sec.  7-56] 


BEAMS  AND  SLABS 


349 


tion  (I)  for  M;  read  off  the  ordinate  Lc  of  the  intersection  of  the  ])  and  p'  curves  and  evakiate 
equation  (II)  for  M.    Use  the  smaller  value. 

T-beams. — A  T-beam  can  be  regarded  as  a  large  rectangular  beam  minus  two  rectangular 
beams,  or,  if  we  combine  the  two  small  beams,  as  a  large  rectangular  beam  minus  a  smaller 
rectangular  beam.  Referring  to  the  beam-section  on  the  chart,  ABCD  is  the  large  rectangular 
beam  and  the  empty  rectangular  spaces  under  the  flanges  of  the  T-beam  added  together  form 
the  smaller  rectangular  beam. 

Let  M,  the  allowable  and  the  allowable  fc  be  given.  First,  design  a  simple  rectangular 
beam  that  will  carry  the  given  M  with  the  given  allowable  /,  and  fc.  Having  found  hcP,  assign 
to  6  a  value  in  accordance  with  some  rules,  such  as  those  of  the  Joint  Committee,  and  then  solve 
for  d.  Ascertain  the  amount  of  tensile  steel  reinforcement  required  and  make  the  width  of  the 
stem  such  that  it  can  be  properly  arranged.  We  now  have  the  approximate  dimensions  of  the 
T-beam.  At  this  point  it  is  well  to  investigate  the  shear  in  different  sections  of  the  beam.  As- 
suming that  we  have  found  that  the  shear  is  sufficiently  well  taken  care  of,  we  can  proceed  to 
finish  the  design  for  moment. 

The  expression  for  the  value  for  k  can  ])e  written  as  a  function  of  "j  (assuming  n  =  15). 
This  means  that  for  every  value  of  y  there  will  be  found  on  the  same  vertical  line  a  point  on  the 

k  curve  (or  straight  line)  whose  ordinate  gives  the  value  of  k  corresponding  to  the  value  of 

Having  found  the  value  of  A;,  locate  the  neutral  axis  of  the  T-beam.  If  kd  is  less  than, 
equal  to,  or  ver}^  nearly  equal  to  /  (the  thickness  of  the  flange  usually  determined  by  the  floor 
slab  design)  the  neutral  axis  lies  in  the  flange,  at  the  bottom  of  the  flange  or  but  a  short  distance 
below  the  flange,  in  which  case  the  design  of  our  T-beam  for  moment  is  already  complete.  If 
kd  is  much  greater  than  t,  the  neutral  axis  lies  well  down  in  the  web.  To  secure  a  correct  theo- 
retical solution  it  then  is  necessary  to  ascertain  how  much  M  is  carried  by  the  two  imaginary 
beams  under  the  flanges.  At  this  point  a  little  thought  discloses  that  since  these  imaginary 
beams  cause  a  loss  of  resisting  ilf ,  it  is  necessary  to  deepen  d.  Having  depeened  d  according 
to  our  best  judgment,  the  next  thing  is  to  find  by  the  formula  M  =  LJ)d~fs  how  much  resisting 
M  the  deepened  beam  is  capable  of  sustaining  at  the  allowable  unit  stresses,  the  beam  being 
considered  as  a  simple  rectangular  beam,  of  width  b,  and  depth  d,  equal  to  the  deepened  d. 
The  p  to  use  is  that  of  the  p  curve  which  intersects  the  p'  =  0  curve  at  the  point  whose  abscissa 
is  Ls.  Again  the  neutral  axis  is  located  by  "the  same  process  as  before,  and  as  before,  if  the 
neutral  axis  is  in  the  flange,  in  the  lower  edge  of  the  flange  or  very  close  up  to  the  bottom  of  the 
flange  the  design  for  moment  is  complete.  If  the  neutral  axis  comes  well  down  in  the  web  it  is 
necessary  to  ascertain  how  much  resisting  moment  is  carried  by  the  imaginary  beams  under  the 

kd  —  t 

flanges.    From  the  stress  diagram,  A'l  =  —  '  .the  svmbols  for  the  imaginary  beam  being 

distinguished  by  the  subscript  1.  The  Lsi  corresponding  to  this  ki  is  the  abscissa  of  the  ki 
on  the  chart.  Solve  the  equation  Mi  =  Lsibidrfs  in  which  bi  is  the  combined  width  of  the  two 
imaginary  beams  and  di  their  depth.  This  Mi  is  the  resisting  moment  carried  by  the  two  im- 
aginary beams.  The  pi  to  use  is  that  of  the  p  curve  which  intersects  the  p'  =  0  curve  at  the 
point  whose  abscissa  is  L,i.  If  to  Mi  we  add  the  M  caused  by  the  loading  and  thus  obtain  a 
sum  equal  to  the  resisting  M  of  the  enlarged  beam,  our  solution  for  moment  is  complete.  If 
their  sum  is  considerably  different  from  it,  d  should  be  increased  or  decreased  until  they  are 
closely  equal,  the  same  procedure  being  gone  through  as  before.  The  amount  of  tensile  steel 
needed  for  the  T-beam  is  equal  to  pbd  —  pibidi.  If  ki  should  be  so  small  as  not  to  come  within 
the  scope  of  the  chart.  Mi  can  be  obtained  from  the  equation 

fcikibidi/^      kidA      fcikibjidi^  fckidi    ■    ,      ,  Mi 

Ml  =^—2-  (^^  -  -J-)  2^mwhichA..  Also  A.i  =  pMi 

in  which  is  the  same  a«  in  the  large  beam  ABCD  for  the  of  the  large  beam  is  the  same  as 
the  fs  of  the  smaller  imaginarj^  beam. 


350 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-57 


Note  that  this  solution  of  a  T-beam  does  not  neglect  the  stress  in  the  stem. 

Doubly  Reinforced  T-beams. — After  the  reader  has  thoroughly  grasped  the  foregoing  solu- 
tions of  the  "Doubly  Reinforced  Rectangular  Beams"  and  the  "Simply  Reinforced  T-beam" 
he  will  find  it  easy  to  devise  a  method,  parallel  to  that  given  for  simple  T-beams,  for  designing 
doubly  reinforced  T-beams;  it  being  only  needful  to  remember  that  the  resisting  M  of  the  larger 

fs 

beam  is  that  of  a  doubly  reinforced  beam  and  that    is  a  function  of  j  only,  and  as  such  is  pri- 

Jc 

marily  independent  of  the  amount  or  location  of  the  compressive  steel  reinforcement.  It  is 
j  that  is  primarily  dependent  on  the  amount  and  location  of  the  compressive  steel  reinforcement. 

57.  Beard  and  Schuler's  Comprehensive  Charts. ^    Rectangular  Beams  and  Floor  Slabs. — 
The  moment  caused  by  a  uniformly  distributed  load  at  any  point  on  any  beam  which  is  fixed, 
partially  restrained,  or  simply  supported  at  the  ends  may  be  expressed  in  inch-pounds  by  the 
w  .  . 

formula,  M  =  12  —     in  which  w  is  the  uniform  load  in  pounds  per  foot,  I  is  the  span  in  feet,  and 
<p 

(f>  is  the  moment  denominator.  ^  is  8  for  the  moment  at  the  center  of  a  simply  supported 
beam. 

The  formula  for  the  resisting  moment  of  a  simple  rectangular  reinforced-concrete  beam 
is  M  =  Kbd"^  in  which  K  —l^^  fckj  for  the  compression  couple  and  fspj  for  the  tension  couple. 
When  the  beam  is  supporting  a  uniformly  distributed  load  the  general  formula  may  be  expanded 
into  the  two  forms 

12'^  f  ^  fsivbd^ 
<p 

and 

i2'{f  =  yijc-kjbd-' 

In  the  upper  left-hand  quadrant  of  Diagram  14,  which  is  called  the  moment  chart,  the 
logarithmic  abscissas  and  ordinates  represent  the  spans  in  feet  and  moments  in  inch-pounds 

w  w 

respectively.    Each  sloping  line  on  the  diagram  represents  a  particular  value  of  -  •   With-  a 

•   <p  <p 

constant,  the  formula  takes  the  form  M  =  Cp  and,  when  expressed  in  logarithms,  the  form  log 
M  =  log  C  +  2  log  j.  The  moment  chart  is  a  graphical  representation  of  this  family  of  curves, 
which  are  parallel  straight  lines. 

The  upper  right-hand  quadrant,  or  the  depth  chart,  is  the  logarithmic  plat  of  the  equation 
M  =  Kbd^.  In  this  case  also  the  logarithmic  ordinates  represent  the  moments  but  the  loga- 
rithmic abscissas  represent  values  of  K.  Each  sloping  line  represents  a  particular  value  of  bd"^. 
b  is  taken  as  12  in.  in  all  cases  and  the  line  is  designated  by  the  corresponding  value  of  d. 

This  plat  then  represents  the  general  equation 

log  M  =  log  C  +  log  A' 

It  is  a  series  of  parallel  45-deg.  lines. 

The  lower  right-hand  quadrant  or  the  stress  chart  is  a  logarithmic  plat  of  the  two  families 
of  curves: 

K  =  f4>j  and  K  =  Mfckj 

In  the  stress  chart  the  logarithmic  abscissas  and  ordinates  represent  values  of  K  and  p 
respectively,  and  the  sloping  lines  represent  particular  values  of  fc  and  fs. 

As  =  pbd.  In  the  lower  left-hand  quadrant  or  the  steel  chart,  the  lines  sloping  upward 
to  the  right  represent  constant  values  of  d  and  the  abscissas  and  the  ordinates,  as  numbered 
at  the  right-hand  side  of  the  diagram,  represent  values  of  As  and  p  respectively. 

\2<x 

When  the  cross-sectional  area  of  a  round  rod  is  a  and  the  rod  spacing  is  s,  =  — ^  •  Each 
1  By  Robert  S.  Beard  and  Don  B.  Schuler. 


Sec.  7-57] 


BEAMS  AND  SLABS 


351 


line  sloping  upward  to  the  left  in  the  steel  chart  is  marked  with  the  diameter  of  the  rod  whose 
area  it  represents.  The  abs3issas  represent  the  steel  area  and  the  ordinates,  as  marked  at 
the  left  side  of  the  diagram,  represent  the  round-rod  spacing.  The  spacing  for  square  rods  is 
4 

-  times  the  spacing  of  round  rods  of  the  same  thickness.  The  k  and  j  curves  are  also  platted 
in  this  steel  chart. 

Illustrative  Problem. — Suppose  that  it  is  required  to  design  a  slab  to  carry  a  total  live 
and  dead  load  of  400  lb.  per  sq.  ft.  over  a  simple  span  of  20  ft.  with  limiting  stresses  of  fc  =  050 
and/s  =  16,000  1b. 

Before  entering  Diagram  14  the  load  per  square  foot,  400  lb.,  must  be  divided  by  the 
moment  denominator  which  is  8  in  this  case. 


400 
8 


50 


In  the  stress  chart,  the  intersection  of  the  values  fc  =  650  and  fs  =  16,000  gives  a  value 
oi  K  =  107.  Any  designer  who  uses  a  particular  set  of  stresses  constantly  remembers  the 
corresponding  value  of  K,  and  omits  this  operation. 

w 

Now  in  the  moment  chart  find  the  intersection  of  the  sloping  line  —  =  50  with  the  line 

representing  a  span  of  20  ft.,  as  indicated  in  Fig.  75.  The  ordinate  of  this  intersection  corre- 
sponds to  a  moment  of  240,000  in. -lb.  Follow  this  ordinate  into 
the  depth  chart  to  its  intersection  with  K  =  107.  At  this  intersec- 
tion d  =  13.6  in.  It  is  decided  to  use  a  depth  of  14  in.  which  cor- 
responds to  K  =  102  for  this  moment.  Follow  the  line  K  =  102 
into  the  stress  chart.  At  the  point  where  fc  =  650,  fs  =  17,600, 
at  the  point  where  fs  =  16,000,  fo  =  630.  This  second  set  are  there- 
fore the  limiting  working  stresses.  At  this  point  p  =  0.0073.  Follow 
this  abscissa  into  the  steel  chart  to  =  14  in.  At  this  intersection 
As  =  1.23  sq.  in.  Follow  this  As  line  to  the  1-in.  line.  The  required 
spacing  for  1-in.  round  rods  is  7.7  in.    Use  a  spacing  of  7}^  in.  If 

.     .  4 

it  is  required  to  use  1-in.  square  rods,  the  necessary  spacing  is  -  X 

7.7  =  9.8  in.    Use  9^:4-in.  spacing. 

If  it  is  desired  to  find  the  resisting  moment  when  every  other 
rod  is  turned  up,  this  process  is  reversed.    In  the  steel  chart  follow 

the  rod  spacing  of  15  in.  to  the  1-in.  line.  As  =  0.626  sq.  in.  Follow  this  As  line  lo  d  = 
14  in.,  p  =  0.00372.  Follow  this  p  line  to  fs  =  16,000,  fc  =  430,  K  =  54.  Follow  the  K  =  54 
line  to  d  =14  in',  in  the  depth  chart,  M  =  128,000  in. -lb. 

T-heams. — The  moment  caused  by  a  uniformly  distributed  load  at  any  point  on  any  beam 

may  be  expressed  in  inch -pounds  by  the  formula,  M  =  ^'  1-. 


Fig.  75. 


The  resisting  moment  of  the  steel  reinforcement  in 


T-beam  is  Rbt^  where  R  =  and 


A  = 


^-    Then  when  the  T-beam  is  supporting  a  uniformly  distributed  load 

M  =  12- f=  Rbt^ 

0 

In  order  to  make  Diagram  15  of  more  general  application  the  moment  is  divided  by  b,  the 
breadth  of  the  beam  in  inches.    The  moment  formula  then  takes  the  form 


M 

'b 


I2w 


352 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-57 


B  is  used  to  express  the  width  of  the  beam  in  feet,     then  expresses  the  uniformly  distributed 

load  in  terms  of  live  load  per  square  foot  of  flange. 

In  the  upper  left-hand  quadrant  of  Diagram  15  the  logarithmic  abscissas  and  ordinatei 
represent  the  spans  in  feet  and  moments  in  inch-pounds  divided  by  the  breadth  of  beam  i 

w         .  w 

inches  respectively.    Each  sloping  line  represents  a  particular  value  of  With  — ^  a 

M 

stant,  the  formula  takes  the  form =Cp.    The  moment  chart  is  a  logarithmic  graphica. 

representation  of  this  family  of  curves. 

The  upper  right-hand  quadrant  or  the  slab  chart  is  the  logarithmic  plat  of  the  equation 
M    ,        .  _  M 


Rt^.    The  abscissas  represent  values  of  R,  and  the  ordinates,  values  of 


The  sloping 


lines  correspond  to  particular  values  of  t. 

The  lower  right-hand  quadrant  or  steel  chart  is  a  logarithmic  plat  of  the  equation  R  =  fs-^^^' 

VJ 

In  this  steel  chart  the  abscissas  and  ordinates  represent  values  of  R  and  ^  or  y  respectively. 

The  sloping  lines  represent  particular  values  of /s. 

In  the  lower  left-hand  quadrant  or  proportional  chart,  the  lines  sloping  upward  to  the 


right  are  the  logarithmic  plat  of  the  family  of  curves  y  = 


V3 


The  abscissas  and  ordinates  of 


the  proportional  chart  represent  values  of  p  and  y  respectively,  and 
the  sloping  straight  lines  represent  particular  values  of  A. 

The  curved  lines  on  the  proportional  chart  have  been  platted 
from  this  formula  by  solving  for  the  values  of  p  corresponding  to 

fc 


particular  values  of 


fs 


e  and  A,  and  then  drawing  the  d  curves 


through  the  intersections  of  these  values  of  p  with  the  correspond- 
ing A  lines  in  the  proportional  chart.  The  curve  A  =  /c  is  the  line 
of  division  between  the  T-beam  and  the  simple  beam. 

Illustrative  Problem. — Design  a  simply  supported  T-beani 
with  the  following  factors  predetermined:  I  =  40ft.,  w  =  40001b. 
per  lin.  ft.,  fc  =  600,  /,  =  15,000,  t  =  8  in.,  and  b  =  QA  in. 

Before  entering  Diagram  15,  the  total  load  per  linear  foot  of 
4000  lb.  must  be  divided  by  both  the  moment  denominator,  8,  and 
the  breadth  of  the  beam  in  feet,  5}i 

IV         4000        ^„  „^     „  600 


Fig.  76. 


<f>B     8  X  SVs 


157000 


0.04 


Now  perform  the  operations  on  the  T-beam  chart  indicated  in  Fig.  76.    At  the  inter- 
im M 
section  of^  =  93.75  with  the  line  I  =  40  ft.,  the  ordinate  is       =  150,000  at  the  intersection 

of  this  ordinate  with  /  =  8  in.,  R  =  2350.  At  the  intersection  of  the  abscissas,  R  =  2350 
with  fs  =  15,000,  y  =  0.157.  Now  follow  the  ordinate  y  =  0.157  to  its  intersection  with  the 
line  d  =  0.04.    At  this  point  A  =  0.179  and  p  =  0.00548. 

'^  =  1  =0.179= 
A,  =  pbd  =  0.00548  X  64  X  44.7  =  15.67  sq.  in. 

The  T-beam  chart  is  worked  in  the  reverse  direction  when  it  is  desired  to  know  what 
resisting  moment  a  given  section  can  exert.  Buppose  that  the  bending  up  of  four  rods  has 
reduced  the  steel  ratio  to  0.00358. 


i 


Sec.  7-57] 


BEAMS  AND  SLABS 


353 


In  the  proportional  chart  follow  the  abscissa,  p  =  0.00358  to  its  intersection  with  the 
sloping  line  A  =  0.1791.    At  this  point  6  =  0.00285  and  y  =  0.103. 

If /c  =  600,  0=5^?  =  0.00285,  /.  -  21,100  lb. 

J  s 

lifs  =  15,000,  d  =  =  0.00285,  fc  =  428  lb. 

This  second  group  are  the  working  stresses.  Now  follow  the  ordinate  y  =  0.103  to  its  inter- 
section with  the  value  fc  =  15,000.    At  this  point  R  =  1540.   Trace  this  abscissa,  R  =  1540, 

M 

to  its  intersection  with  the  line  i  =  8  in.  At  this  point  =  98,000.  Then  M  =  98,000  X  64  = 
6,270,000  in.-lb. 

The  handling  of  problems  on  both  Diagrams  14  and  15  is  facilitated  by  the  use  of  two 
pointers.  The  last  value  found  is  held  by  one  pointer  while  the  other  is  used  to  pick  out 
the  value  determined  by  the  next  step  in  the  problem. 


23 


354 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-57 


Table  1. — Areas,  Perimeters,  and  Weights  of  Rods 


Round  rods 

,             Square  rods 

Area 

Perimeter 

Weight  per 

Area 

Perimeter 

Weight  per 

Siz6  (incliGs) 

(square  inches) 

(inches) 

foot  (pounds) 

(square  inches) 

(inches) 

foot  (pounds) 

/4 

n 
u 

r»/i  01 

u 

/  OO 

U 

1  7 

n 
u 

UDZO 

i 

uu 

0.21 

He 

U 

U 

U 

OR 
ZD 

u 

nQ77 

1 

ZO 

0.33 

% 

0 

1104 

1 

178 

0 

38 

0 

1406 

1 

50 

0.48 

0 

1503 

1 

374 

0 

51 

0 

1914 

1 

75 

0.65 

/2 

U 

1  OAQ 

lyoo 

i 

0/1 

U 

fl7 

U 

zouu 

Z 

uu 

0.  85 

U 

Z4oO 

i 

/  D/ 

u 

QK 
oO 

U 

o  lD-± 

Z 

ZO 

1.08 

H 

0 

3068 

1 

964 

1 

04 

0 

3906 

2 

50 

1.33 

0 

3712 

2 

160 

1 

26 

0 

4727 

2 

75 

1.61 

/4 

U 

i  i  1  Q 
441o 

o 
Z 

Q  KA 

1 
i 

KH 

ou 

U 

OOZO 

Q 

o 

UU 

1 .91 

U 

KICK 

o 

z 

OOO 

1 

7A 

0 

DOUZ 

6 

Zo 

2.25 

Vs 

0 

6013 

2 

749 

2 

04 

0 

7656 

3 

50 

2.60 

0 

6903 

2 

945 

2 

35 

0 

8789 

3 

75 

2.99 

0 

7854 

3 

142 

2 

67 

1 

0000 

4 

00 

^  40 

0 

9940 

3 

534 

3 

38 

1 

2656 

4 

50 

4.30 

iM 

1 

2272 

3 

927 

4 

17 

1 

5625 

5 

00 

5.31 

1 

4849 

4 

320 

5 

05 

1 

8906 

5 

50 

6.43 

1 

7671 

4 

712 

6 

01 

2 

2500 

6 

00 

7.65 

\% 

2 

0739 

5 

105 

7 

05 

2 

6406 

6 

50 

9.98 

1% 

2 

4053 

5 

498 

8 

18 

3 

0625 

.7 

00 

10.41 

m 

2 

7612 

5 

891 

9 

39 

3 

5156 

7 

50 

11.95 

2 

3 

1416 

6 

283 

10 

68 

4 

0000 

8 

00 

13.60 

3 

9761 

7 

069 

13 

52 

5 

0625 

9 

00 

17.22 

4 

9087 

7 

854 

16 

69 

6 

2500 

10 

00 

21.25 

2M 

5 

9396 

8 

639 

20 

20 

7 

5625 

11 

00 

25.72 

3 

,  7 

0686 

9 

425 

24 

03 

9 

0000 

12 

00 

30.09 

BEAMS  AND  SLABS  355 

Table  2. — Use  for  Rectangular  Beams  and  Slabs 

k                   \'2  fkj 
i  =  1  —  Q'      V     J^TT  \  '     ^  =  Vf^jj  or-|r-  (from  Formula  M  =  Khd'^) 


Ratio  of  Moduli  n  =  12 


fc 

A; 

j 

P 

K 

fs 

fc 

k 

j 

P 

K 

500 

0 

332 

0 

889 

u . uuoy 

73 

6 

500 

0 

273 

0 

909 

0 

0043 

62 

0 

550 

0 

354 

0 

882 

n  nnci 

U . UUOi 

85 

7 

oou 

0 

292 

0 

903 

0 

0050 

72 

2 

600 

0.375 

0 

875 

u . uuyt 

98 

4 

Ann 
uuu 

0 

310 

0 

897 

0 

0058 

83 

2 

650 

0 

394 

0 

869 

U . UiU/ 

111 

3 

650 

0 

328 

0 

891 

0 

0067 

95 

0 

12,000 

16,000 

Tnri 
/UU 

0 

412 

0 

863 

u .  yjizu 

124 

4 

•ynn 
/  uu 

0 

344 

0 

885 

0 

0075 

106 

2 

800 

0 

444 

0 

852 

0.0148 

151 

3 

800 

0 

375 

0 

875 

0 

0094 

131 

3 

900 

0 

475 

0 

842 

0.0177 

178 

8 

900 

0 

403 

0 

866 

0 

0113 

156 

5 

500 

0.300 

0 

900 

0.0054 

67 

5 

500 

0 

261 

0 

917 

0 

0038 

59 

2 

550 

0 

320 

0 

893 

0.0063 

78 

6 

550 

0 

280 

0 

907 

0 

0045 

69 

4 

600 

0 

340 

0 

888 

0 . 0073 

90 

6 

600 

0 

298 

0 

901 

0 

0052 

79 

6 

650 

0 

358 

0 

881 

0.0083 

102 

5 

650 

0 

314 

0 

895 

0 

0060 

91 

3 

14,000 

17,000 

700 

0 

375 

0 

875 

0.0094 

114 

8 

700 

0 

331 

0 

890 

0 

0068 

102 

9 

800 

0 

407 

0 

864 

0.0116 

140 

4 

800 

0 

361 

0 

880 

0 

0085 

127 

1 

900 

0 

435 

0 

855 

0.0140 

167 

5 

900 

0 

390 

0 

870 

0 

0103 

152 

2 

500 

0 

286 

0 

905 

0.0048 

64 

7 

500 

0 

230 

0 

923 

0 

0029 

53 

1 

550 

0 

306 

0 

898 

0.0056 

75 

4 

550 

0 

248 

0 

917 

0 

0034 

62 

4 

600 

0 

325 

0 

892 

0.0065 

86 

7 

600 

0 

264 

0 

912 

0 

0040 

72 

2 

650 

0 

343 

0 

886 

0.0074 

98 

4 

650 

0 

280 

0 

907 

0 

0046 

82 

4 

1.5,000 

20,000 

700 

0 

360 

0 

880 

0.0084 

110 

3 

700 

0 

295 

0 

902 

0 

0052 

93 

3 

800 

0 

391 

0 

870 

0.0105 

135 

7 

800 

0 

324 

0 

892 

0 

0065 

115 

6 

900 

0 

418 

0 

861 

0.0125 

161 

5 

900 

0 

351 

0 

883 

0.0079 

139 

5 

Ratio  of  Moduli  n  = 

=  15 

/. 

fc 

fc 

3 

p 

1 

/. 

fc 

it 

J 

V 

K 

500 

0 

384 

0 

872 

0.0080 

83 

7 

500 

0 

319 

0 

894 

0 

0050 

71 

3 

550 

0 

407 

0 

864 

0 . 0093 

96 

4 

550 

0 

339 

0 

887 

0 

0058 

82 

3 

GOO 

0 

428 

0 

857 

0.0107 

110 

0 

600 

0.358 

0 

881 

0 

0067 

94 

4 

12,000 

16,000 

650 

0 

448 

0 

851 

0.0121 

123 

6 

650 

0 

378 

0 

874 

0 

0077 

107 

4 

700 

0 

467 

0 

844 

0.0136 

138 

0 

700 

0 

397 

0 

868 

0 

0087 

120 

6 

750 

0 

484 

0 

839 

0.0151 

152 

0 

750 

0 

414 

0 

862 

0 

0097 

133 

8 

800 

0 

501 

0 

833 

0.0167 

166 

9 

800 

0 

429 

0 

857 

0 

0107 

146 

7 

500 

0 

348 

0 

884 

0 . 0062 

76 

7 

500 

0 

306 

0 

898 

0 

0045 

68 

5 

550 

0 

372 

0 

876 

0.0073 

89 

5 

550 

0 

326 

0 

892 

0 

0053 

80 

4 

600 

0 

391 

0 

870 

0 . 0084 

102 

0 

600 

0 

346 

0 

885 

0 

0061 

91 

8 

14  000 

17,000 

650 

0 

410 

0 

863 

0 . 0095 

114 

8 

650 

0 

365 

0 

878 

0 

0070 

103 

5 

700 

0 

428 

0 

857 

0.0107 

128 

3 

700 

0 

382 

0 

873 

0 

0079 

116 

1 

750 

0 

446 

0 

851 

0.0120 

142 

3 

750 

0 

398 

0 

866 

0 

0088 

129 

5 

800 

0 

462 

0 

846 

0.0132 

156 

3 

800 

0 

415 

0 

862 

0 

0097 

141 

9 

500 

0 

334 

0 

889 

0 . 0056 

74 

1 

500 

0 

272 

0 

909 

0 

0034 

61 

8 

550 

0 

355 

0 

882 

0.0065 

86 

1 

550 

0 

292 

0 

903 

0 

0040 

72 

2 

600 

0 

375 

0 

875 

0.0075 

98 

3 

600 

0 

311 

0 

897 

0 

0047 

83 

7 

15,000 

20,000 

650 

0 

393 

0 

869 

0.0085 

111 

3 

650 

0 

328 

0 

891 

0 

0053 

94 

4 

700 

0 

411 

0 

863 

0.0096 

124 

2 

700 

0 

344 

0 

885 

0 

0060 

106 

2 

750 

0 

429 

0 

857 

0.0107 

137 

9 

750 

0 

359 

0 

880 

0.0067 

117 

9 

800 

0 

445 

0 

852 

0.0118 

151 

2 

800 

0 

374 

0 

875 

0.0075 

130 

9 

Sec.  7-57 


k  = 


1  + 


nfc 


356  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  7-57 


Table  3. — Values  of  k  and  j  for  Rectangular  Beams  and  Slabs 
k  =  \/ 2pn  +  ipn)^  —  pn     j  =  I  —  H  k 


V 

n  = 

12 

n  = 

15 

n  = 

=  12 

71  = 

=  15 

A; 

j 

3 

k 

i 

k 

j 

n 
u 

UUlw 

0 

0 
u 

0 

158 

0 

947 

0 
u 

OOQO 

0 

■^70 

0.877 

0.402 

0 
u 

OOO 

n 
u 

u 

lOO 

0 
U 

0 

169 

0 

944 

u 

00Q9 
uuyz 

0 
u 

Q7Q 
o  <  o 

0.876 

0.405 

0 
u 

oOO 

u 

(\(\^A 

UU11 

0 
u 

iOD 

0 
U 

0 

181 

0 

940 

0 
u 

OOQ/t 
uuyi 

0 
u 

O  /  o 

0.875 

0.407 

0 
u 

004: 

u 

0 
u 

1  77 

0 
u 

0 

192 

0 

936 

0 
u 

0 

O  1  i7 

0.874 

0.411 

0 
u 

OOO 

0 

0018 

0 

186 

0 

938 

0 

202 

0 

933 

0 

0098 

0 

381 

0.873 

0.414 

0 

862 

u 

uuzu 

u 

1  QA 

lyo 

u 

yoo 

0 

217 

0 

928 

u 

01  00 
UlUU 

0 
u 

OoO 

0.872 

0.418 

0 
u 

OOl 

u 

u 

90zL 

0 
u 

0*^9 
yoz 

0 

222 

0 

926 

0 
u 

01  09 
UlUZ 

0 
u 

Q87 
Oo  / 

0.871 

0.420 

0 
u 

oou 

n 
u 

u 

91  9 
Zl^ 

u 

Q9Q 
yzy 

0 

231 

0 

923 

0 
u 

01  04. 

0 

u 

QQ1 
oy  1 

0.870 

0.423 

0 
u 

ooy 

n 
u 

009fi 

0 

990 
^ZU 

0 

Q97 
yz  I 

0 

240 

0 

920 

u 

01  Ofi 

yj  i  uo 

0 
u 

oyi 

0.869 

0.426 

0 

OOO 

0 

0028 

0 

227 

0 

924 

0 

248 

0 

917 

0 

0108 

0 

396 

0.868 

0.429 

0 

857 

n 
U 

\j\}o\) 

u 

u 

Q99 
yzz 

0 

258 

0 

914 

u 

Olio 

Ul  lU 

0 
U 

oyo 

0.867 

0.432 

0 
u 

OOO 

n 
u 

OOQ9 

u 

9zl1 

Z'il 

u 

Q90 
yzu 

0 

263 

0 

912 

0 
u 

0119 
Ui  IZ 

0 
u 

/109 
lUZ 

0.866 

0.434 

0 
u 

OOO 

u 

00^4 

u 

9/18 

0 
u 

Q1 7 
y  1  < 

0 

271 

0 

910 

0 
u 

0114 

Ul  1^ 

0 
u 

4-04. 

0.865 

0.437 

0 

u 

^^A 

OOt: 

u 

UUoD 

u 

u 

Q1  ^ 

y  lo 

0 

277 

0 

908 

u 

01  1  A 
Ul  lO 

u 

ACYJ 

0.864 

0.440 

0 
u 

OOO 

0 

0038 

0 

260 

0 

913 

0 

284 

0 

905 

0 

0118 

0 

410 

0.863 

0.443 

0 

852 

u 

u 

9AA 
ZOO 

u 

Q1  1 

y  1 1 

0 

292 

0 

903 

u 

01  90 
UIZU 

u 

/t1 9 
^iz 

0.863 

0.446 

0 
u 

OOl 

n 
u 

OOzL9 

u 

970 
Z  /  U 

0 
u 

Q1  0 
y  lu 

0 

297 

0 

901 

0 
u 

01  99 
\J  1  zz 

0 
u 

4.1  ^ 

4:10 

0.862 

0.448 

yj 

OO  1 

u 

(\r\AA 

u 

97A 
Z  /  O 

u 

yuo 

0 

303 

0 

899 

n 
u 

Ol  9/1 

u 

4.1  7 
"±1  < 

0.861 

0.451 

n 
u 

oou 

u 

nO/LA 
UU'iO 

u 

9C1 
Zol 

u 

QOA 

yuo 

0 

309 

0 

897 

u 

01  9fi 
UIZO 

u 

4.1  Q 

4:iy 

0.860 

0.454 

n 

u 

Ot:c7 

0 

0048 

0 

286 

0 

904 

0 

315 

0 

895 

0 

0128 

0 

422 

0.859 

0.457 

0 

848 

u 

no  f^o 

U 

901 

zyi 

u 

QOQ 

yuo 

0 

320 

0 

893 

u 

Ol  QO 
UloU 

u 

AOA 

0.859 

0.459 

0 
u 

84-7 

04:  / 

u 

OOPi9 

U 

zyo 

u 

Q01 

yul 

0 

324 

0 

892 

u 

Ol  Q9 
UloZ 

u 

4.97 
IZ  i 

0.858 

0.461 

0 
u 

R4.fi 

OtcU 

u 

OOCiA 
UUO'l 

u 

QOO 
oUU 

u 

QOO 

yuu 

0 

329 

0 

891 

u 

01  Q/1 

U104: 

u 

A9Q 
izy 

0.857 

0.464 

n 

04:0 

U 

OOtiA 
UUOO 

U 

QO/t 
oU'± 

u 

oyy 

0 

333 

0 

889 

u 

Ol  QA 
UloO 

n 
u 

/LQ9 
lOZ 

0.856 

0.466 

0 
u 

RA^ 

04:0 

0 

0058 

0 

309 

0 

897 

0 

337 

0 

888 

0 

0138 

0 

434 

0.855 

0.468 

0 

844 

U 

OOAO 

u 

Q1  A 
Oil 

u 

oyo 

0 

344 

0 

885 

u 

Ol  /to 

Ui'iU 

u 

AQA 
'±oO 

0.855 

0.471 

0 
u 

04:0 

U 

OOA9 

u 

u 

CQ/l 

oy'l 

0 

348 

0 

884 

u 

Ol  A9 
Ul'iZ 

u 

AQ7 

0.854 

0.473 

0 
u 

04:0 

U 

OOAA 

u 

Q99 
OZZ 

n 
u 

oyo 

0 

352 

0 

883 

n 
u 

Ol  AA 
U144 

u 

AACi 

0.853 

0.475 

0 
u 

R4-9 

U 

OOAA 
UUOO 

u 

oZO 

u 

QQ9 

oyz 

0 

356 

0 

881 

u 

Ol  zLA 
UIttO 

u 

AA9 

0.853 

0.477 

0 
u 

R4.1 

O^l 

0 

0068 

0 

330 

0 

890 

0 

360 

0 

880 

0 

0148 

0 

444 

0.852 

0.479 

0 

840 

0 

0070 

0 

334 

0 

889 

0 

365 

0 

878 

0 

0150 

0 

446 

0.861 

0.481 

0 

840 

0 

0072 

0 

338 

0 

887 

0 

369 

0 

877 

0 

0152 

0 

449 

0.850 

0.483 

0 

839 

0 

0074 

0 

342 

0 

886 

0 

372 

0 

876 

0 

0154 

0 

451 

0.850 

0.485 

0 

838 

0 

0076 

0 

345 

0 

885 

u 

QTA 
O/O 

u 

575 

0 

0156 

0 

453 

U .  o4y 

0 

838 

0 

0078 

0 

349 

0 

884 

0 

380 

0 

873 

0 

0158 

0 

455 

0.848 

0.489 

0 

837 

0 

0080 

0 

353 

0 

882 

0 

384 

0 

872 

0 

0160 

0 

457 

0.848 

0.493 

0 

836 

0 

0082 

0 

356 

0 

881 

0 

387 

0 

871 

0 

0170 

0 

467 

0.845 

0.502 

0 

833 

0 

0084 

0 

360 

0 

880 

0 

390 

0 

870 

0 

0180 

0 

476 

0.841 

0.513 

0 

829 

0 

0086 

0 

363 

0 

879 

0 

394 

0 

869 

0 

0190 

0 

485 

0.838 

0.522 

0 

826 

0 

0088 

0 

366 

0 

878 

0 

398 

0 

867 

0 

0200 

0 

493 

0.836 

0.531 

0 

823 

Sec.  7-S7 


BEAMS  AND  SLABS 


357 


Table  4. — Values  of  hd^  for  Different  Values  of  b  and  d 


Values 
of 

b  = 

=  12 

b  = 

=  10 

d 

bd 

d 

bd 

3 

36 

3 

3 

32 

8 

192 

4 

48 

4 

4 

43 

7 

300 

5 

60 

5 

5 

54 

8 

432 

6 

72 

6 

6 

65 

7 

588 

7 

84 

7 

7 

76 

5 

/  Do 

8 

96 

8 

8 

87 

5 

972 

9 

108 

9 

9 

98 

5 

1,200 

10 

120 

10 

9 

109 

4 

1,452 

11 

132 

12 

1 

120 

2 

1,728 

12 

144 

13 

1 

131 

2 

13 

156 

14 

3 

142 

3 

2,352 

14 

168 

15 

4 

153 

6 

2,700 

15 

180 

16 

4 

164 

0 

3,072 

16 

192 

17 

5 

175 

0 

3,468 

17 

204 

18 

6 

186 

0 

Q  QCC 

o,ooo 

18 

216 

19 

7 

197 

0 

4,332 

19 

228 

20 

8 

208 

0 

4,800 

20 

240 

21 

9 

218 

8 

5,292 

21 

252 

23 

0 

229 

8 

5,808 

22 

264 

24 

1 

240 

6 

0,<54fS 

23 

276 

25 

2 

252.0 

6,912 

24 

288 

26 

3 

263 

0 

7,500 

25 

300 

27 

4 

274 

0 

8,112 

26 

312 

28 

5 

285 

0 

8,748 

27 

324 

29 

6 

295 

8 

y,4Uo 

ooD 

30 

7 

307 

0 

10,092 

29 

348 

31 

9 

318 

2 

10,800 

30 

360 

32 

9 

328 

3 

11,532 

31 

372 

33 

9 

339 

4 

12,288 

32 

384 

35.0 

350 

0 

13,068 

33 

396 

36 

2 

361 

8 

13,872 

34 

408 

37 

2 

372 

1 

14,700 

35 

420 

38 

3 

383 

3 

15,552 

36 

432 

39 

4 

394 

0 

16,428 

37 

444 

40 

6 

406 

0 

17,328 

38 

456 

41 

6 

416 

0 

18,252 

39 

468 

42 

7 

427 

1 

19,200 

40 

480 

43 

8 

438 

0 

d  bd 


d  =  0.56 


bd 


bd 


1.5b 


bd 


d  =  1.76 


6    I   d  bd 


d  =  2b 


b       d  bd 


2.7 
3.6 
4.5 
5.4 
6.3 

7.2 
8.1 
8.9 
9.8 
10.7 

11.6 
12.6 
13.5 
14.3 
15.2 

16.1 
17.0 
17.9 
18.8 
19.7 

20.6 
21.5 
22.4 
23.2 
24.1 

25.0 
25.9 
26.8 
27.7 
28.6 

29 
30 
31 
32 
33 

33 
34 
35 


40 
54 
67 
81 

94, 

108 
121 
133 
147, 
160 

174 

189 
202 
214 
228 

241 

255 
268 
282 
295 

309 
323 
336 
348 
361, 

375, 
388, 
402 
416 
429, 

442 
456 
469, 
482, 
495, 

508, 
522, 
536. 


3.8 
4.6 
5.3 
6.0 
6.7 


7 

9.2 
10.6 
12.0 
13.4 

14.6 
15 

17.0 
18.0 
19.0 

20.010. 
21.010, 
22.011 
23.011 
24.012 

25.012 
25.812 
26.813 
27.813 
28.614 

29.414 
30.215 
31.015 
32.016 
32.816 

33.616 


34.4 
35.217 
35.817 
36.618 


17.2 

6 
9 
3 


37.418.7 
38.219.1 
38.8 19.4 
39.619.8 
40.420.2 

41.2  20.6 
41.820.9 
42.4121.2 


28.8 
41.4 
56.2 
72.0 
89.8 
106.5 
124.9 
144.5 
162.0 
180.5 

200.0 
220.2 
242.0 
264.2 
288.0 

312.2 
332.7 
359.5 
387.0 
409.0 

7  432.0 


456.0 
480.0 
522.0 
537.5 

565.0 
592.0 
620.0 
642.0 
670.0 

700.0 
730.0 
753.0 
784.0 
816.0 

847.0 
875.0 
900.0 


4.8 
5.8 
6.7 
7.6 
8.4 

9.2 


10 
11 

12, 

12 
13 
13 
14 

15, 

15 
16 
16 
17 
18 

18 
19 
19 
20 
20 
21 
21 
22.1 
22.6 
23.1 

23.6 
24.1 
24.5 
25.0 
25.4 

25.9 
26.4 
26.8 


23 
33 
44, 
57, 
70. 

84, 
98. 
114, 
129, 
144, 

161 
176 
193 
213 
231, 


246, 
265, 
285, 
306 
324 

345 
364 
384 
.2  408 
424 

449 
.  7  470 


488 
510 
533 

557 
580 
600 
625 
645 

670 
697 
718 


3.6 
4.4 
5.1 
5.8 
6.4 


7.010 
7.611 


8.1 


8.713 
9.213 

9.714 
10.215 
10.716 
11.216 
11.617 

12.1 

12.518 
12.919 
13.319 
13.8  20 

14.221 
14.621 
15.022 
15.423 
15.823 

16.124 
16.524 
16.925 
17.326 
17.626 

18. 

18 
18 
19 
19 


19 
20.1 
20 


5.4 
6.6 
7.7 
8.7 
9.6 


12 


.4 

.0 
.5 

7  28.0 
128.6 
4  29.1 


.027 

.3  27 


8  29 


7 

30.1 
6 


4  30 


19.8 
29.0 
39.2 
50.1 
61.5 

73.5 
86.7 
98.0 
114.0 
127.0 

141.6 
156.0 
172.0 
188.2 
202.0 

219.0 
235.0 
249.0 
265.0 
286.0 

302.0 
320.0 
338.0 
356.0 
375.0 

388.0 
410.0 
430.0 
0  450.0 


465.0 

186.0 
503.0 
524.0 
546.0 
565.0 

588.0 
605.0 
624.0 


5.7 
6.9 
8.0 
9.1 
10.0 

10.9 
11.8 
12.7 
13. 
14. 


19.4 
28.3 
37.6 
49.2 
59.0 

69.8 
81.4 
95.2 
.0 
.0 


6109 
3120 


15.2136. 
15.9149. 
16.7163. 
17.4177. 


8 
3 
5 
5 

192.0 


18.1 

18.8207, 
19.5224 
20 . 2  240 
20.8254 


3.0 
3.6 
4.2 
4.8 
5.3 

5.8 
6.3 
6.7 
7.2 
7.6 

8.0 
8.4 
8.8 
9.2 
9.6 

9.9 
10.3 
10.7 


6.0 
7.3 
8.4 
9.5 
10.6 

11.5 
12.5 
13.4 
14.3 
15.2 

15.9 
16.8 
17.6 
18.3 
19.1 


18.0 
26.3 
35.2 
45.6 
56.2 

66.8 
78.8 
89.8 
103.0 
115.6 

127.0 
141.0 
155.0 
168.0 
184.0 


19, 
20, 
21 
11.0  22 


21.5273.0 


11.4 


22 


196.0 
6212.0 
3228.0 
0  242.0 
7  258.5 


22.1288, 
22.8306, 
8  23.4323 
24.0339 

5  24.6356 

25.2373 
25.8  392 
26.4410 
27.0429 
27.6447 

28 . 1 464 
28.7  485 
29 . 3  504 

6  29.8525 
9 


30 . 4  544 , 
30.9562 
31.4581 
32.0602 


11.7  23 


12.1 
12.4 
12.7 


13.3 
13.7 


274.0 
292.0 
7  306.0 
323.0 


24. 
24. 
25.4 
13.0  26.0338.0 

6  354.0 
3  374.0 
390.0 
5408.0 
2  424.0 


14.0  27.9 
28 


14.3 
14.6  29 

29 
30 
30 
31 
32 

16.4  32 
16.6 
16.9 


14.9 
15.2 
15.5 
15.8 
16.1 


7  443.0 
4462.0 
9478.0 
5498.0 

517.0 

537.0 
2  552  .0 

8  572.0 


Table  o. — Number  of  Rods  and  Sectional  Area  in  Square  Inches  for  Beam  and  Column 

Reinforcement 


Size  of  rod 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

in. 

/  round. .  . 

0 

39 

0 

58 

0 

78 

0 

98 

1 

18 

1 

37 

1 

57 

1 

77 

1 

96 

2 

16 

2 

36 

2 

55 

2 

75 

2 

94 

3.10 

'A 

\  square .  . 

0 

50 

0 

75 

1 

00 

1 

25 

1 

50 

1 

75 

2 

00 

2 

25 

2 

50 

2 

75 

3 

00 

3 

25 

3 

50 

3 

75 

4.04 

in. 

f  round. .  . 

0 

49 

0 

74 

0 

99 

1 

24 

1 

49 

1 

74 

1 

99 

2 

24 

2 

48 

2 

73 

2 

98 

3 

23 

3 

48 

3 

73 

3.98 

1  square.  . 

0 

63 

0 

94 

1 

27 

1 

58 

1 

90 

2 

21 

2 

53 

2 

85 

3 

16 

3* 

48 

3 

80 

4 

11 

4 

43 

4 

75 

5.06 

in. 

!  round. .  . 

0 

61 

0 

91 

1 

23 

1 

53 

1 

84 

2 

15 

2 

45 

2 

76 

3 

07 

3 

37 

3 

68 

3 

99 

4 

30 

4 

60 

4.91 

\  square .  . 

0 

78 

1 

07 

1 

56 

1 

95 

2 

34 

2 

73 

3 

12 

3 

52 

3 

91 

4 

30 

4 

69 

5 

08 

5 

47 

5 

86 

6.25 

in. 

/  round. .  . 

0 

74 

1 

11 

1 

48 

1 

86 

2 

23 

2 

60 

2 

97 

3 

34 

3 

71 

4 

08 

4 

45 

4 

83 

5 

20 

5 

57 

5.94 

\  square .  . 

0 

94 

1 

41 

1 

89 

2 

36 

2 

84 

3.31 

3 

78 

4 

25 

4 

73 

5 

20 

5 

67 

6 

15 

6 

62 

7 

09 

7.56 

in. 

/ round. .  . 

0 

88 

1 

32 

1 

77 

2 

21 

2 

65 

3.09 

3 

53 

3 

98 

4 

42 

4 

86 

5 

30 

5 

74 

6 

19 

6 

63 

7.07 

H 

\  square .  . 

1 

12 

1 

68 

2 

25 

2 

81 

3 

38 

3 

94 

4 

50 

5 

06 

5 

62 

6 

19 

6 

75 

7 

31 

7 

88 

8 

44 

9.00 

in. 

/  round. .  . 

1 

03 

1 

55 

2 

07 

2 

59 

3 

11 

3 

63 

4 

15 

4 

67 

5 

18 

5 

70 

6 

22 

6 

74 

7 

26 

7 

78 

8.30 

me 

\  square.  . 

1 

32 

1 

98 

2 

64 

3 

30 

3 

96 

4 

62 

5 

28 

5 

94 

6 

60 

7 

26 

7 

92 

8 

58 

9 

24 

9 

90 

10.56 

in. 

f  round. .  . 

1 

20 

1 

80 

2 

41 

3 

01 

3 

61 

4 

21 

4 

81 

5 

41 

6 

01 

6 

61 

7 

22 

7 

82 

8 

42 

9 

02 

9.62 

H 

1  square .  . 

1 

53 

2 

29 

3 

06 

3 

83 

4 

59 

5 

36 

6 

12 

6 

89 

7 

66 

8 

42 

9 

19 

9 

95 

10 

72 

11 

48 

12.25 

[\n. 

/ round. .  . 

1 

38 

2 

07 

2 

76 

3 

45 

4 

14 

4 

83 

5 

52 

6 

21 

6 

90 

7 

59 

3 

28 

8 

97 

9 

66 

10 

35 

11.04 

\  square .  . 

1 

75 

2 

63 

3 

52 

4 

39 

5 

27 

6 

15 

7.03 

7 

91 

8 

79 

9 

67 

10 

55 

11 

43 

12 

30 

13 

18 

14.06 

in. 

f  round. .  . 

1 

57 

2 

35 

3 

14 

3 

93 

4 

71 

5 

50 

6 

28 

7 

07 

7 

85 

8 

64 

9 

43 

10 

21 

11 

00 

11 

78 

12.57 

1 

1  square .  . 

2.00 

3 

00 

4 

00 

5 

00 

6 

00 

7 

00 

S.OO 

9 

00 

10 

00 

11 

00 

12 

00 

13 

00 

14 

00 

15 

00 

16.00 

in. 

/ round. .  . 

1 

98 

2 

98 

3 

98 

4 

97 

5 

96 

6 

96 

7 

95 

8 

95 

9 

94 

10 

94 

11 

93 

12 

92 

13 

92 

14 

91 

15.90 

m 

\ square.  . 

2 

53 

3 

79 

5.06 

6 

33 

7 

59 

8 

86 

10 

12 

11 

39 

12 

66 

13 

92 

15 

19 

16 

45 

16 

72 

18 

98 

20.25 

in. 

f  round. .  . 

2 

45 

3 

68 

4 

91 

6 

14 

7 

36 

8 

59 

9 

82 

11.04 

12 

2.7 

13 

50 

14 

73 

15 

95 

17.18 

18 

41 

19.64 

VA 

1  square.  . 

3 

12 

4 

68 

6 

25 

7 

81 

9 

37 

10 

94 

12 

50 

14 

06 

15 

62 

17 

19 

18 

75 

20 

31 

21.87 

23 

44 

25.00 

CONCRETE  ENGINEERS'  HANDBOOK 
Table  6. — Spacing  of  Round  Rods  in  Slabs 


[Sec. 


Diam- 


Sectional  area  of  steel  per  foot  of  slab  when  spaced  as  follows: 


eier 
(inches) 

2  in. 

21/^ 

in. 

3 

in. 

in. 

4 

in. 

41/2 

in. 

5  in. 

5}^  in. 

6 

n. 

7  in. 

8 

n. 

9  in. 

10  in. 

12 

in. 

0 

29 

0 

23 

0.20 

0 

17 

0 

15 

0 

13 

0.12 



He 

0 

46 

0 

36 

0 

31 

0 

26 

0 

23 

0 

20 

0.18 

0.17 

0 

15 

0.13 

H 

0 

66 

0.53 

0.44 

0 

38 

0.33 

0 

29 

0.26 

0.24 

0 

22 

0.19 

0 

17 

0.15 

0.13 

Vie 

0 

90 

0.72 

0.60 

0.51 

0.45 

0.40 

0.36 

0.33 

0 

30 

0.26 

0 

23 

0.20 

0.18 

0 

15 

y2 

1 

18 

0 

94 

0.78 

0 

6/ 

0 

59 

0 

52 

0.47 

0.43 

0 

39 

0.34 

0 

29 

0.26 

0.24 

0 

20 

He 

1 

49 

1 

19 

0 

99 

0 

85 

0 

75 

0.66 

0.60 

0.54 

0 

50 

0.43 

0 

37 

0.33 

0.30 

0 

25 

'A 

1 

84 

1 

47 

1 

23 

1 

05 

0 

92 

0.82 

0.74 

0.67 

0 

61 

0.53 

0 

46 

0.41 

0.37 

0 

31 

^He 

2 

23 

1 

78 

1 

48 

1 

27 

1 

11 

0 

99 

0.89 

0.81 

0 

74 

0.64 

0 

56 

0.49 

0.45 

0 

37 

H 

2 

65 

2 

12 

1 

77 

1 

51 

1 

32 

1 

18 

1.06 

0.96 

0 

88 

0.76 

0 

66 

0.59 

0.53 

0 

44 

^He 

3 

11 

2 

48 

2 

07 

1 

78 

1 

56 

1 

38 

1.24 

1.13 

1 

04 

0.89 

0 

78 

0.69 

0.62 

0 

52 

14 

/8 

3 

61 

2 

88 

2 

40 

2 

06 

1 

80 

1 

60 

1.44 

1.31 

1 

20 

1.03 

0 

90 

0.80 

0.72 

0 

60 

4 

14 

3 

31 

2 

76 

2 

37 

2 

07 

1 

84 

1.66 

1.51 

1 

38 

1.18 

1 

03 

0.92 

0.83 

0 

69 

1 

4 

71 

3 

77 

3 

14 

2 

69 

2 

36 

2 

09 

1.88 

1.71 

1 

57 

1.35 

1 

18 

1.05 

0.94 

0 

78 

4 

77 

3 

98 

3 

41 

2 

98 

2 

65 

2.39 

2.17 

1 

99 

1.70 

1 

49 

1:33 

1.19 

0 

99 

m 
m 

4 

91 

4 

21 

3 

68 

3 

27 

2.95 

2.68 

2 

45 

2.10 

1 

84 

1.64 

1.47 

1 

23 

5 

09 

4 

45 

3 

96 

3.56 

3.24 

2 

97 

2.55 

2 

23 

1.98 

1.78 

1 

48 

5 

30 !  4 

71 

4.24 

3.86 

3 

53 

3.03 

2 

65 

2.36 

2. 12 

1 

77 

Table  7. — Spacing  of  Square  Rods  in  Slabs 


Di- 


Sectional  area  of  steel  per  foot  of  slab  when  spaced  as  follows: 


sion 
(inches) 

2  in. 

2H 

in. 

3 

in. 

3H 

in. 

4 

in. 

4 1/2 

in. 

5 

in. 

in. 

6  in. 

j  7  in. 

8  in. 

9  in. 

10  in. 

12  in. 

0.37 

0.30 

0.25 

0 

.21 

0 

.19 

0 

.17 

0 

.15 

0.13 

0.12 

Vie 

0.59 

0.47 

0.39 

0 

.33 

0 

.29 

0 

.26 

0 

.23 

0.21 

0.19 

0.17 

0.15 

0.13 

% 

0.84 

0.67 

0 

.56 

0.48 

0 

.42 

0 

.37 

0 

.34 

0.31 

0.28 

0.24 

0.21 

0.19 

0.17 

0.14 

He 

1.15 

0 

92 

0 

77 

0.66 

0 

.57 

0 

51 

0 

.46 

0.42 

0.38 

0.33 

0.29 

0.25 

0.23 

0.19 

1.50 

1 

20 

1 

00 

0 

86 

0 

75 

0 

67 

0 

60 

0.55 

0.50 

0.43 

0.37 

0.33 

0.30 

0.25 

He 

1.90 

1 

52 

1 

27 

1 

08 

0 

95 

0 

84 

0 

76 

0.69 

0.63 

0.54 

0.47 

0.42 

0.38 

0.32 

% 

2.34 

1 

87 

1 

56 

1 

34 

1 

17 

1 

04 

0 

94 

0.85 

0.78 

0.67 

0.59 

0.52 

0.47 

0.39 

'He 

2.84 

2 

27 

1 

99 

1 

62 

1 

42 

1 

33 

1 

13 

1.03 

0.94 

0.81 

0.71 

0.66 

0.57 

0.47 

H 

3.37 

2 

70 

2 

25 

1 

93 

1 

69 

1 

50 

1 

35 

1.23 

1.12 

0.96 

0.84 

0.75 

0.67 

0.56 

'He 

3.96 

3 

17 

2 

64 

2 

26 

1 

98 

1 

76 

1 

58 

1.44 

1.32 

1.13 

0.99 

0.88 

0.79 

0.66 

Vs 

4.59 

3 

67 

3 

06 

2 

62 

2 

30 

2 

04 

1 

84 

1.67 

1.53 

1.31 

1.15 

1.02 

0.92 

0.77 

'He 

5.27 

4 

22 

3 

52 

3 

01 

2 

64 

2 

34 

2 

11 

1.92 

1.76 

1.51 

1.32 

1.17 

1.05 

0:88 

1 

6.00 

4 

80 

4 

00 

3 

43 

3 

00 

2 

67 

2 

40 

2.18i  2.00 

1.71 

1.50 

1.33 

1.20 

1.00 

iH 

6.08 

5 

06 

4 

34 

3 

80 

3 

37 

3 

04 

2.76 

2.53 

2.17 

1.89 

1.69 

1.52 

1.27 

I'A 

m 

6 

25 

5 

36 

4 

69 

4 

17 

3 

75 

3.41 

3.12 

2.68 

2.34 

2.0^ 

1.87 

1.56 

6 

48 

5 

67 

5 

04 

4 

54 

4.12 

3.78 

3  24 

2.84 

2.52 

2.27 

1.89 

IK 

6 

75 

6 

00 

5 

40 

4.91 

4.50 

3.86 

3.37 

3.00 

2.70 

2.25 

1 

Sec.  7-57] 


BEAMS  AND  SLABS 


359 


Table  8. — Values  of 


k  k 

- — j-r  IN  Formula      =      ,  /, 

-  k)  n(l  -  A;) 


Applies  to  Rectangular  Beams,  T-beams,  and  Beams  With  Steel  Top  and  Bottom 

Based  on  n  =  12 


0.200 
0.202 
0.204 
0.206 
0.208 

0.210 
0.212 
0.214 
0.216 
0.218 

0.220 
0.222 
0.224 
0.226 
0.228 

0.230 
0.232 
0.234 
0.236 
0.238 

0.240 
0.242 
0.244 
0.246 
0.248 


0.0214 
0.0216 
0.0219 


0.0222  0.260 
0.0224  0.262 
0.0227  0.264 
0.0230  0.266 
0 . 0232  0 . 268 


0.0208  0.250 
0.0211  0.252 


0.254 
0.256 
0.258 


0 . 0235 
0.0238 
0.0240 
0 . 0243 
0 . 0246 

0 . 0249 
0.0252 
0 . 02.54 
0.0257 
0 . 0260 

0.0263 
0.0266 
0.0269 
0.0272 
0.0275 


0.270 
0.272 
0.274 
0.276 
0.278 

0.280 
0.282 
0.284 
0.286 
0.288 

0.290 
0.292 
0.294 
0.296 
0.298 


0278 
0281 
0284 
0287 
0290 

0293 
0296 
0299 
0302 
0305 

0308 
0311 
0315 
0318 
0321 

0324 
0327 
0331 
0334 
0337 

0341 
0344 
0347 
0350 
0354 


300 
302 
304 
306 
308 

310 
312 
314 
316 
318 

320 
322 
324 
326 
328 

330 
332 
334 
336 
338 

340 
342 
344 
346 
348 


0.0357 
0.0360 
0.0364 
0.0367 
0.0371 

0.0375 
0 . 0378 
0.0381 
0 . 0385 
0.0389 

0 . 0392 
0 . 0396 
0 . 0400 
0 . 0403 
0 . 0406 

0.0410 
0.0414 
0.0417 
0.0421 
0.0426 

0 . 0429 
0 . 0433 
0.0437 
0 . 0440 
0.0444 


0 . 350 
0 . 352 
0 . 354 
0 . 356 
0.358 


0.0448  0. 
0.0452  0. 
0 . 0457 
0.0461 
0.0465 


0 .  360  0 .  0469 
0 . 362  0 . 0473 
0.364  0.0477 
0.366  0.0481 
0.368  0.0485 


0.370 
0.372 
0 . 374 
0.376 
0.378 

0.380 
0.382 
0.384 


0 . 0489 
0 . 0493 
0.0497 
0 . 0502 
0  0507 

0.0511 
0.0515 
0.0520 


0.386  0.0524 
0.388  0.0529 


400 1 0. 0556  0, 
40210.0560  0, 
404:0.056510, 
406l0.0570|0, 
408  0.0575  0, 


410 
412 
414 
416 
418 

420 
422 
424 
426 
428 


430 
432 
434 


0.057910. 
0.058310. 
0.0588:0. 
0.0593|0. 
0.0598  0, 


0 . 0603 
0 . 0608 
0.0613 
0.0618 
0 . 0623 


0.0629 
0.0634 
0 . 0639 
436  0.0644 
438  0.0650 


0.390  0.0533  0 
0.39210.0537  0 
0.394  0.0542  0 
0.396  0.0546  0, 
0 . 398  0 . 05.50  0 


440  0.0655 
442  0.0660 
444  0 . 0665 
446  0.0671 
448  0.0677 


450 
452 
454 
456 
458 

460 
462 
46i 
466 
468 

4-70 
472 
474 
476 
478 

480 
482 
484 
486 
488 


0 .  0682  0 .  500  0  . 0834 
0.0687  0.502 iO.  0840 
0.0693  0.504,0.0846 
0.0697  0.506,0.0853 
0.0704  0.508  0.0860 


0.0710  0.510 
0.0716  0.512 


0.0721 
0.0727 
0.0733 

0.0739 
0 . 0744 
0 . 0750 
0 . 0756 
0 . 0763 

0.0770 
0 . 0776 
0.0781 
0 . 0788 
0.0795 


490  0.0801 
492  0.0807 
494  0.0813 
496  0.0820 
498  0.0828 


0.514 
0.516 
0.518 

0.520 
0.522 
0 . 524 
0.526 
0.528 

0 . 530 
0.532 
0.534 


0.0867 
0 . 0873 
0 . 0880 
0 . 0888 
0.0895 

0.0903 
0.0910 
0.0917 
0.0925 
0.0933 

0.0940 
0.0947 
0.0954 


0.536  0.0962 
0.538  0.0970 

0.540  0.0979 
0.542 1 0.0985 
0.-544  0.0913 
0.546  0. 1002 
0.548  0.1011 


5.W,0. 
552  iO. 


554 
556 
558 

500 
562 
564 
566 
568 

570 
572 
574 
576 
578 

580 
582 
584 
■586 
588 

590 
592 
.594 
596 
598 


1019 
1027 
1035 
1043 
1052 

1060 
1070 
1079 
1089 
1097 

1105 
1112 
1 122 
1132 
1143 

1152 
1160 
1170 
1180 
1190 

1200 
1210 
1220 
1230 
1240 


Table  9. — Values  of 


k 


IN  Formula  fc  = 


n(l  -  k)       ^  — —  jc  _ 

Applies  to  Rectangular  Beams,  T-beams,  and  Beams  With  Steel  Top  and  Bottom 

Based  on  n  =  15 


0.200 
0.202 
0.204 
0.206 
0.208 

0.210 
0.212 
0.214 
0.216 
0.218 

0.220 
0.222 
0.224 
0.226 
0.228 

0.230 
0.232 
0.234 
0.236 
0.238 

0.240 
0.242 
0.244 
0.246 
0.248 


0.0166 
0.0169 
0.0171 
0.0173 
0.0175 

0.0177 
0.0179 
0.0181 

0.0183 
0.0186 

0.0188 
0.0190 
0.0192 
0.0194 
0.0196 

0.0199 
0.0201 
0 . 0203 
0.0205 
0 . 0207 

0.0210 
0.0212 
0.0214 
0.0217 
0.0219 


0.250 
0 . 252 
0 . 2.54 
0.256 
0.258 


260 
262 
264 
266 
268 


0 . 0222 
0.0224 
0.0226 
0.0229 
0.0231 

0.0234 
0 . 0236 
0 . 0238 
0.0241 
0.0243 


0.300 
0.302 
0 . 304 
0.306 
0.308 

0.310 
0.312 
0.314 
0.316 
0.318 


270  0.0246 
272  0.0248 
27410.0251 
27610.0254  0.326 
278  0.0257  0.328 


0 . 320 
0.322 
0.324 


280 
282 
284 
286 
288 

290 
292 
294 
296 
298 


0.0259 
0.0261 
0 . 0264 
0.0267 
0 . 0269 

0.0272 
0.0275 
0.0278 
0.0280 
0.0283 


0.330 
0.332 
0.334 
0.336 
0.338 

0.340 
0.342 
0.344 
0.346 
0.348 


0.0286 
0.0288 
0.0291 
0.0293 
0.0296 

0 . 0299 
0.0301 
0 . 0305 
0.0.308 
0.0311 

0.0314 
0.0317 
0.0319 

0.0322  0.376  0 
0.0325  0.378,0 

0.0328  0.380  0 
0.0331  0.382  0 
0.0334  0.384  0 
0.0337  0.386  0, 
0.0340:0.388  0 

0.034410. 390,0 
0.0347  0.392  0, 
0.0350  0.394  0, 
0.0353  0.396  0, 
0.0356  0.398  0, 


0 

350  0 

0 

352  0 

0 

354  0 

0 

356 

0 

0 

358 

0 

0 

360 

0 

0 

302 

0 

0 

364 

0 

0 

366 

0 

0 

368 

0 

0 

370 

0 

0 

372 

0 

0 

374  0 

0.400 
0.402 
0.404 
0.406 
0.408 


.  0375 
.0378 
.0381 
.0384 
.0387  0 


0391 
0394 
,0398 
0401 
0404 

0408 
0411 
0415 
0419 
0422 

0426 
0429 
0433 
0437 
0440 


410 
412 
414 
410 
418 


0.0444 
0.0447 
0.0451 
0.0455 
0.0459 

0.0463 
0 . 0406 
0.0470 
0 . 0474 
0.0478 


420  0.0482 
422  0 . 0486 
424  0.0490 
426  i  0.0494 
428|0.0498 

430 '  0.0.502 
432^0. 0506 
434  0.0511 
436  0.0515 
4.38|0.0520 

440  0.0524 
442 1 0.0528 
444  0.0532 
446  0.0536 
448  0.0540 


450 
452 
454 
456 
458 


0.0666 
0.0671 
0.0677 
0 . 0682 
0.0562  0.508  0.0688 


0.0545  0.500 
0.0549  0.502 
0 . 05.54  0 .  504 
0 . 0558  0 .  506 


460  0.0567 
402  0.0571 
0.0576 
0.0581 
0.0586 


464 
466 
468 


470  0 
472  0 

474,0 
476|0 
478  0 

480  0 

48210 
484  0 
486i0 
488  iO 


.0591 
.0,595 
.0600 
.  0005 
.0610 

.0615 
.0620 
.0625 
.0630 
.  0635 


490  0.0640 
492  0.0645 
494  0.0650 
496  0.0656 
498  0.0660 


510 
512 
514 
516 
518 


0.0694 
0 . 0699 
0 . 0705 
0.0711 
0.0717 


550 
5.52 
554 
556 
558 

560 
562 
564 
566 
568 


0.0815 
0.0821 
0 . 0827 
0 . 0834 
0.0841 

0 . 0848 
0 . 0855 
0 . 0862 
0 . 0869 
0.0870 


520  0.0723  0. 
522  0.0728  0. 
524  0.0733  0. 


52610.0739 
528  0.0745 


530 
532 
5.34 
536 
538 

540 
542 
544 
546 
548 


0.0751 
0.0757 
0.0763 
0.0770 
0.0776 

0.0783 
0.0789 
0 . 0795 
0.0802 
0 . 0808 


570  0.0884 
572  0.0891 
574  0 . 0898 
576  0.0905 
578  0.0912 


580 
582 
584 
586 
588 

590 
592 
594 
596 
598 


0.0920 
0.0927 
0.0935 
0.0943 
0.0951 

0 . 0959 
0.0967 
0.0975 
0.0984 
0.0993 


Sec.  7-57 


BEAMS  AND  SLABS 


361 


Diagram  3. — Use  for  Wedge-shaped  Beams. 

In  designing,  use  Diagram  1  or  2  and  then  multiply  the  values  of  K  and  p  obtained  by  cos-Pc  and  --^^  f "  respec- 

cospi 

lively.    (These  products  may  be  obtained  directly  from  diagram  given  below.) 

In  reviewing,  determine  K  and  p  in  the  usual  manner  and  then  multiply  these  values  by   and  S^^^L 

COS-pc  CO.S'^c 

respectively  before  using  Diagram  1  or  2.    (These  products  may  be  obtained  directly  from  diagram  given  below.) 


Values  "C"  =(Va lues  'A'  x  -§||^ ) 
17       16       15       U       13       12       n       -10       9       6        7        6        5        4        3        2        1  0 


O        I         2        3        -4-        5        6        7        8        9        10        U       12        13       14       15        16  17 


Values X  =  (Values "CVf§|^)=CVaIue5'B"x  c5i%c) 


Diagram  4. —Use  for  Finding  Approximate  Weight  of  Rectangular  Beams. 


0.70      0.75        0.80        085       090        095        1.00        1.05         1.10  K15 

Values  j>f  V 


CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  7-g' 

DiAGKAM  5. 

Bending  Moments  in  Slabs  for  Uniformly  Distributed  Loads. 

Span  \n  Feei- 

14       13        12        f1        10        9         8       .7         6        5        4  3 


0  H  M  I II  M  M  1 1 1 1  1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1  1 1 1 1  n  I  1 1 1 1 1  n  M  M  II 1 1  inrrmi 

3       4        5        6        7        8        9        10       11       IE       13       14  15 

Span  in  Feet 


362 


15 


Sec.  7-57] 


BEAMS  AND  SLABS 


363 


o  in  o  in 

epuno^  qoui  j.o  spuosnoty^  u!  4.usuuov\  Suipusg 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7 


Diagram  7. 
Use  for  T-beams. 

Based  on  fs  =  16,000;  n  =  12. 
.3    ■  .4,       300       400  SOO  600 


700 


800 


Values  of  ^ 


500  600  VOO 

Values  of  fc 


Diagram  8. 
Use  for  T-beams. 

Based  on  fs  =  16,000;  n  =  15. 
.4      30d  400 


500 


600, 


700 


Sec.  7-57] 


BEAMS  AND  SLABS 


365 


Diagram  9. 
Use  for  T-beams. 

Values  of  k  and  j  for  various  percentages  of  steel.    Based  on  n  =  12. 


Values  of  J 


Values  of  3 


Diagram  10. 
Use  for  T-beams. 

Values  of  k  and  j  for  various  percentages  of  steel.   Based  on  n  =  15. 


.65 


^^^^ 


3  AO 
35 


20 


:2t 


Vciiwes  of  -I 


Values  of  J 


366  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  7 


Diagram  11. 

Use  for  Rectangular  Beams  With  Steel  in  Top  and  Bottom. 

Based  onn  =  12. 


Vofluea  of  p' 


Sec.  7-57]  BEAMS  AND  SLABS  367 

Diagram  11. — (Continued) 


Values  of  d' 


368 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7 


Diagram  12. 

Use  for  Rectangular  Beams  With  Steel  in  Top  and  Bottom. 

Based  on  re  =  15. 


370 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  7-57 


Diagram  13. 
Leffler's  Comprehensive  Beam  Chart. 


Curves  for  -r 
a 


0.10  and  n  =  15. 


Values  of  Ls 

.005        006     .007     .008  .009  OlO 


D25       fi30  .030 


.lol  I  M  M  M  M  I 

V  X  Zf'Zf    Along  p'O  asl'TSOandg 

8  2  a  I      Li  .ncneases  U  ^8 

s      g    Along  p=0  osl-eSOortl- 


m  I 

» i 

lis 

lili 

II 
o  a 


I 


SECTION  8 


COLUMNS 


1.  Column  Types. — Concrete  columns  are  of  four  principal  types: 

1.  Plain  concrete  columns  or  piers. 

2.  Columns  reinforced  with  longitudinal  rods  only. 

3.  Columns  reinforced  with  both  hoops  and  longitudinal  rods. 

4.  Columns  reinforced  with  structural-steel  shapes. 

2.  Plain  Concrete  Columns  or  Piers. — The  Joint  Committee  does  not  consider  any  com- 
pression member  a  column  unless  it  is  reinforced  and  has  a  ratio  of  unsupported  length  to  least 
width  greater  than  four  (see  Art.  7  and  Appendix  B).  Compression  mem- 
bers in  which  the  unsupported  length  to  least  width  is  four  or  less  are  referred 
to  as  piers.  Piers  may  or  may  not  be  reinforced  depending  upon  the  stresses 
to  which  they  are  subjected. 

Bending  stresses  in  columns  due  to  eccentric  loads  must  be  provided  for 
by  increasing  the  section  until  the  maximum  stress  does  not  exceed  the  allow- 
able. A  formula  for  homogeneous  columns  or  piers  follows.  Formulas  applic- 
able to  reinforced-concrete  columns  or  reinforced  piers  are  given  under  "Bend- 
ing and  Direct  Stress,"  Sect.  9. 

The  ordinary  formula  for  the  compressive  fiber  stress  due  to  eccentric 
loading  upon  solid  rectangular  columns  or  piers  of  homogeneous  materials 
(Fig.  1)  is  as  follows: 

N  =  total  load. 
A  =  area  of  column. 
Xq  =  eccentricity. 
t  =  breadth  of  column. 


I 

i 


Fig. 


fc  =  total  unit  pressure  on  outer  fiber  nearest  to  line  of  vertical  pressure. 


Then 


0  +  "?) 


and  the  additional  intensity  of  compressive  stress  due  to  eccentric  loading  is  seen  to  be  equal 
N  6xo 

^""A'-T' 

3.  Columns  with  Longitudinal  Reinforcement. — Since  the  modulus  of  elasticity  of  a  mate- 
rial is  the  ratio  of  stress  to  deformation,  it  follows  that  for  equal  deformations  the  stresses  in  the 
steel  and  concrete  of  a  concrete  column  will  be  as  their  moduli  of  elasticity.  Thus 


or  fs   -  ScU 


fs  ^  E. 
fc  Ec 
Let  A  =  total  net  area. 
Ac  =  area  of  concrete. 
As  =  area  of  longitudinal  steel. 

As 

p  =  steel  ratio  =  ^  • 

fs  =  tensile  unit  stress  in  steel. 

fc  =  compressive  unit  stress  in  concrete. 

371 


372 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  8-4 


Es 

P  =  total  strength  of  a  reinforced  column  for  the  stress  fc. 

Then 

P  =fcAc  +fsAs  =fc{A  -  vA)  +fcnpA 

or 

P  =  fcA  [1  +  (n  - 

Tests^  on  columns  with  vertical  steel  bar  reinforcement  indicate  that  the  steel  may  be 
counted  upon  in  design  to  take  its  portion  of  the  loading  as  computed  from  the  above  equation. 

The  economy  of  steel  reinforcement  is  dependent  upon  the  working  stresses  permissible 
in  the  concrete  and  the  value  of  n,  since  the  stress  in  the  steel  =  fcTi.  The  stresses  in  the  steel 
will  be  relatively  low  except  in  the  unusual  combination  of  high  working  stresses  in  the  com- 
crete  with  a  large  value  of  n. 

4.  Columns  with  Hooped  and  Longitudinal  Reinforcement. — Whenever  a  material  is 
subjected  to  compression  along  one  axis,  then,  as  a  consequence,  there  will  be  an  expansion  of 
the  material  along  axes  which  are  perpendicular  to  the  one  first  considered.  Thus,  if  the  mate- 
rial of  a  column  is  held  laterally,  then  lateral  compressive  stresses  are  developed  which  tend  to 
neutralize  the  effect  of  the  longitudinal  compressive  stresses  and  thus  to  increase  the  resistance 
against  failure.  This  is  the  principle  involved  in  the  use  of  spiral  or  banded  reinforcement. 
The  addition  of  bands  or  spirals  to  columns  having  longitudinal  reinforcement  does  not  have 
much  effect  upon  the  deformation  of  such  -columns  up  to  the  point  of  failure  without  hooping. 
In  fact  the  elastic  limit  and  rigidity  of  the  column  appears  to  be  decreased  if  anything.  The 
effect  of  such  hooping,  however,  raises  slightly  the  ultimate  strength  and  increases  the  capacity 
of  the  column  to  deform  at  loads  beyond  the  elastic  limit,  so  that  a  somewhat  higher  working 
stress  may  be  employed  on  the  concrete  than  for  plain  concrete  columns.  Tests  show  that  about 
1  %  of  a  closely  spaced  spiral  of  high-carbon  steel  is  sufficient  to  prevent  the  longitudinal  rods 
from  bulging  outward  and  will  provide  a  satisfactory  amount  of  toughness  with  a  corresponding 
raising  of  the  ultimate  strength  beyond  the  elastic  limit. 

The  following  notation  will  be  used  for  hooped  reinforcement. 

Let  di  =  diameter  of  enclosed  concrete  to  center  line  of  hooping. 
Ah  =  sectional  area  of  one  strand  of  hooping  for  given  pitch, 
s  =  pitch  allowed. 

Ih  =  length  of  hooping  in  1  ft.  in  height  of  column, 
p  =  percentage  of  hooping. 


Then 

For  p  =  1% 
Also 


Ah=  ^ 


spdi 


(0.0025)  (s)((ii)  or 


AhIh  ='^'(12)  (0.01) 


0.0025di 


37.7rfi 

ih  =  —  

s 

Results  for  banded  and  spiral  reinforcement  will  not  differ  appreciably  and  the  above 
formulas  may  be  used  for  both  bands  and  spirals. 

5.  Columns  Reinforced  with  Structural-steel  Shapes. — If  a  structural-steel  column  is 
designed  to  take  all  the  load  and  then  is  simply  fireproofed  with  a  covering  of  concrete,  it 

»  For  tests  on  columns,  see  "Concrete,  Plain  and  Reinforced,"  by  Taylor  and  Thompson,  3d  Edition,  1916. 


Sec.  8-6] 


COLUMNS 


373 


cannot  properly  be  called  a  reinforced-concrete  column.  To  be  classed  under  this  heading  the 
steel  must  be  designed  so  that  it  takes  a  load  in  combination  with  the  concrete;  that  is,  the 
steel  must  be  figured  in  the  same  way  as  vertical  rods  and  the  stresses  determined  by  the  formu- 
las previously  given. 

Structural-steel  reinforcement  is  sometimes  in  the  form  of  a  cross  in  the  center  of  the  column 
or  more  often  angles  are  employed  connected  by  riveted  latticing.  Tests  of  columns  of  this 
character  generally  show  lower  ultimate  strength  than  similar  columns  reinforced  with  the  same 
quantity  of  steel  in  the  form  of  vertical  rods.  This  is  most  likely  due  to  the  difficulty  of  prop- 
erly placing  the  concrete  around  the  steel,  and,  furthermore,  to  the  fact  that  the  adhesion  of 
concrete  to  steel  where  the  latter  presents  broad  flat  surfaces  is  not  good. 

To  be  able  to  count  upon  the  concrete  in  columns  reinforced  with  structural  forms,  the 
steel  should  be  well  enclosed  either  by  the  form  itself  or  by  means  of  bands  or  hooping.  How- 
ever, when  the  amount  of  steel  becomes  very  large,  the  relative  value  of  the  concrete  becomes 
more  uncertain,  and  it  would  be  good  design  to  neglect  its  element  of  strength. 

6.  Working  Stresses. — Working  stresses  recommended  by  the  Joint  Committee  are  given 
in  Art.  7. 

7.  Recommendations  of  the  Joint  Committee. — The  form  given  below  is  essentially  that 
of  the  Special  Committee  on  Concrete  and  Reinforced  Concrete  of  the  American  Society  of 
Civil  Engineers,  Proc.  Am.  Soc.  C.  E.,  Dec,  1916,  p.  1688. 

By  columns  are  meant  compression  members  of  which  the  ratio  of  unsupported  length  to  least  width 
exceeds  about  four,  and  which  are  provided  with  reinforcement  of  one  of  the  forms  hereafter  described. 

It  is  recommended  that  the  ratio  of  unsupported  length  of  column  to  its  least  width  be  limited  to  15. 

The  effective  area  of  hooped  columns  or  columns  reinforced  with  structural  shapes  shall  be  taken  as  the  area 
within  the  circle  enclosing  the  spiral  or  the  polygon  enclosing  the  structural  shapes. 

Columns  may  be  reinforced  by  longitudinal  bars;  by  bands,  hoops,  or  spirals,  together  with  longitudinal  bars; 
or  by  structural  forms  which  are  sufficiently  rigid  to  have  value  in  themselves  as  columns.  The  general  effect  of 
closely  spaced  hooping  is  to  greatly  increase  the"  toughness  of  the  column  and  to  add  to  its  ultimate  strength, 
but  hooping  has  little  effect  on  its  behavior  within  the  limit  of  elasticity.  It  thus  renders  the  concrete  a  safer  and 
more  reliable  material,  and  should  permit  the  use  of  a  somewhat  higher  working  stress.  The  beneficial  effects  of 
toughening  are  adequately  provided  by  a  moderate  amount  of  hooping,  a  larger  amount  serving  mainly  to  increase 
the  ultimate  strength  and  the  deformation  possible  before  ultimate  failure. 

Composite  columns  of  structural  steel  and  concrete,  in  which  the  steel  forms  a  column  by  itself,  should  be 
designed  with  caution.  To  classify  this  type  as  a  concrete  column  reinforced  with  structural  steel  is  hardly  per- 
missible, as  the  steel  generally  will  take  the  greater  part  of  the  load.  When  this  type  of  column  is  used,  the  con- 
crete should  not  be  relied  upon  to  tie  the  steel  units  together  nor  to  transmit  stresses  from  one  unit  to  another.  The 
units  should  be  adequately  tied  together  by  tie-plates  or  lattice  bars,  which,  together  with  other  details,  such  as 
splices,  etc.,  should  be  designed  in  conformity  with  standard  practice  for  structural  steel.  The  concrete  may  exert 
a  beneficial  effect  in  restraining  the  steel  from  lateral  deflection  and  also  in  increasing  the  carrying  capacity  of  the 
column.  The  proportion  of  load  to  be  carried  by  the  concrete  will  depend  on  the  form  of  the  column  and  the 
method  of  construction.  Generally  for  high  percentages  of  steel,  the  concrete  will  develop  relatively  low  unit 
stresses,  and  caution  should  be  used  in  placing  dependence  on  the  concrete. 

The  following  recommendations  are  made  for  the  relative  working  stresses  in  the  concrete  for  the  several 
types  of  columns: 

(a)  For  concentric  compression  on  a  plain-concrete  pier,  the  length  of  which  does  not  exceed  four  diameters, 
22.5%  of  the  compressive  strength  may  be  allowed. 

(6)  Columns  with  longitudinal  reinforcement  to  the  extent  of  not  less  than  1  %  and  not  more  than  4  %,  and 
with  lateral  ties  of  not  less  than  J-i  in.  in  diameter,  12  in.  apart,  nor  more  than  16  diameters  of  the  longitudinal 
bar:  the  unit  stress  recommended  for  (a). 

(c)  Columns  reinforced  with  not  less  than  1  %  and  not  more  than  4  %  of  longitudinal  bars  and  with  circular 
hoops  or  spirals  not  less  than  1  %  of  the  volume  of  the  concrete  and  as  hereinafter  specified:  a  unit  stress  55% 
higher  than  given  for  (a),  provided  the  ratio  of  unsupported  length  of  column  to  diameter  of  the  hooped  core  is  not 
more  than  10. 

The  foregoing  recommendations  are  based  on  the  following  conditions: 

It  is  recommended  that  the  minimum  size  of  columns  to  which  the  working  stresses  may  be  applied  be  12  in., 
out  to  out. 

The  hoops  or  bands  are  not  to  be  counted  on  directly  as  adding  to  the  strength  of  the  column. 

Longitudinal  reinforcement  bars  should  be  maintained  straight,  and  shall  have  sufficient  lateral  support 
to  be  securely  held  in  place  until  the  concrete  has  set. 

Where  hooping  is  used,  the  total  amount  of  such  reinforcement  shall  not  be  less  than  1  %  of  the  volume  of  the 
column,  enclosed.    The  clear  spacing  of  such  hooping  shall  be  not  greater  than  one-sixth  the  diameter  of  the  en- 


374 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  8-8 


closed  column,  and  preferably  not  greater  than  one-tenth,  and  in  no  case  more  than  2H  in.  Hooping  is  to  be 
circular  and  the  ends  of  bands  must  be  united  in  such  a  way  as  to  develop  their  full  strength.  Adequate  means 
must  be  provided  to  hold  bands  or  hoops  in  place  so  as  to  form  a  column,  the  core  of  which  shall  be  straight  and 
well-centered.  The  strength  of  hooped  columns  depends  very  much  upon  the  ratio  of  length  to  diameter  of  hooped 
core,  and  the  strength  due  to  hooping  decreases  rapidly  as  this  ratio  increases  beyond  five.  The  working  stresses 
recommended  are  for  hooped  columns  with  a  length  of  not  more  than  10  diameters  of  the  hooped  core.  The  Com- 
mittee has  no  recommendations  to  make  for  a  formula  for  working  stresses  for  columns  longer  than  10  diameters. 

Bending  stresses  due  to  eccentric  loads,  such  as  unequal  spans  of  beams,  and  to  lateral  forces,  must  be  pro- 
vided for  by  increasing  the  section  until  the  maximum  stress  does  not  exceed  the  values  above  specified.  Where 
tension  is  possible  in  the  longitudinal  bars  of  the  column,  adequate  connection  between  the  ends  of  the  bars  must 
be  provided  to  take  this  tension. 

8.  Tables  and  Diagrams. — Table  1  gives  the  allowable  load  P  for  different  sizes  and  shapes 
of  columns  reinforced  with  longitudinal  bars  and  reinforced  with  both  longitudinal  bars  and  spiral 
reinforcement.  The  area  of  longitudinal  steel  is  given  for  each  size  of  column  and  percentage 
of  reinforcement.  It  is  assumed  that  the  longitudinal  bars  in  the  round  and  octagonal  columns 
are  arranged  to  form  a  circle  in  the  cross-section  of  the  column  with  the  hooping  immediately 
outside  this  circle. 

Table  2  gives  the  sectional  area  of  hooping  and  length  of  hooping  per  foot  of  column  for 
a  maximum  pitch  of  one-sixth  (3-^)  the  diameter  of  the  enclosed  concrete  but  not  to  exceed  2}-2 
in.  according  to  the  recommendations  of  the  Joint  Committee  (see  Art.  7).  For  some  diam- 
eters, values  are  given  for  a  pitch  of  about  one-tenth  {}io)  the  diameter  of  enclosed  concrete. 
This  table  can  be  used  for  spiral  reinforcement  without  material  error. 

Table  3  gives  the  volume  of  column  in  cubic  feet  per  foot  of  length  for  diameter  D. 

The  column  diagram  given  can  be  used  for  either  designing  or  reviewing  designs  of  columns. 

Ili^ustrative  Problem. — What  size  of  square  column  reinforced  with  2%  of  longitudinal  steel  and  with  the 
required  number  of  lateral  ties  will  be  required  to  support  a  centrally  applied  load  of  900,000  lb.?  A  3000-lb. 
concrete  is  to  be  used  and  the  unsupported  length  of  column  is  less  than  15  diameters. 

From  Art.  3, 

P 


P  =  fcA[l  +  (n  -  Dp] 


Ml  +  {n-  Dp] 


From  Art.  7(6),  fc  =  22.5%  of  -3000  lb.  =  675  lb.  per  sq.  in.  Also  n  =  10  (see  Appendix  B).  Then  the 
effective  area  of  column 

 900.000   _  900,000  _ 

~  675[1  +  (10  -  1)(0.02^]  ~      797     ~  ^^^^ 

The  value  of /c[l  -f  (n  —  1)]  =  797  may  be  obtained  directly  from  the  column  diagram. 
The  side  of  effective  square  area 

d  =  ■v/1130  =  33.6  in.,  say  34  in. 

A  column  37  in.  square  will  suffice  considering  D/i  in.  of  concrete  all  around  as  fireproofing. 

The  problem  may  be  readily  solved  by  using  Table  1.  For  a  3000-lb.  concrete  and  p  =  0.02,  we  find  that  a 
column  36  in.  square  will  support  868,000  lb.  and  a  37-in.  square  column  will  support  922,000  lb.  Thus  a  column 
37  in.  square  is  ample. 

Illustrative  Problem. — What  size  of  round  column  and  area  of  longitudinal  steel  will  be  required  to  sup- 
port a  load  of  1,100,000  lb.?  A  3000-lb.  concrete  is  to  be  used  with  1  %  of  spiral  reinforcement.  Unsupported 
length  is  less  than  10  diameters.    Take  p  =  0.025  and  n  =  10. 

From  Art.  7(c)  we  find  that  the  value  of /c  may  be  taken  55%  greater  than  for  (a),  or  (1.55) (3000) (0.225^)  = 
1050  lb.  per  sq.  in. 

Then  from  Art.  3 

P  =  fcA[l  +  (n  -  Dp] 
The  column  diagram  shows  /c[l  +  (w  —  l)p]  =  1287.  Therefore 

P  =  1287(A)  or  A  =  ^'^^287^^  ^ 


!^^  =  855         d  =  \[^^  =  SSiu.        D  =  36in. 

4  ^  TT 

As  =  (0.025) (855)  =  21.4  sq.  in. 

From  Table  1  we  find  directly  that  a  36-in.  column  will  be  of  sufficient  size  and  that  As  =  21.4  sq.  in. 

Table  2  shows  that  for  a  column  with  d  =  33  in.,  the  pitch  of  spiral  should  not  exceed  2V2  in.,  with  a  sectional 
area  o£  spiral  of  0.206  sq.  in.  and  with  a  length  of  spiral  per  foot  of  column  height  of  498  ia. 


Sec,  8-8] 


COLUMNS 


375 


Table  1.— Use  for  Round,  Octagonal  and  Square  Columns 
P  -  fcA[l  +  (n  -  l)p]        A>  =  pA 
D  =  outside  diameter.    For  octagonal  columns  D  =  short  diameter.    For  square  colomns  D  =  side 

A  »        for  round  and  octagonal  columns. 
A  =      for  square  columns. 


of  square. 


1:2:4  (2,000-lb.  concrete) 

1  :  11/2  :  3 

(2,500-lh.  concrete) 

1:1:2 

( 3, 000-1 b.  concrete) 

n  =  15 

n  =  12 

n  =  10 

A, 
(sa.  in.) 

og 

eg 

1  %  spiral 
/c  =  7001b. 

1  %  spiral 
/e  =  8701b. 

1  %  spiral 
/c=  1,050 

^§ 

fc  =  4^0  lb. 

fc  =  565  lb. 

fc  =  675  lb. 

amet( 
umns 

ctive 
olum 

per  sq 

.  in. 

per  sq.  in. 

per  sq.  in. 

per  sq.  in. 

per  sq.  in. 

lb.  per 
sq.  in. 

0) 

i-i 

o 

onal 

C3 

-d 

M 

Qg 

Square 

Round 

Round 

Square 

Round 

Round 

Square 

Round 

Round 

3 
D* 

c 

3 

03 

W  o 

or  oct. 

or  oct. 

or  oct. 

or  oct. 

or  Oct. 

or  oct. 

O 
« 

O 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  =  0.01 

10 

7 

25,100 

19,700 

30,700 

30,700 

24,100 

37,200 

36,100 

28,300 

44,100 

0.5 

0 

4 

11 

8 

32,800 

25,800 

40,100 

40,100 

31,500 

48,600 

47,100 

37,000 

57,600 

0.6 

0 

5 

12 

9 

41,500 

32,600 

50,800 

50.800 

39,900 

61,500 

59,600 

46,800 

72,800 

0.8 

0 

6 

13 

10 

51,300 

40,300 

62,700 

62,700 

49,300 

75,900 

73,600 

57,800 

89,900 

1.0 

0 

8 

14 

11 

62,100 

48,800 

75,800 

75,800 

59,600 

91,800 

89,100 

70,000 

103,800 

1.2 

1 

0 

1 5 

12 

73  900 

58  100 

90,200 

90,200 

71,900 

109,300 

106,000 

83  300 

129  700 

1.4 

1 

I 

16 

13 

86!  700 

681200 

105^900 

105^900 

83^500 

128,' 200 

124^400 

97;600 

152^000 

1.7 

1 

3 

17 

14 

100,700 

79,000 

122,300 

122,800 

96,600 

148,700 

144,200 

113,200 

176,000 

2.0 

1 

5 

18 

15 

115,500 

90,800 

141,000 

141,000 

110,800 

171.000 

166,000 

130,000 

;j03,000 

2.3 

1 

3 

19 

16 

131,500 

103,200 

161,000 

161,000 

126,100 

194.000 

183,000 

148,000 

230,000 

2.6 

2 

0 

20 

17 

148,300 

116,400 

181.000 

181,000 

142,300 

219,000 

213.000 

167,000 

260,000 

2.9 

2 

3 

21 

18 

166,000 

130,500 

203,000 

203,000 

159,000 

246.000 

239,000 

188,000 

291,000 

3.2 

2 

6 

22 

19 

185,000 

145,500 

220,000 

226,000 

178,000 

274,000 

266,000 

209.000 

325,000 

3.6 

2 

8 

23 

20 

205.000 

161,000 

251,000 

251,000 

197,000 

303,000 

295,000 

231.000 

360,000 

4.0 

3 

1 

24 

21 

226,000 

178,000 

276,000 

276,000 

217,000 

335,000 

325,000 

255,000 

397,000 

4.4 

3 

5 

25 

22 

249,000 

195,000 

303,000 

303,000 

235,000 

367,000 

356,000 

280,000 

435,000 

4.8 

3 

8 

26 

23 

272,000 

213,000 

332,000 

332,000 

260,000 

401,000 

389,000 

306,000 

476,000 

5.3 

4 

2 

27 

24 

295,000 

232,000 

361,000 

361,000 

283,000 

437,000 

424,000 

333,000 

518,000 

5.8 

4 

5 

28 

25 

321,000 

252,000 

392,000 

392,000 

308,000 

474,000 

460,000 

361,000 

562,000 

6.3 

4 

9 

29 

26 

347,000 

272,000 

424,000 

424,000 

333,000 

513,000 

498,000 

381,000 

608,000 

6.8 

5 

3 

30 

27 

374,000 

294,000 

457,000 

457,000 

359,000 

553,000 

537,000 

422,000 

656,000 

7.3 

5 

7 

31 

28 

403,000 

316,000 

491,000 

491,000 

386,000 

595,000 

577,000 

453,000 

705,000 

7.8 

6 

2 

32 

29 

432,000 

339,000 

527,000 

527,000 

414,000 

638,000 

619,000 

486,000 

757.000 

8.4 

6 

6 

33 

30 

462,000 

362,000 

564,000 

564,000 

443,000 

683,000 

663,000 

520,000 

808,000 

9.0 

7 

1 

34 

31 

493,000 

387,000 

602,000 

602,000 

473,000 

729,000 

708,000 

555,000 

864,000 

9.6 

6 

35 

32 

526,000 

413,000 

642,000 

642,000 

504.000 

777,000 

755,000 

592,000 

922,000 

10.2 

I 

0 

36 

33 

559,000 

438,000 

683,000 

683,000 

536,000 

826,000 

802,000 

630,000 

980,000 

10.9 

8 

6 

37 

34 

593,000 

406,000 

725,000 

725,000 

569,000 

877,000 

851,000 

668,000 

1,039,000 

11.6 

1 

38 

35 

629,000 

494,000 

768,000 

768,000 

603,000 

929,000 

901,000 

708,000 

1,100,000 

12.3 

I 

6 

39 

36 

665,000 

523,000 

812,000 

812,000 

638,000 

983,000 

953,000 

750,000 

1,170,000 

13.0  10 

2 

40 

37 

703,000 

542,000 

858,000 

858,000 

675,000 

1,040,000 

1.007,000 

792,000 

1,230,000 

13.7  10 

8 

41 

38 

742,000 

582,000 

905,000 

905,000 

711,000 

1,100,000 

1,060,000 

835,000 

1,300,000 

14.4  11 

3 

42 

39 

780,000 

613,000 

954,000 

951,000 

749,000 

1,150,000 

1,120,000 

879,000 

1,370,000 

15.2  12 

0 

p  =  0.015 

10 

7 

26,700 

21,000 

32.600 

32,200 

25,300 

39,000 

37,500 

29,500 

45,900 

0.7 

0 

6 

11 

8 

34,900 

27,400 

42,600 

42,100 

33,100 

51,000 

49,100 

38,500 

59,900 

1.0 

0 

8 

12 

9 

44,100 

36,700 

53,900 

53,300 

41,800 

64,500 

62,100 

48,800 

75,800 

1.2 

1 

0 

13 

10 

54,500 

42,800 

66,500 

65,800 

51,700 

79,600 

76,600 

60,200 

93,600 

1.5 

1 

2 

14 

11 

65,900 

51,800 

80,500 

79,700 

62,500 

96,400 

92,700 

72,800 

113,200 

1.8 

1 

4 

15 

12 

78,500 

61,700 

95,800 

94,800 

74,400 

114,700 

110,300 

86,600 

134,800 

2.2 

1 

7 

16 

13 

92,100 

72,400 

112,400 

111,100 

87,400 

134,600 

129,400 

101,700 

158,000 

2.5 

2 

0 

17 

14 

106,800 

83,900 

130,400 

129,000 

101,300 

156,000 

150,000 

118,000 

183,000 

2.9 

2 

3 

18 

15 

122,700 

96,300 

150,000 

148,000 

116,400 

179,000 

172,000 

135,300 

211,000 

3.4 

2 

7 

19 

16 

139,500 

109,600 

170,000 

169,000 

132,300 

204,000 

196,000 

154,000 

240,000 

3.8 

3 

0 

20 

17 

157,500 

123,700 

192,000 

190,000 

149,400 

230,000 

221,000 

174,000 

271,000 

4.3 

3 

4 

21 

18 

176,500 

138,600 

216,000 

213,000 

168,000 

258,000 

249,000 

195,000 

304,000 

4.9 

3 

8 

22 

19 

196,800 

155,000 

240,000 

237,000 

187,000 

288,000 

277,000 

217,000 

338,000 

5.4 

4 

3 

23 

20 

218,000 

171,000 

266,000 

263,000 

207,000 

319,000 

307,000 

241,000 

374,000 

6.0 

4 

7 

24 

21 

240,000 

189,000 

293,000 

290,000 

228,000 

351,000 

338,000 

265,000 

413,000 

6.6 

5 

2 

25 

22 

264,000 

207,000 

322,000 

319,000 

250,000 

385,000 

371,000 

291,000 

453,000 

7.3 

5 

7 

26 

23 

288,000 

227,000 

352.000 

348,000 

273,000 

422,000 

415,000 

318,000 

495,000 

7.9 

6 

2 

27 

24 

314,000 

247,000 

383,000 

379,000 

297,000 

459,000 

442,000 

347,000 

538,000 

8.6 

6 

8 

23 

25 

341,000 

267,000 

416,000 

411,000 

323,000 

498,000 

479,000 

376,000 

585,000 

9.4 

7 

4 

29 

26 

368,000 

289,000 

450,000 

444,000 

349,000 

538,000 

518,000 

407.000 

633,000 

10. 1 

8 

0 

30 

27 

397,000 

312,000 

485,000 

480,000 

377,000 

581,000 

558,000 

439,000 

682,000 

10.9 

8 

6 

31 

28 

428,000 

335,200 

522,000 

516,000 

405,000 

624,000 

601,000 

465,000 

733,000 

11.8 

9 

2 

32 

29 

458,000 

360,000 

559,000 

554,000 

434,000 

670,000 

644,000 

506,000 

787,000 

12.6 

9 

9 

33 

30 

481,000 

385,000 

599,000 

593,000 

465,000 

716,000 

690,000 

541,000 

841,000 

13.5 

10 

6 

34 

31 

524,000 

412,000 

639,000 

632,000 

497,000 

765,000 

736,000 

577,000 

899,000 

14.4 

11 

3 

35 

32 

559,000 

438,000 

681,000 

674,000 

529,000 

816,000 

775,000 

616,000 

953,000 

15.4 

12.1 

36 

33 

594,000 

466,000 

724,000 

717,000 

563,000 

867,000 

835,000 

655,000 

1,019,000 

16.3 

12 

8 

•37 

34 

630,000 

495,000 

769,000 

761,000 

598,000 

921,000 

887,000 

696,000 

1,081,000 

17.3 

13 

6 

38 

35 

668,000 

525,000 

815,000 

806,000 

634,000 

976,000 

938,000 

737,000 

1,146,000 

18.4 

14 

4 

39 

36 

706,000 

555,000 

862,000 

853,000 

670,000 

1,032,000 

993,000 

770,000 

1,212,000 

19.4 

15 

3 

40 

37 

746,000 

586,000 

911,000 

901,000 

708,000 

1,090,000 

1,050,000 

824,000 

1,280,000 

20.5 

16 

1 

1  4^ 

38 

787,000 

618,000 

961,000 

950,000 

746,000 

1,150,000 

1,110,000 

868,000 

1,350,000 

21.7 

17 

0 

(42 

39 

829,000 

651,000 

1,012,000 

]  ,000,000 

786,000 

1,211,000 

1,170,000 

915,000 

1,420,000 

22.8 

17 

9 

376 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  8-8 


1:2:4 

(2,000-lb.  concrete) 

1:  VA:3 

(2,500-lb.  concrete) 

1:1:2 

(3,000-lb. 

concrete) 

n  =  15 

n  =  12 

n  =  10 

(sq. 

in.) 

1  %  spiral 
A  =  700  lb. 

1  %  spiral 
/c  =  8701b. 

1  %  spiral 

fc  =  450  lb. 

fc  =  565  lb. 

fc  =  675  lb. 

/c=  1,050 
lb.  per 
sq.  in. 

Diamet< 
columns 

tive 
lum: 

per  sq 

.  in. 

per  sq.  in. 

per  sq.  in. 

per  sq.  in. 

per  s 

q.  m. 

(U 

ta 

73  O 

of  c- 

Square 

Round 
or  oct. 

Round 
or  oct. 

Square 

Round 
or  oct. 

Round 
or  oct. 

Square 

Round 
or  oct. 

Round 
or  oct. 

Squi 

Roun 
octag 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

V  =  0.02 

10 

7 

28,200 

22,200 

34,500 

33,800 

26.500 

40,800 

.39,100 

30,700 

47,700 

1.0 

0.8 

11 

8 

36,900 

29,000 

45,000 

44,100 

34,600 

53,300 

51,000 

40,100 

62,300 

1.3 

1.0 

12 

9 

46,700 

36,700 

57.000 

55,700 

43,800 

67,500 

64,600 

50,700 

78,800 

1.6 

1.3 

13 

10 

57,600 

45,300 

70,400 

68,900 

54,100 

83,300 

79,700 

62,600 

97,400 

2.0 

1.6 

14 

11 

69,600 

54,800 

85,200 

83,400 

65,500 

100,800 

96,400 

75,800 

117,800 

2.-^ 

1.9 

15 

12 

83,000 

65,200 

101,300 

99,300 

78,000 

120,000 

114,600 

90,100 

140,000 

2.9 

2.3 

16 

13 

97,300 

76,500 

118,900 

116,500 

91,500 

140,800 

134,800 

105,800 

165,000 

3.4 

2.7 

17 

14 

113,000 

88,700 

137,900 

135,000 

106,100 

163,000 

156,000 

123,600 

191,000 

3.9 

3.1 

18 

15 

129,600 

101,800 

153,000 

155,000 

121,800 

187,000 

179,000 

140,900 

219,000 

4.5 

3.5 

19 

16 

147,400 

115,900 

180,000 

176,000 

138,600 

213,000 

204,000 

160.000 

249,000 

5,1 

4.0 

20 

17 

166,000 

130,700 

203,000 

199,000 

156,000 

241,000 

230,000 

181,000 

281,000 

5.8 

4.5 

21 

18 

187,000 

146,500 

228,000 

223,000 

175,000 

270,000 

258,000 

203.000 

316,000 

6  5 

5  1 

22 

19 

208,000 

163,000 

254,000 

249,000 

195,000 

301,000 

288,000 

226,000 

351,000 

7.2 

5^7 

23 

20 

230,000 

181,000 

281,000 

276,000 

217,000 

,333,000 

319,000 

250,000 

389,000 

8.0 

6  3 

24 

21 

254,000 

200,000 

310,000 

304,000 

239,000 

367,000 

351,000 

276,000 

430,000 

8.8 

6.9 

25 

22 

279,000 

219,000 

341,000 

333,000 

262,000 

403,000 

386,000 

303,000 

471,000 

9,7 

7.6 

26 

23 

305,000 

239,000 

372,000 

364,000 

286,000 

441,000 

422,000 

331,000 

515,000 

10.6 

8.3 

27 

24 

332,000 

261,000 

400,000 

397,000 

311,000 

480,000 

459,000 

361,000 

561,000 

11.5 

9.0 

28 

25 

360,000 

283,000 

440,000 

431,000 

338,000 

521,000 

498,000 

391,000 

608,000 

12.5 

9.9 

29 

26 

389,000 

306,000 

476,000 

466,000 

366,000 

563,000 

538,000 

423,000 

658,000 

13.5 

10.6 

30 

27 

420,000 

330,000 

513,000 

503,000 

395,000 

607,000 

581,000 

456,000 

710,000 

14.6 

11.5 

31 

28 

452,000 

355,000 

552,000 

540,000 

424,000 

653,000 

625,000 

491,000 

763,000 

15.7 

12.3 

32 

29 

485,000 

380,000 

592,000 

579,000 

455,000 

701,000 

670,000 

526,000 

818,000 

16.8 

13.2 

33 

30 

519,000 

407,000 

633,000 

620,000 

487,000 

750,000 

717,000 

563,000 

876,000 

18.0 

14. 1 

34 

31 

554,000 

435,000 

676,000 

662,000 

520,000 

801,000 

766,000 

603,000 

935,000 

19.2 

15.1 

35 

32 

590,000 

464,000 

721,000 

706,000 

5.54,000 

853,000 

817,000 

641,000 

997,000 

20.5 

16.1 

36 

33 

628,000 

493,000 

766,000 

750,000 

589,000 

907,000 

868,000 

682,000 

1,060,000 

21.8 

17.1 

37 

34 

666,000 

523,000 

814,000 

797,000 

625,000 

963,000 

922.000 

723,000 

1,125,000 

23.1 

18.2 

38 

35 

706,000 

555,000 

862,000 

844,000 

663,000 

1,021,000 

976,000 

767,000 

1,190,000 

24.5 

19.2 

39 

36 

746,000 

587,000 

912,000 

893,000 

702,000 

1,080,000 

1,032,000 

811,000 

1,260,000 

25.9 

20.4 

40 

37 

789,000 

620,000 

963,000 

943,000 

742,000 

1,141,000 

1,090,000 

857,000 

1,330,000 

27.4 

21.5 

41 

38 

832,000 

653,000 

1,016,000 

985,000 

782,000 

1,200,000 

1,150,000 

904,000 

1,410,000 

28.9 

22.7 

42 

39 

876,000 

688,000 

1,070,000 

1,048,000 

824,000 

1,270,000 

1,210,000 

952,000 

1,480,000 

30.4 

23.9 

p  =  0.025 

10 

7 

29,800 

23,400 

36,370 

35,300 

27,700 

42,700 

40,500 

31,800 

49,500 

1.2 

1.0 

11 

8 

38,900 

30,600 

47,500 

46,100 

362,00 

55,800 

52,900 

41,600 

64,700 

1.6 

1.3 

12 

9 

49,300 

38,700 

60,100 

58,200 

45,800 

70,600 

67,000 

52,600 

81,800 

2.0 

1.6 

13 

10 

60,800 

47,800 

74,200 

72,000 

56,500 

87,100 

82,700 

64,500 

101,000 

2.5 

2.0 

14 

11 

73,500 

57,800 

89,800 

87,100 

68,500 

105,400 

100,000 

78,600 

122,000 

3.0 

2.4 

15 

12 

87,600 

68,  sop 

106,900 

103,700 

81,500 

125,400 

119,000 

93,500 

145,600 

3.6 

2.8 

16 

13 

102,900 

80,700 

125,000 

121,800 

95,600 

147,200 

140,000 

109,800 

171,000 

4.2 

3.3 

17 

14 

119,200 

93.600 

145,000 

141,200 

111,000 

171,000 

162,000 

127,200 

198,000 

4.9 

3.9 

18 

15 

136,900 

107,500 

167,000 

162,000 

127,000 

196,000 

186,000 

146,100 

227,000 

5.6 

4.4 

19 

16 

156,000 

122,300 

190,000 

184,000 

145,000 

223,000 

212,000 

166,000 

259,000 

6.4 

5.0 

20 

17 

176,000 

138,000 

215.000 

208,000 

163,000 

252,000 

239,000 

188,000 

292,000 

7.2 

5.7 

21 

18 

197,000 

155,000 

240,000 

233,000 

183,000 

282,000 

268,000 

211,000 

328,000 

8.1 

6.4 

22 

19 

219,000 

173,000 

268,000 

260,000 

204,000 

314,000 

298,000 

235,000 

365,000 

9.0 

7.1 

23 

20 

243.000 

191,000 

297,000 

288,000 

226,000 

348,000 

331,000 

260,000 

404,000 

10.0 

7.9 

24 

21 

268,000 

211,000 

327.000 

317,000 

249,000 

384,000 

365,000 

286,000 

445,000 

11.0 

8.7 

25 

22 

295,000 

231,000 

359,000 

348,000 

274,000 

422,000 

400,000 

314,000 

489,000 

12.1 

9.5 

26 

23 

322,000 

253,000 

393,000 

381,000 

299,000 

461,000 

438,000 

344,000 

534,000 

13.2 

10.4 

27 

24 

351,000 

275,000 

428,000 

415,000 

325,000 

.502,000 

476,000 

374,000 

582,000 

14.4 

11.3 

28 

25 

380,000 

299,000 

464,000 

450,000 

353,000 

544,000 

517,000 

406,000 

631,000 

15.6 

12.3 

29 

26 

418,000 

323,000 

502,000 

486,000 

382,000 

589,000 

559,000 

439,000 

683,000 

16.9 

13.3 

30 

27 

443,000 

348,000 

541,000 

525,000 

413,000 

635,000 

603,000 

474,000 

736,000 

18.2 

14.3 

31 

28 

477,000 

374,000 

582,000 

565,000 

443,000 

683,000 

649,000 

509,000 

792,000 

19.6 

15.4 

32 

29 

512,000 

459,000 

594,000 

606,000 

476,000 

733,000 

696,000 

546,000 

850,000 

21.0 

16.5 

33 

30 

548,000 

430,000 

668,000 

648,000 

508,000 

784,000 

744,000 

535,000 

908,000 

22.5 

17.7 

34 

31 

585,000 

459,000 

713,000 

692,000 

544,000 

837,000 

795,000 

624,000 

970,000 

24.0 

18.9 

35 

32 

628,000 

489,000 

760,000 

738,000 

579,000 

892,000 

848,000 

665,000 

1,034,000 

25.6 

20.1 

36 

33 

663,000 

520,000 

808,000 

784,000 

616,000 

949,000 

901,000 

708,000 

1,100,000 

27.2 

21  .4 

37 

34 

703,000 

553,000 

858,000 

833,000 

654,000 

1,007,000 

958,000 

751,000 

1,170,000 

28.9 

22.7 

38 

35 

745,000 

585,000 

909,000 

882,000 

693,000 

1,070,000 

1,012,000 

796,000 

1,240,000 

30.6 

24.1 

39 

36 

789,000 

619,000 

962,000 

933,000 

733,000 

1,130,000 

1,110,000 

842,000 

1,310,000 

32.4 

25.5 

40 

37 

833,000 

654,000 

1,016,000 

985,000 

775,000 

1,190,000 

1,130,000 

889,000 

1,380,000 

34.2^26.9 

41 

38 

878,000 

690,000 

1,070,000 

1,040,000 

817,000 

1,260,000 

1,190,000 

938,000 

1,460,000  36.0  28.4 

42 

39 

925,000 

727,000 

1,130,000 

1,095,000 

860.000 

1,320,000 

1,260,000 

988,000 

1,540,000  38.0  29.9 

Sec.  8-8] 


COLUMNS 


377 


1:2:4 

(2,000-lb  concrete) 

1  :        :  3  (2,500-lb.  concrete) 

1:1:2 

(3,000-lb.  concrete) 

n  =  15 

71  =  12 

n  =  10 

A 

0)  OQ 

is 

1  %  spiral 
/c  =  7001b. 

1  %  spiral 
/c  =  8701b. 

1  ^0  Spiral 

'tl 

fc  =  450  1b. 

fc=  505  lb. 

fc  =  075  lb. 

/c=  1,050 

s  § 

per  sq.  in. 

per  sq.  in. 

per  sq.  in. 

per  sq.  in. 

per  sq.  in. 

sq.  in. 

Dia 
coll 

Effec 

of  CO 

Square 

Round 
or  Oct. 

Round 
or  oct. 

oquare 

Round 
or  oct. 

Round 
or  Oct. 

oquare 

Round 
or  Oct. 

Round 
or  oct. 

Squai 

Round 
octago: 

P  (lb.) 

P  (lb.) 

P  (lb). 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P(lb.) 

P  (lb.) 

P  =  0.03 

10 

7 

31,300 

24.600 

38,200 

30,800 

02  Qnr> 

44,500 

42  000 

00  000 

t3o,UUU 

51,400 

1 

5 

1 

2 

g 

41,900 

32,100 

50,000 

48^100 

0  /  ,oUU 

58,200 

01,oUU 

A'i  ^  no 

'iO,  lUU 

67,100 

1 

9 

1 

5 

12 

9 

51,800 

40^600 

03,200 

00,700 

1  /  ,oUU 

73,000 

no  400 

uy,'-rUU 

54  500 

84,900 

2 

4 

1 

9 

13 

10 

63,900 

50,200 

78,100 

75,100 

oy  ,uuu 

yu,yu() 

85  700 

07  300 

104,700 

3 

n 

2 

4 

14 

1 1 

77,300 

00,700 

94,500 

90,800 

/  I , 'JUU 

1  1  n  nnn 
1 10,000 

1 0*^  700 
luo,  /  uu 

81  45C 

126,700 

3 

6 

2 

9 

15 

12 

92,100 

72^300 

112,400 

losiloo 

oo,uuu 

1  Q  7  nnn 
1 0 1 ,  UUO 

1  9"^  "^00 

t70,  tjyjyj 

151,000 

4 

Q 

0 

3 

4 

16 

13 

108,000 

84,800 

132,000 

127,000 

QQ  7nn 

t  ^  1  nnn 

144  800 

1  1  Q  COO 
1  io,ouu 

177,000 

c 
0 

1 

4 

0 
6 

17 

14 

125,200 

98,200 

153,000 

147^200 

lie:  nnn 

1  7c  nnn 
1  /o,000 

1  fis  000 

1  Uo,UUU 

1  "^9  000 

205,000 

5 

Q 

y 

4 

18 

15 

143,900 

113^000 

170,000 

109^000 

1 oz,  /  uu 

ociA  nnn 

1  n  Q  000 
1  y«3,uuu 

1  K-l  000 
10  X  ,UUU 

236,000 

0 

0 
0 

5 

3 

19 

16 

164,000 

128^400 

200,000 

192,000 

10 1  ,uuu 

00 Q  nnn 

91  Q  000 

172  000 

268,000 

7 
i 

1 

6 

0 

20 

17 

185,000 

145,000 

220,000 

2 17]  000 

171,000 

203,000 

04.0  oon 

1 04  000 

1  £7^,UUW 

303,000 

8 

7 
i 

0 

8 
0 

21 

18 

207^000 

1 03,000 

253,000 

24  si  000 

191,000 

294,000 

070  000 

/  OjUUU 

910  000 
z  1  y  ,uuu 

339,000 

0 
y 

7 

7 

22 

19 

231^000 

181^000 

282,000 

271^000 

213,000 

328,000 

30Q  000 

94*^  000 

378,000 

1 0 

lU 

0 

8 

5 

23 

20 

256,000 

201,000 

312,000 

300^000 

230,000 

303,000 

'^4'^  000 

9fiQ  000 

419,000 

1 0 

n 
u 

9 

4 

24 

21 

282,000 

22l[000 

344,000 

331^000 

200,000 

401,000 

000 

0  /  0,  WO\7 

9Q7  000 

462,000 

13 

2 

10 

.4 

25 

22 

310!000 

243^000 

378,000 

3  03!  000 

286,000 

430,000 

415  000 

320,000 

507,000 

14 

0 

11 

.4 

26 

23 

338,000 

205^000 

413,000 

397^000 

312,000 

481,000 

453  000 

350,000 

555.000 

15 

Q 

y 

12 

.5 

27 

24 

368,000 

289!000 

450,000 

433!000 

349,000 

523,000 

494!000 

387^000 

004,000 

17 

3 

13 

.6 

28 

25 

A  no  oon 
40U,UUu 

314,UUU 

488,000 

Add  r\f\n 
409.000 

309,000 

508,000 

530,000 

421,000 

055,000 

18 

14 

.7 

29 

26 

432,000 

339,000 

528.000 

508,000 

399,000 

014,000 

579,000 

455,000 

708,000 

20 

15 

.9 

30 

27 

466,000 

306,000 

509,000 

548,000 

430,000 

002,000 

025,000 

491,000 

705,000 

21 

g 

17 

.2 

31 

28 

501,000 

393,000 

012,000 

588,000 

402,000 

712,000 

072,000 

528,000 

822,000 

23 

18 

.5 

32 

29 

537,000 

422,000 

057,000 

032,000 

496,000 

704,000 

721,000 

500,000 

8^1,000 

25 

2 

19 

.8 

33 

30 

575,000 

452,000 

703,000 

070,000 

531,000 

818,000 

772,000 

005,000 

943,000 

27 

.0 

21 

.2 

34 

31 

614,000 

482,000 

750.000 

722,000 

507,000 

873,000 

824,000 

040,000 

1,006,000 

28 

.8 

22 

.0 

35 

32 

655,000 

514,000 

799.000 

709,000 

004,000 

931,000 

878,000 

089,000 

1,072,000 

30 

.7 

24 

.1 

36 

33 

695,000 

540,000 

850.000 

818,000 

043,000 

990,000 

933,000 

733,000 

1,140,000 

32 

.7 

25 

.7 

37 

34 

739,000 

580,000 

902,000 

807,000 

082,000 

1,050,000 

991,000 

778,000 

1,210,000 

34 

.7 

27 

.2 

38 

35 

783,000 

015,000 

950,000 

920,000 

723,000 

1,113,000 

1,050,000 

825,000 

1,280,000 

30 

.8 

28 

.9 

39 

36 

829,000 

050,000 

1,012,000 

973,000 

765,000 

1,178,000 

1,120,000 

873,000 

1,360,000 

38 

.9 

30 

.5 

40 

37 

875,000 

087,000 

1,009,000 

1,028,000 

808,000 

1,240,000 

1,170,000 

921,000 

1,440,000 

41 

.1 

32 

.3 

41 

38 

923,000 

725.000 

1,127,000 

1,084,000 

852,000 

1,310,000 

1,240,000 

972,000 

1,510,000 

43 

.3 

34 

.0 

42 

39 

972,000 

704,000 

1,187,000 

1.140.000 

898,000 

1,380,000 

1,300,000 

1,023,000 

1,590,000 

45 

.6 

35 

.8 

p  =  0.035 

10 

7 

32,900 

25,800 

40,200 

38,400 

30,100 

40,400 

43,500 

34,200 

53.200 

1 

.7 

1 

.4 

M 

8 

42,900 

33,800 

52,400 

50,200 

39,400 

00,000 

50,800 

44,000 

69,400 

2 

2 

1 

.8 

12 

9 

54,300 

42.700 

00,400 

03,300 

49,800 

70,700 

72,000 

50,500 

87,900 

2 

8 

2 

.2 

13 

10 

67,100 

52,700 

81,900 

78,300 

61,500 

94,000 

88,800 

09,800 

108,500 

3 

5 

2 

.8 

14 

11 

81,100 

03.800 

99,100 

94,800 

75,500 

114,500 

107,500 

84,500 

131,300 

4 

2 

3 

.3 

15 

12 

96,500 

75.900 

118,000 

112,800 

88,600 

136,300 

127,800 

100,500 

156,000 

5 

0 

4 

0 

16 

13 

113,400 

89.100 

138.400 

132,100 

104,000 

160,000 

150,000 

117,900 

183,000 

5 

9 

4 

0 

17 

14 

131,500 

103.300 

101.000 

153,000 

120,000 

186,000 

174,000 

130,800 

213,000 

6 

9 

5 

4 

18 

15 

151,000 

118.700 

184,000 

170,000 

138,400 

213,000 

200,000 

155,000 

244,000 

7 

9 

0 

2 

19 

16 

172,000 

135,000 

210,000 

201.000 

158,000 

242,000 

227,000 

179,000 

279,000 

9 

0 

7 

0 

20 

17 

194,000 

152,000 

237,000 

220.000 

178,000 

274,000 

257,000 

202,000 

313,000 

10 

1 

7 

9 

21 

IS 

217,000 

171,000 

205,000 

254,000 

199,000 

307.000 

289,000 

220,000 

352,000 

11 

3 

8 

9 

22 

19 

242.000 

190,000 

296,000 

283,000 

222,000 

342,000 

320,000 

252,000 

391,000 

12 

7 

9 

9 

23 

20 

268,000 

211.000 

328,000 

313,000 

246,000 

379.000 

355,000 

279,000 

434,000 

14 

0 

11 

0 

24 

21 

296.000 

232,000 

301,000 

345,000 

271,000 

417,000 

392,000 

308,000 

478,000 

15 

4 

12 

1 

25 

22 

325,000 

255,000 

390,000 

379,000 

298,000 

458,000 

430,000 

338,000 

525,000 

17 

0 

13 

3 

26 

23 

355,000 

279,000 

433,000 

414,000 

325,000 

501,000 

470,000 

309,000 

500,000 

18 

5 

14 

5 

27 

24 

386.000 

303,000 

472,000 

451,000 

354,000 

545,000 

512,000 

402,000 

025,000 

20. 

2 

15 

8 

28 

25 

419,000 

329,000 

512,000 

490,000 

384,000 

592,000 

555,000 

435,000 

078,000 

21  . 

9 

17 

2 

29 

26 

453,000 

350,000 

554,000 

529,000 

416,000 

640,000 

000,000 

471.000 

733,000 

23. 

7 

18. 

0 

30 

27 

489,000 

384,000 

597,000 

571,000 

448,000 

090,000 

048,000 

509.000 

791,000 

25. 

5 

20. 

0 

31 

28 

520,000 

413,000 

042,000 

014,000 

482,000 

742,000 

097,000 

547,000 

850,000 

27. 

4 

21. 

5 

32 

29 

504,000 

443.000 

089,000 

059,000 

517,000 

796,000 

740,000 

580,000 

912,000 

29. 

5 

23. 

1 

33 

30 

004,000 

404,000 

737,000 

705,000 

553,000 

852,000 

800,000 

028,000 

970,000 

31. 

5 

24. 

7 

34 

31 

045.000 

500,000 

787,000 

752,000 

591,000 

910,000 

854.000 

070,000 

1,042,000 

33. 

7 

20. 

4 

35 

32 

088,000 

540,000 

839,000 

802,000 

020,000 

969,000 

910.000 

714.000 

1,110,000 

35.8 

28. 

1 

36 

33 

731,000 

574,000 

892,000 

853,000 

070,000 

1,031,000 

908.000 

700,000 

1,181,000 

38. 

1 

29. 

9 

37 

34 

770,000 

010,000 

947,000 

905,000 

711,000 

1,094,000 

1,027,000 

816,000 

1,254,000 

40. 

4 

31. 

8 

38 

35 

822,000 

040,000 

1,003,000 

959,000 

754,000 

1,159,000 

1,088,000 

855,000 

1,330,000 

42. 

8 

33. 

7 

39 

36 

870,000 

083,000 

1,002,000 

1,015,000 

798,000: 

l,230,00()i 

1,150,000 

904,000 

1,410,000 

45. 

3 

35. 

6 

40 

37 

919,000 

722.000 

1,120,000 

1,072,000 

842,000 

1,300,0001 

1,220,000 

955.000 

1,490,000 

47. 

8 

37. 

0 

41 

38 

969,000 

701,000 

1,180,000 

1,130,000 

888,0001 

1,370,000 

1,280,000 

1,007,000 

1,570,000 

50. 

6 

39. 

7 

42 

39 

1,021,000 

802,000 

1,250,000 

1,190,000 

930,000 

1,440,000 

1.350.000 

1,061,000 

1,050,000|53.2 

41. 

8 

378 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  8-8 


1:2:4 

(2,000-lb  concrete) 

1  :  IH  :  3 

(2,500-lb.  concrete) 

1:1:2 

(3,000-lb.  concrete) 

n  =  15 

n  =  12 

n  =  10 

A 

8 

1  %  spiral 
fc  =  700  lb. 

1  %  spiral 
/c  =  8701b. 

1  %  spiral 

O  m 

^  c 

fc  =  450  lb. 

fc  =  565  lb. 

fc  =  675  lb. 

/c==  1,050 

"S  2 
11 

tive 
•lum 

per  sq 

.  in. 

per  sq.  in. 

per  s 

q.  in. 

per  sq.  in. 

per  sq.  in. 

lb.  per 
sq.  in. 

u 

Round  or 
octagonal 

q2 

Effec 

of  CO 

Square 

Round 
or  Oct. 

Round 
or  oct. 

Square 

Round 
or  oct. 

Round 
or  oct. 

Square 

Round 
or  Oct. 

Round 
or  oct. 

Squa 

P  (lb.) 

P  (lb.) 

P  (lb). 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

V  =  0.04 

10 

7 

34,400 

27.000 

42,000 

39,900 

31.300 

48,200 

45,000 

35,300 

55,000 

2 

0 

1 

5 

11 

8 
9 

44.900 

35.300 

54,900 

52,100 

41,000 

63,000 

58,800 

46,200 

71,800 

2 

6 

2 

0 

12 

56,900 

44.600 

69,500 

65,800 

51,800 

79, 700 

74,400 

58,400 

90,900 

3 

2 

2 

5 

13 

10 

70,200 

55.100 

85,800 

81,400 

64,000 

98,400 

91,800 

72,100 

112,200 

4 

0 

3 

1 

14 

11 

84,900 

66.700 

103.800 

98,500 

77,400 

119,100 

111,000 

87,300 

135,800 

4 

8 

3 

8 

15 

12 

101,000 

79,400 

123,500 

117,200 

92,000 

141,700 

132,200 

103,800 

162,000 

5 

8 

4 

5 

16 

13 

118,600 

93,200 

144,900 

137,600 

108,100 

166,000 

155,000 

121,900 

190,000 

6 

8 

5 

3 

17 

14 

137,500 

108,000 

168,000 

160,000 

125,300 

193,000 

180,000 

141,400 

220,000 

7 

8 

6 

2 

18 

15 

158,000 

124,000 

193.000 

183,000 

143.900 

221,000 

207,000 

162,000 

252,000 

9 

0 

7 

.1 

19 

16 

180,000 

141,200 

220,000 

208,000 

164,000 

252,000 

235,000 

185,000 

287,000 

10 

2 

8 

0 

20 

17 

203,000 

159,000 

248,000 

235,000 

185,000 

234,000 

265,000 

208,000 

324,000 

11 

6 

9 

.1 

21 

18 

227,000 

179,000 

278,000 

264.000 

207,000 

319,000 

297.000 

234,000 

364,000 

13 

0 

10 

.2 

22 

19 

253,000 

199,000 

310,000 

294,000 

231,000 

355,000 

331.000 

261,000 

405,000 

14 

4  11 

.3 

23 

20 

281,000 

221,000 

343,000 

326,000 

256,000 

394,000 

367.000 

289,000 

448,000 

16 

0  12 

6 

24 

21 

310,000 

243,000 

378,000 

349,000 

282,000 

434,000 

405.000 

318,000 

495,000 

17 

6 

13 

.9 

25 

22 

830,000 

267,000 

415,000 

394,000 

309,000 

476,000 

445,000 

349,000 

543,000 

19 

4  15 

.2 

26 

23 

371,000 

292.000 

454,000 

430,000 

338,000 

521,000 

486,000 

382,000 

593,000 

21 

2  16.6 

27 

24 

404,000 

317.000 

494,000 

468,000 

368,000 

567,000 

529,000 

415,000 

646,000 

23 

0  18 

1 

28 

25 

439,000 

345,000 

536,000 

509,000 

399,000 

615,000 

574,000 

451,000 

701,000 

25 

0  19 

.6 

29 

26 

474,000 

373,000 

580,000 

550,000 

432,000 

665.000 

620,000 

487,000 

758,000 

27 

0  21 

.2 

30 

27 

512,000 

402,000 

625,000 

593,000 

466,000 

717,000 

670,000 

526,000 

818,000 

29 

2 

22 

.9 

31 

28 

551,000 

432,000 

672,000 

638,000 

501,000 

772,000 

720,000 

565,000 

880,000 

31 

4 

24 

.6 

32 

29 

591,000 

464,000 

721,000 

685,000 

538,000 

828,000 

772,000 

606,000 

943,000 

33 

6 

26 

4 

33 

30 

632,000 

496,000 

772,000 

733,000 

575,000 

886,000 

826,000 

648,000 

1,009,000 

36 

0 

28 

.3 

34 

31 

675,000 

530,000 

824,000 

782,000 

614,000 

946,000 

882,000 

693,000 

1,080,000 

38 

4 

30 

2 

35 

32 

719,000 

665,000 

878.000 

834,000 

655,000 

1,008,000 

940.000 

738,000 

1,150,000 

41 

0 

32 

2 

36 

33 

764,000 

601.000 

934.000 

886,000 

698,000 

1,072,000 

1.000.000 

785,000 

1,220,000 

43 

6 

34 

2 

37 

34 

811,000 

637,000 

991.000 

941,000 

739,000 

■  1,140,000 

1.060.000 

834,000 

1,300,000 

46 

2 

36 

.3 

38 

35 

860,000 

675,000 

1,051,000 

996,000 

784,000 

1.210,000 

1,130,000 

883,000 

1,370,000 

49 

0 

38 

.5 

39 

36 

910,000 

715,000 

1,112,000 

1,054,000 

828,000 

1,280,000 

1,190,000 

935,000 

1,450,000 

51 

8 

40 

.7 

40 

37 

961,000 

755,000 

1,170,000 

1,110,000 

876,000 

1,350,000 

1,260.000 

987,000 

1,540,000 

54 

0 

43 

.0 

41 

38 

1,014,000 

796,000 

1,240,000 

1,180,000 

923,000 

1.420.000 

1,330,000 

1,0.0,000 

1,620,000 

57 

8 

45.4 

42 

39 

1,068,000 

838,000 

1,300,000 

1,240,000 

973,000 

1,500,000 

1,400,000 

1,097,000 

1,710,000 

60 

.8 

47 

.8 

V  =  0.045 

10 

7 

36,000 

28,100 

43,900 

41,400 

32,500 

50,100 

46,500 

36,500 

56,800 

2 

2 

1 

.7 

11 

8 

47,000 

36,900 

57,400 

54,100 

42,500 

65,400 

60,700 

47,700 

74,200 

2 

9 

2 

.3 

12 

9 

59,500 

46.700 

72,600 

68,400 

53,800 

82,800 

71,800 

60,300 

93,800 

3 

7 

•2 

.9 

13 

10 

73,400 

57.500 

89,600 

84,500 

66,400 

101,200 

94,800 

74,500 

115,900 

4 

5 

3 

.5 

14 

11 

88,800 

69,700 

108,400 

102,200 

80,300 

123,600 

114,800 

90,100 

140,200 

5 

4 

4 

3 

15 

12 

105,700 

83,000 

129,000 

121,700 

95,500 

147,000 

136,500 

'107,200 

167,000 

6 

5 

5 

1 

16 

13 

124,000 

97.500 

151,000 

142,800 

112,200 

173,000 

160,000 

126,000 

196,000 

7 

6 

6 

0 

17 

14 

143,800 

113,000 

176,000 

165,600 

130,000 

200,000 

186,000 

146,000 

227,000 

8 

8 

6 

9 

18 

15 

165,000 

130.000 

202,000 

190,000 

149,000 

230,000 

213,000 

168,000 

261,000 

10 

2 

8 

0 

19 

16 

188,000 

148,000 

229,000 

216,000 

170,000 

262,000 

243,000 

191,000 

297.000 

11 

5 

9 

0 

20 

17 

212,000 

167,000 

259,000 

244,000 

192,000 

295,000 

274,000 

215,000 

335.000 

13 

0 

10.4 

21 

18 

238,000 

187,000 

290,000 

274,000 

215,000 

331,000 

307,000 

242,000 

376.000 

14 

6 

11 

5 

22 

19 

265,000 

208,000 

324,000 

305,000 

240,000 

369,000 

342,000 

269,000 

418,000 

16 

3 

12 

8 

23 

20 

294,000 

231,000 

358,000 

338,000 

265,000 

409,000 

389,000 

298,000 

463.000 

18 

0 

14 

1 

24 

21 

323,000 

254,000 

395,000 

372,000 

293,000 

451,000 

418,000 

329,000 

511.000 

19 

9 

15 

6 

25 

22 

356,000 

279,000 

434,000 

409,000 

321,000 

495,000 

459,000 

361,000 

561,000 

21 

8 

17 

1 

26 

23 

388,000 

305,000 

474,000 

447,000 

351,000 

541,000 

502,000 

394,000 

613.000 

23 

8 

18.7 

27 

24 

423,000 

332,000 

516,000 

486,000 

384,000 

589,000 

546,000 

418,000 

668.000 

25 

9 

20 

3 

28 

25 

459,000 

365,000 

560,000 

528,000 

415,000 

639,000 

593,000 

465,000 

724.000 

28 

1 

22 

1 

29 

26 

496,000 

390.000 

606,000 

571,000 

448.000 

691,000 

641,000 

503,000 

783.000 

30 

4 

23 

9 

30 

27 

535,000 

420.000 

653,000 

616,000 

484,000 

745,000 

691,000 

543,000 

845.000 

32 

8 

25 

8 

31 

28 

576,000 

452,000 

703,000 

663,000 

520,000 

801,000 

744,000 

584,000 

908.000 

35 

3 

27 

7 

32 

29 

617,000 

485,000 

754,000 

711,000 

558,000 

859,000 

805,000 

626,000 

974.000 

37 

9 

29.7 

33 

30 

661,000 

518,000 

807,000 

760,000 

597,000 

920,000 

854,000 

670,000 

1,042.000 

40 

5 

31 

8 

34 

31 

705,000 

554,000 

861,000 

812,000 

638,000 

982,000 

911,000 

715,000 

1,110,000 

43. 

3 

34 

0 

35 

32 

752,000 

590,000 

918,000 

865,000 

679,000 

1,046,000 

971,000 

762,000 

1,190,000 

46. 

1 

36 

2 

36 

33 

800,000 

628,000 

976,000 

920,000 

723,000 

1,110,000 

1,032,000 

812,000 

1.260.000 

49. 

0 

38 

5 

37 

34 

849,000 

666.000 

1,036,000 

977,000 

767,000 

1,180,000 

1,100,000 

861,000 

1,340.000 

51. 

9 

40 

8 

38 

35 

899,000 

706.000 

1,098,000 

1,035,000 

813,000 

1,250,000 

1,160,000 

913,000 

1,4'?0,000 

55. 

2 

43 

3 

39 

36 

951,000 

747.000 

1,160,000 

1,094,000 

860,000 

1,320,000 

1,230,000 

965,000 

l,5u0,000 

58. 

3 

45 

7 

40 

37 

1,005,000 

790.000 

1,230,000 

1,160,000 

910,000 

1,400,000 

1,300,000 

1,020,000 

1,590,000 

61. 

5 

48.4 

41 

38 

1,060,000 

833,000 

1,290,000 

1,220,000 

958,000 

1,480,000 

1,370,000 

1,075,000 

1,670,000 

65. 

0 

51. 

0 

42 

39 

1,109.000 

877,000 

1,360,000 

1.290,000 

1,010,000 

1,550,000 

1,440,000 

1,130,000 

1,760,000 

68. 

4 

53. 

8 

I    Sec.  8-8J  COLUMNS  379 


1:2:4 

(2,000-lb.  concrete) 

1:  1}^  :  3  (2,500-lb.  concrete) 

1:1:2 

(3,000-lb.  concrete) 

TO  =  15 

n  =  12 

re  =  10 

At 

fan.  in."> 

meter  of 
mns  (D) 

1  %  spiral 
/c  =  7001b. 

1  %  spira! 
/c  =  8701b 

1  %  spiral 

t3  on 

fc  =  450  lb. 

fc  =  565  lb. 

fc  =  675  lb. 

/c=  1,050 

>  6 

per  sq.  in. 

per  sq.  in. 

per  sq.  in. 

per  sq.  in 

per  sq.  in. 

lb.  per 
sq.  in. 

V 

(.< 

0  ee 

51 

Square 

Round 

Round 

Square 

Round 

Round 

Square 

Round 

Round 

cfl 
3 
O* 

c  be 

or  oct. 

or  oct. 

or  oct. 

or  oct. 

or  oct. 

or  oct. 

tc 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

P  (lb.) 

p  =  0.05 

10 

7 

37,500 

29,400 

45,800 

42,900 

oo  TAA 

51,900 

48,000 

0  T  TAA 

o7,700 

58,600 

2 . 5 

1  .9 

11 

8 

49,000 

38,500 

59,800 

56, 100 

44,000 

67,800 

63,300 

49,200 

76,600 

3 . 2 

2.5 

12 

9 

62,000 

48,700 

75,700 

70,800 

55,700 

85,800 

80,200 

62,300 

96,900 

4 .  1 

3.2 

13 

10 

76,500 

60,100 

93,500 

87,600 

63,800 

1  A^  AAA 

1U().0U0 

97.900 

Tr*  AAA 

76,900 

119,600 

5 . 0 

3.9 

14 

11 

92,600 

72,700 

11^,000 

i  AC  AAA 

lOb.OUU 

O  O  O  AA 

128.000 

1 18.400 

93,000 

144,900 

6 .  1 

4  .8 

15 

12 

110,201) 

86,500 

1c54,dOU 

1  Ofi  AAA 

An  AAA 

153.000 

142.400 

1  1  A  TAA 

1 10,  /OO 

1  TO  AAA 

172,000 

7 . 2 

5 . 7 

16 

13 

129,400 

101,600 

ICO  f\r\f\ 
158,000 

t  A  O  AAA 

1  1  ^5  OAA 

1  lb,  oUU 

1  TA  AAA 

1  Ci'7  OAA 

Io7,.ii00 

1  OA  AAA 

loO,OOU 

OAO  AAA 

202,000 

8 . 5 

6.6 

17 

14 

150,000 

1 17,oUU 

TOO  AAr\ 

18o,UUU 

172,000 

1  O  'I  QAn 

OAO  AAA 

1  AO  AAA 

151,000 

OOyI  AAA 

zc>4,000 

9 . 8 

7 . 7 

18 

15 

172,000 

IOC  onn 

zlU.UuU 

1  A  7  AAA 

ly  /  ,uuu 

155.000 

OOO  AAA 

OOA  AAA 

zz(J,(jUU 

1  "70  AAA 

OCA  AAA 

zby,ooo 

11.3 

8.8 

19 

16 

196,000 

154,000 

j,5y,ouo 

OOi  AAA 

Z24,UUU 

1  Tfi  AAA 

OTI  AAA 

0  C  1  AAA 

zol  .OOU 

1  Cl'y  AAA 

iy7,uoo 

OA^^  AAA 

oOb,000 

12.8 

10. 1 

20 

17 

221,000 

174,000 

270,000 

253,000 

199.000 

306.000 

283.000 

222.000 

346,000 

14.5 

11.4 

21 

18 

248,000 

195,000 

303,000 

284,000 

223.000 

343.000 

317.000 

250.000 

388,000 

16.2 

12.7 

22 

19 

278,000 

217,000 

337,000 

316.000 

248.000 

383,000 

353.000 

278.000 

432,000 

18.1 

14.2 

23 

20 

306,000 

241,000 

374,000 

350.000 

275,000 

424.000 

392.000 

308.000 

478,000 

20.0 

15.7 

24 

21 

337,000 

265,000 

412,000 

386.000 

303.000 

467.000 

432.000 

339.000 

528,000 

22.1 

17.3 

25 

22 

371,000 

291,000 

452,000 

424.000 

333.000 

513.000 

474.000 

372.000 

579,000 

24.2 

19.0 

26 

23 

405,000 

318,000 

494,000 

464.000 

364.000 

560,000 

518.000 

406.000 

633,000 

26.5 

20.8 

27 

24 

441,000 

346,000 

548,000 

505.000 

396.000 

610,000 

564.000 

443.000 

689,000 

28.8 

22.6 

28 

25 

478,000 

376,000 

584,000 

548.000 

430,000 

662.000 

612,000 

481.000 

748,000 

31.3 

24.5 

29 

26 

517,000 

406,000 

632,000 

.592.000 

465.000 

716.000 

662,000 

520.000 

809,000 

33.8 

26.6 

30 

27 

558,000 

438,000 

680,000 

639,000 

512.000 

772.000 

714.000 

561,000 

872,000 

36.5 

28.6 

31 

28 

600,000 

471,000 

733,000 

686.000 

539,000 

831.000 

768.000 

603,000 

938,000 

39.2 

30.8 

32 

29 

644,000 

501,000 

786.000 

737,000 

578.000 

891.000 

823,000 

647,000 

1,006,000 

42.1 

33.0 

33 

30 

688,000 

541,000 

841,000 

788,0f)0 

619.000 

954,000 

881,000 

692,000 

1,077,000 

45.0 

35.3 

34 

31 

735,000 

578,000 

898.000 

841,000 

666.000 

1,018,000 

941,000 

739,000 

1,150,000 

48.1 

37.7 

35 

32 

784,000 

615,000 

957,000 

897,000 

704,000 

1,085,000 

1,002.000 

787,000 

1,230,000 

51.2 

40.2 

36 

33 

833,000 

655,000 

1,018,000 

954.000 

750,000 

1,150,000 

1,066,000 

837,000 

1,300,000 

54.5 

42.8 

37 

34 

885,000 

695,000 

1,080,000 

1,012,000 

795.000 

1,220,000 

1,130,000 

889,000 

1,380,000 

57.8 

45.4 

38 

35 

937,000 

736,000 

1,140,000 

1,073,000 

843,000 

1,300,000 

1,200,000 

942,000 

1,470,000 

61.3 

48.1 

39 

36 

992,000 

779,000 

1,210,000 

1,130,000 

892,000 

1,370,000 

1,270,000 

996,000 

1,550,000 

64.8 

50.9 

40 

37 

1,047,000 

823,000 

1,280,000 

1,200,000 

942,000 

1,4.50,000 

1,340,000 

1,052,000 

1,640,000 

68.5 

53.8 

41 

38 

1,105,000 

879.000 

1,350,000 

1,270,000 

993.000 

1,530,000 

1,410,000 

1,110,000 

1,730,000 

72.2 

56.7 

42 

39 

1,160,000 

914,000 

1,420,000 

1,330,000 

1,046,000 

1,610,000 

1,490,000 

1,170,000 

1,820,000 

76.1 

59.7 

380  CONCRETE  ENGINEERS'  HANDBOOK  [See.  8-8 


Table  2. — Hooped  Column  Reinforcement 


Diameter  of 
enclosed  con- 
crete to 
center  line 
of  hooping 
(inches) 

Pitch 
(inches) 

Sectional 
area  of 
hooping 
(square 
inches) 

Length  of 
hooping  in 
I  ft.  in  height 
(inches) 

Diameter  of 
encosed  con- 
crete to 
center  line 
of  hooping 
(inches) 

Pitch 
(inches) 

Sectional 
area  of 
hooping 
(square 
inches) 

Length  of 
hooping  in 
1  ft.  in  height 
(inches) 

8 

1 

max. 

0.020 
0.025 

1 

302 
242 

24 

2H 

2)4  max. 

0.142 
0.150 

381 
362 

9 

1 

max. 

0.022 
0.034 

339 
226 

25 

2}^  max. 

0. 156 

377 

10 

1 

l^i  max. 

0.025 
0.041 

377 
232 

26 

2}y-2  max. 

0. 162 

392 

11 

m 

l^i  max. 

0.031 
0.048 

369 
237 

27 

2>^  max. 

0. 169 

407 

12 

m 

2  max. 

0.037 
0.060 

362 
226 

28 

23-^  max. 

0. 175 

422 

13 

2}^i  max. 

0.045 
0.069 

356 
230 

29 

2}-^  max. 

0.181 

437 

14 

2}i  max. 

0.048 
0.079 

384 
234 

30 

23^  max. 

0. 187 

452 

15 

2}i  max. 

0.056 
0.094 

377 
226 

31 

23-^  max. 

0.194 

467 

16 

2}^  max. 

0.065 
0.100 

371 
241 

32 

23^  max. 

0.200 

483 

17 

2)-^  max. 

0.074 
0.106 

366 
256 

33 

23^  max. 

0.206 

498 

18 

2}^  max. 

0.084 
0.112 

362 
271 

34 

23^^  max. 

0.212 

513 

19 

2^2  max. 

0.089 
0.119 

382 
287 

35 

2}i  max. 

0.219 

528 

20 

2 

23^  max. 

0. 100 
0.125 

377 
302 

36 

23^  max. 

0.225 

543 

21 

2H 

2}4  max. 

0.112 
0.131 

373 
317 

37 

23^  max. 

0.231 

558 

22 

2)^^  max. 

0.124 
0.137 

369 
332 

38 

2}'2  max. 

0.238 

574 

23 

2H  ■ 
2)^  max. 

0.130 
0.144 

386 
347 

39 

23^  max. 

0.244 

588 

I     Sec.  8-9]  COLUMNS  381 


Table  3. — Volume  of  Column  in  Cubic  Feet  per  Foot  of  Length  for  Diameter  D 


n 
U 

Square 

xvouncl 

vJct  agonal 

Square 

Round 

Octagonal 

10 

0.69 

0.55 

0.58 

27 

5.06 

3.98 

4.19 

11 

0.84 

0.66 

0.70 

28 

5.44 

4.28 

4.51 

12 

1.00 

0.79 

0.83 

29 

5.84 

4.62 

4.84 

13 

1.17 

0.92 

0.97 

14 

1.36 

1.07 

1.13 

30 

6.25 

4.91 

5.18 

31 

6.68 

5.24 

5.53 

15 

1.56 

1.23 

1.29 

32 

7.11 

5.58 

5.88 

16 

1.78 

1.40 

1.47 

33 

7.55 

5.94 

6.26 

17 

2.01 

1.58 

1.66 

34 

8.02 

6.31 

6.64 

18 

2.25 

1.77 

1.87 

19 

2.51 

1.97 

2.08 

35 

8.50 

6.67 

7.05 

36 

8.98 

7.05 

7.46 

20 

2.78 

2.18 

2.30 

37 

9.49 

7.46 

7.88 

21 

3.06 

2.41 

2.54 

38 

10.00 

7.87 

8.30 

22 

3.36 

2.64 

2.78 

39 

10.60 

8.29 

8.75 

23 

3.67 

2.89 

3.05 

24 

4.00 

3.14 

3.32 

40 

11.10 

8.71 

9.20 

41 

11.70 

9.15 

9.67 

25 

4.34 

3.41 

3.59 

42 

12.30 

9.61 

10.10 

26 

4.70 

3.68 

3.89 

9.  Reduction  Formula  for  Long  Columns. — Where  long  columns  must  be  used,  the  reduc- 
tion formula  which  follows,  taken  from  the  Los  Angeles  Building  Ordinance,  may  be  safely 
employed  in  the  design  of  columns  whose  unsupported  length  {I)  is  between  15  and  30  times 
the  least  dimension  of  effective  section  (d).    Let  r  represent  the  quantity  by  which  the  working 

stress  for  columns  with  ^  less  than  15  should  be  multiplied  to  give  a  working  stress  which  may 

be  used  for  long  columns.  Then 

r  =  1.6-K;5(J) 

10.  Columns  Supporting  Bracket  Loads. — A  column  supporting  a  roof  is  frequently  made 
to  carry  a  traveling  crane  which  runs  on  a  track  supported  by  side  brackets  or  at  one  side  of  the 
column.  To  compute  the  maximum  stress  in  such  a  column,  it  is  necessary  to  find  the  maximum 
bending  moment  at  whatever  section  it  occurs,  and  then  combine  the  stresses  due  to  bending 
and  thrust  by  the  general  method  explained  in  Sect.  9. 

The  maximum  bending  moment  occurs  at  the  load,  and  depends  upon  the  height  at  which 
the  load  is  placed  and  the  end  conditions  of  the  column.  To  simplify  the  calculations,  the 
depth  of  the  bracket  will  be  considered  small  in  comparison  with  the  length  of  the  column. 
This  is  not  strictly  correct  but  the  error  involved  will  be  on  the  safe  side  since  any  increase  in 
the  depth  of  a  bracket  reduces  the  maximum  amount. 

Columns  supporting  bracket  loads  will  be  considered  for  the  three  conditions:  (1)  both 
ends  free  to  turn,  (2)  both  ends  fixed,  and  (3)  one  end  fixed  and  the  other  end  free.  Columns 
in  practice  will  have  conditions  intermediate  to  these  and  good  judgment  as  to  flexibility  of  the 
end  connections  is  necessary  to  arrive  at  correct  results  in  any  particular  case. 

Column  Free  to  Turn  at  Both  Ends.— The  bending-moment  diagram  for  this  case  is  shown 
in  Fig.  2.  The  bending  moment  Px  of  the  eccentric  load  is  resisted  by  horizontal  forces  at 
the  ends  of  the  column  which  form  a  couple,  the  value  of  which  is  also  Px.    The  maximum  pos- 


382 


CONCRETE  ENGINEERS'  HANDBOOK 


Sec.  8-10] 


COLUMNS 


383 


sible  value  of  the  bending  moment  is  evidently  Px,  which  would  occur  with  tiie  load  at  either 
end  of  the  column.    The  minimum  value  of  the  maximum  bending  moment  occurs  when 

a  =  b  and  equals  VzPx. 

Column  Fixed  at  Both  Ends. — Analysis  shows  that  the  least  value  of  the  maxinuin  bending 
moment  is         and  occurs  when  h  has  the  following  values:  0.21  IL,  0.500L,  and  0.789L.  The 


Fig.  2. 


moment  diagrams  for  these  cases  are  shown  in  Fig.  3,  The  greatest  value  of  the  maximum 
moment  is  Px  and  occurs  when  the  bracket  is  either  at  the  top  or  bottom  of  the  column. 

The  following  general  formulas  may  also  be  obtained : 

At  A  (Fig.  3) 


Just  above  C, 
Just  below  C, 
or 

At  O, 


M 
M 
M 


Ma  -  Ra 

Ma  -  Ra  -\-Px 

Mo  +  Rh 


Column  Fixed  at  One  End  and  Free  to  Turn  at  the  Other.— The  minimum  value  of  the  maxi- 
mum bending  moment  equals  }iPx  and  occurs  when  b  is  equal  to  0.258L  or  0.605L.    The  bend- 


384  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  8-10 

ing-moment  diagrams  for  these  cases  are  shown  in  Fig.  4  which  also  shows  the  condition  to 
make  the  bending  moment  at  the  base  zero,  and  the  particular  case  of  b  =  L. 
The  following  general  formulas  apply : 


Fig.  4. 


Just  above  C  (Fig.  4), 

M  =  -  Ra 

Just  below  C, 

M  =  Px  -  Ra 

At  O 

Mo  =  Px  -  %Px  ■  -j) 


SECTION  9 


BENDING  AND  DIRECT  STRESS 

1.  Theory  in  General. — If  a  beam  is  acted  upon  by  forces  which  are  all  normal  to  its  length, 
then  the  stresses  resulting  are  due  to  simple  bending,  and  the  formulas  deduced  in  Sect.  7  may 
be  employed.  If,  however,  any  of  the  forces  acting  throughout  the  length  of  a  beam  be  in- 
clined, or  if  additional  forces  be  applied  at  the  ends,  then  our  beam  formulas  for  simple  bending 
will  not  apply.  Likewise,  in  columns,  if  the  load  be  eccentrically  applied  or  if  lateral  pressure 
be  exerted,  both  bending  and  direct  stresses  will  result  and  the  ordinary  column  formulas  given 
in  Sect.  8  cannot  be  used  except  to  give  approximate  results  when  the  amount  of  bending  is 
small. 

The  same  combination  of  stresses  occurs  also  in  arch  rings  and  may  occur  in  special  cases. 
The  formulas  to  be  derived  can  be  employed  in  any  type  of  reinforced-concrete  structure  pro- 
vided the  normal  component  of  the  resultant  thrust  on  the  given  section  acts  with  a  lever  arm 
about  the  center  of  gravity  of  the  section.  In  long  beams  and  columns,  the  deflection  resulting 
from  flexure  should  be  given  consideration  when  determining  the 
eccentricity  of  the  axial  and  inclined  forces. 

Let  us  first  consider  structures  of  plain  concrete.  The  distri- 
bution of  pressure  on  any  section  due  to  a  resultant  pressure  act- 
ing at  different  points  will  be  explained.  Consider  a  section 
represented  in  projection  by  EF,  Fig.  1.  When  the  resultant  R 
acts  at  the  center  of  gravity  0,  the  intensity  of  stress  is  uni- 
form over  the  section  and  is  equal  to  the  vertical  component  of 

N 

R  divided  by  the  area  of  section,  or  If  ^  acts  at  any  other 
point,  as  Q,  and  if  the  projection  of  the  section  is  taken  such 

that  the  distance  xo  represents  the  true  lever  arm  of  N  about  the  center  of  gravity,  then 
the  force  N  is  equivalent  to  an  equal  N  at  O  and  a  couple  whose  moment  is  A^.Co.  The  in- 
tensity of  the  uniformly  varying  stress  due  to  this  bending  moment  at  a  distance  x  from  0 

is  (by  the  common  flexure  formula  for  homogeneous  beams)  in  which  /  is  the  moment 


I 


At 


of  inertia  of  the  section  about  an  axis  through  0  at  right  angles  to  the  plane  of  the  paper, 
the  edges  E  and  F  this  intensity  =  Regarding  compressive  and  tensile  stresses  as  posi 

tive  and  negative  respectively,  the  intensity  of  stress  at  edge  E  is 


r    _  N  NXqXi 

•^-^  "  A  +  / 


At  edge  F  it  is 


NxoXi 


If  the  stress  fj  comes  out  minus,  the  value  obtained  is  the  maximum  tension  as  shown  in  Fig. 
2.  In  plain  concrete  construction  a  greater  tension  than  about  50  lb.  per  sq.  in.  should  not  be 
allowed . 

When  we  come  to  reinforced  concrete,  which  is  composed  of  two  materials  (c'oncrete  and 
steel)  with  different  values  of  E,  then  the  steel  area  at  any  given  cross-section  may  be  replaced 
25  385 


386 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  9-1 


by  an  area  of  concrete  equal  to  n  times  the  area  of  the  steel,  placed  in  the  plane  of  the  steel 
reinforcement.  This  section  may  be  called  the  transformed  section,  or  section  of  concrete 
theoretically  equivalent  in  resistance  to  the  actual  section.  Under  this  heading  rectangular 
sections  only  will  be  considered  and  Fig.  3  represents  a  transformed  section  as  referred  to  above. 

Thus,  if  Ac  is  the  area  of  the  concrete,  and  Ao  is  the  area  of  the  steel  =  As  -\-  A';  then  the 
equivalent  area 

A  =  Ac     nAo  ^  bt  +  n{As  +  A') 


If  Ic  is  the  moment  of  inertia  of  the  concrete  about  the  gravity  axis,  and  Is  is  the  moment  of 
inertia  of  the  steel  about  the  same  axis,  then 


and 


(/o) 

UV) 


I  =  Ic  +-nh 

N      (  +  )  Nxoxi 


Ac-\-  nAo  (  -  )  Ic  +  nis 


A  A' 

If  we  denote  p  and  p'  by  ^  and  respectively,  then  the  distance  from  the  face  most  highly 
stressed  to  the  center  of  gravity  of  the  transformed  section  is  (by  moments) 


u  =■ 


bt^  +  nAsd  +  nA'd' 


bl^ 


+  nAsd  +  nA'd' 


bt  +  n{As  +  A') 


t/2  +  npd  +  np'd' 


1  -\-  np 


np 


N 

Cornpres; 

V 

> 

f 

L 

Q 

<. — 


< 

 u  J 

toi 

1 

'x| 

?i,.--Center  o 
gravity 

1  Pi 

f 

n 
y 

 d  ? 

1 

Fig.  3. 


Ic  =  Hbu'  +  }ib(t  -  uy  =  ^^u'  +  (t  -  uy^ 

Is  =  As{d  -  uy  +  A'(u  -  d'y 


I  ^  Ic  +  nis  =^^u^  +  {t  -  +  7iAs(d  -  uy  +  nA'iu  -  d'y 

t 


If  the  rpinforcement  is  symmetrical,  then  u 


and 


/  =  y^^bt^  +  2nAsiy2t  -  d'y  =  }i2bt''  +  2npbt  {Vzt  -  d'Y 


Sec.  9-2] 


BENDING  AND  DIRECT  STRESS 


387 


Since,  A  =  bt  -\-  n{As  +  A')  =  bt  -\-  nbt(p  +  p') 


(fc) 


N 


(  +  ) 


Nxo 


ifc')     bt  +  nbt(p  +  p')  (-)  yi2bt'  +  2npbt(y2t  -  d'y 

2.  Analytical  Determination  of  Stresses  in  Rectangular  Sections. 

2a.  Compression  Over  the  Whole  Section — Steel  Top  and  Bottom  (Case  I). — 
The  formulas  developed  in  preceding  article  apply  when  the  stress  is  either  compression  over 
the  entire  section,  or  when  there  is  compression  over  a  portion  of  the  section  with  a  tension 
over  the  remainder  not  exceeding  the  allowable  tensile  stress  in  the  concrete.  The  formulas 
we  shall  use  will  apply  to  rectangular  sections  with  symmetrical  reinforcement  and  are  given 
in  the  following  form  for  convenience,  letting  po  denote  the 
quantity  p  -\-  p'\ 

r  =  ;  -  d' 


(fc) 
(fc) 


r    1  (+)    M  1 

Ll  +  npo(-)r^  +  12npor^} 


(1) 
(2) 


By  referring  to  Fig.  4  it  will  be  clear  that  the  stress  in  the  steel 
is  always  less  than  n  X  fc]  thus,  if /c  is  kept  within  its  allow- 
able value,  the  steel  is  sure  to  be  safely  stressed. 

Equation  2  gives  a  means  of  determining  the  eccentricity 
of  the  resultant  force,  or  Xo,  for  which  there  can  be  neither 
tension  nor  compression  at  the  surface  opposite  to  that  near 
which  the  thrust  acts.  To  obtain  the  value  of  Xo  which  gives  a 
zero  value  to  //i  equate  the  two  terms  within  the  brackets, 
and  solve. 

1  6a;o^ 


1  -\-  n(p  +  p')  ■      +  12npor2 


Xo  = 


+  24:npr^ 
1  +  n(p  +  p') 


(3) 


If  n  is  assumed  to  be  15,  and,  if  the  steel  is  embedded  in  the  concrete  one-tenth  of  the  total 
depth  from  each  surface  so  that  2r  =  '^it,  formula  (3)  becomes 


1  +  28. 


If  the  values  n 


t       6  +  90po 

15  and  2r  =  ^^^rare  substituted  in  formula  (1),  this  formula  becomes 


•"^      bt  Ll  +  15po  t 
or  if  the  expression  in  the  brackets  is  denoted  by  K 


1  +  28.8poJ 


NK 
bt 


(4) 


(5) 


(6) 


Diagrams  1  to  6  inclusive  give  values  of  K  for  various  values  of  po,  and  y >  and  for  both 
n  =  12  and  n  =  15.  The  termination  of  the  curves  are  determined  in  Diagram  5  by  equation 
(4)  and  in  the  other  diagrams  by  similar  equations.  For  greater  values  of  Case  I  does  not 
apply;  that  is,  there  is  tension  in  the  concrete  and  Case  II  must  be  employed. 


388 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  9-2a 


«j  ^0  s  an  I  DA 


Sec.  d-2al 


BENDING  AND  DIRECT  STRESS 


389 


~  9  S 

Q  Q  Q 


390 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  ^2a 


Sec.  9-2a] 


BENDING  AND  DIRECT  STRESS 


391 


y  JO  senpA 


392 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  9-^ a 


Sec.  9-2a]  BENDING  AND  DIRECT  STRESS  393 


55 
O 

M 

o 

)^ 

o 

I 

> 
O 

o 

Q  i 


394 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  9-26 


2b.  Tension  Over  Part  of  Section — Steel  Top  and  Bottom  (Case  II).— It  will 
be  on  the  safe  side  and  convenient  as  regards  the  construction  of  working  diagrams  to  consider 
that,  when  any  tension  exists  in  the  concrete,  the  steel  carries  all  the  tensile  stresses.  In  this 
case  there  are  three  unit  stresses  to  be  determined:  namely,  maximum  unit  compression  in 
concrete  fc,  maximum  unit  compression  in  steel  //,  and  maximum  unit  tension  in  steel  fs.  The 
general  formulas  developed  in  Art.  1  are  not  applicable  to  this  case  and  the  following  method 
may  be  used : 


Referring  to  Fig.  5,  it  follows  that 


ktj 


and 


(7) 


(8) 


Sin-ce  the  resultant  fiber  stress  equals 

^  ^  fs'pobt 


+ 


fchkt 


fsPobt 
2 


Eliminating  fs'  and  fs  by  means  of  equations  (7)  and  (8) 


N 


_  fcht  k^  +  2npok  —  npo 

~~2'  k  ■ 

fc.bt  _|_  2nkpo  —  npo 

~2"  k 


(9) 


The  moment  of  the  stresses  about  the  gravity  axis,  eliminating  // 
and  fs  as  before,  is 

/c6i{^f'+^(3  -2A:)]  (10) 


M 


or,  if  the  quantity  within  the  brackets  is  designated  by  L,  then 

M  =fM'L,  or/.  =-^,  (11) 


Fig.  5. 


The  position  of  the  neutral  axis  must  be  determined  before 
equation   (11)  can  be  used.    Since  Nxa  =  M  we  may  multiply 
equation  (9)  by  Xq  and  equate  it  to  equation  (10).    Proceeding  in  this  manner  the  following 
equation  results 

A;3  _  3  1^/^  _  +  Qynp.k'^  =  Snpo  (~  +  2^')  (12) 

Diagrams  7,  8,  9,  11,  12  and  13,  based  on  equation  (12),  give  values  of  k  for  various  values 
Xo  d' 

of  po,  "y'        y'  both  n  =  12  and  n  =  15.    Diagrams  10  and  14  give  values  of  L. 

The  method  of  procedure  in  solving  problems  under  Case  II  is  as  follows:  (1)  Determine  k 
from  the  proper  diagram;  (2)  find  L  from  Diagram  10  or  14;  (3)  solve  equation  (11)  for  /.; 
(4)  find  unit  stresses  in  the  steel  from  formulas  (7)  and  (8). 

Illustrative  Problem. — A  beam  is  9  in.  wide  and  20  in.  deep.  The  reinforcement  both  above  and  below 
consists  of  one  steel  rod  1  in.  in  diameter  embedded  at  a  depth  of  2  in.  At  a  certain  section,  the  normal  component 
of  the  resultant  force  is  60,000  lb.,  acting  at  a  distance  of  3.4  in.  from  the  gravity  axis.  Assume  n  =  15.  Compute 
the  maximum  unit  compressive  stress  in  the  concrete. 


As  +  A' 


(2)  (0.7854) 


(9) (20) 


=  0.0087 


3^ 
20 


0.17 


Sec  9-26] 


BENDING  AND  DIRECT  STRESS 


395 


J.O  S8n|lD/\ 


396 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  9-26 


Sec.  9-26) 


BENDING  AND  DIRECT  STHESS 


397 


s  s9    S3        2  o 

C>     CJ        O       Q       O       Q  P 


tu 

o  o  o 
o     o  o 


5     §     8      §  o. 


398 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  9-25 


^bgS?     S      S.     S     iO     R     lS     S      IJ^     S     !5     5     »     ^     ^.  ^ 
•»»      ■  •  '       ■  •       .      ,       •  • 


Sec.  9-26] 


BENDING  AND  DIRECT  STRESS 


399 


•d  io  can  I  OA 


400 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  9-2?) 


Sec.  9-26] 


BENDING  AND  DIRECT  STRESS 


401 


:5: 


m 


S  5S  S  2 
o       o       o       o  o 


1       1  I 


26 


402 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  9-25 


Sec.  9-2c] 


BENDING  AND  DIRECT  STRESS 


403 


For  these  values  of  po  and        Diagram  5  gives  K  =  1.70  and  shows  that  the  problem  falls  under  Case  I 


Then  by  formula  (6) 


NK 
bt 


(60,000)  (1.70) 
(9) (20) 


567  lb.  per  sq.  in. 


Illustrative  Problem. — Change  the  eccentricity  of  the  preceding  problem  to  6  in.  and  solve. 

Xo 


For  Po  =  0.0087  and 


0.30, 


Diagram  5  shows  that      is  too  great  for  the  problem  to  come  under  Case 


I. 


The  method  of  procedure  for  Case  II  must  then  be  followed. 

Xo 


Diagram  12  gives  k  =  0.73  for  the  values  of  po  and 
Diagram  14  shows  L  to  be  0.123.    Solving  equation  (11) 

_  J/_  _     (60,000)  (6) 
~  Lbt^  ~  (0.123)  (9)  (20)2 


given  above.    With  k  =  0.73  and  po  =  0.0087, 


815  lb.  per  sq.  in. 


Using  formula  (8)  gives 


/.  =  nfc  (^^  -  l)  =  (15)^815) 


18 


73  X  20 


l)  =  2830  lb.  per  sq. 


The  stress  /«'  may  be  found  by  formula  (7)  but  is  always  less  than  n  X  fc- 

Illustrative  Problem. — An  arch  is  20  in.  deep  and  is  reinforced  with  three  rods  H  in.  in  diameter  to 
each  foot  of  width,  both  above  and  below.  If  the  rods  are  embedded  to  a  depth  of  2  in.  and  the  normal  com- 
ponent of  the  resultant  thrust  on  a  section  is  100,000  lb.  for  1-ft.  width  of  arch,  with  an  eccentricity  of  3.4  in., 
determine  the  maximum  intensity  of  compressive  stress  on  the  concrete.    Assume  n  =  15 

(6)  (0.4418) 


PO  = 


=  0.0110 


Diagram  5  gives  K 


(12)  (20) 
Xo  3.4 

T  =  -20  =  ^-^^^ 

1.63  and  the  problem  comes  under  Case  I.    Then  by  formula  (6) 

.  _  NK^  _  (100,000)  (1.63) 
bt  ~ 


679  lb.  per  sq.  in. 


(12)(20) 

2c.  Tension  Over  Part  of  Section — Steel  in  Tension  Face  Only  (Case  III). 
Referring  to  Fig.  6  and  taking  moments  about  the  center  of  the  steel  we 
have 

Ne'  =  y2fckjbd^ 

Since  the  algebraic  sum  of  the  compressive  and  tensile  forces  must  equal 
N,  we  may  write 

N  =  Mfckbd  -  fsVhd 
We  also  know  (see  page  276)  that 


Fig.  6. 


Sc 


n(l  -  k) 


From  these  three  equations  may  be  obtained  the  formulas: 


k^  - 
3  = 
V  = 

K  = 

fc  = 


2pn  (1 

1  -Hk 
k^ 


k)  =  k^j 


.d 


2n{l 
^Ne 

bd^ 
2Ne 


=y2fckj 


bd 


kjbd^ 

Diagrams  15  and  16^  may  be  used  in  designing  and  reviewing  structures  subjected  to  bend- 
ing and  direct  stress  with  steel  in  tension  face  only. 

1  Scheme  of  diagrams  proposed  by  Robert  S.  Beard,  Asst.  City  Engineer,  Kansas  City,  Mo. 


Sec.  9-26] 


BENDING  AND  DIRECT  STRESS 


405 


406 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  9-3 


Illustrative  Problem. — The  vertical  wall  of  a  cantilever  retaining  wall  is  subjected  to  an  earth  pressure 
of  2400  lb.  applied  at  a  distance  of  4.54  ft.  above  the  top  of  footing.    The  weight  of  vertical  wall  is  2200  lb. 
which  can  be  considered  as  applied  5  in.  in  front  of  the  steel.     Determine  the  unit  stresses  fc  and  /«,  assum- 
ing n  =  15,  p  =  0.0077  and  d  =  10.5  in. 
The  moment  at  the  top  of  footing 

M  =  (2400)  (4.54J  (12)  +  (2200)  (5)  =  141,700  in.-lb. 
_  _141^^700  _ 

^  -  (12)  (10757^  - 

e'  141.700 


d  (2200)(10.5) 

Entering  Diagram  16  with  a  value  of  p  =  0.0077  on  the  lower  right-hand  margin  and  tracing  vertically  to 
a  value  of  ^  =  6.1,  then  horizontally  to  the  left  to  a  point  vertically  above  K  =  107,  we  find  /«  =  14,000  and 
fc  =  610. 

Illustrative  Problem. — Design  the  vertical  wall  of  the  retaining  wall  described  in  the  preceding  problem 
so  that  fc  =  750  and  fs  =  16,000.    Assume  the  weight  of  wall  at  2000  lb. 

For  these  unit  stresses  the  left-hand  part  of  Diagram  16  shows  K  =  133.8.  Then 


\(133.i 


(133.8)  (12) 
141,700 


9.4  in.,  say  9^/^  in. 


d       (2000)  (95) 


=  7.45 


Following  across  the  diagram  horizontally  to  the  right  to  a  value  of  ^  =  7.45  and  then  vertically  downward  to  the 
lower  right-hand  margin  we  find  p  —  0.0085. 

3.  Graphical  Determination  of  Stresses. ^ 

3a.  Rectangular  Sections. — Fig.  7a  shows  the  cross-section  of  a  column,  re- 
inforced with  twelve  1-in.  square  bars,  and  of  dimensions  as  shown.  This  column  is  loaded  with 
an  eccentric  load  of  75,000  lb.,  acting  1  in.- outside  the  edge  of  the  column.  It  is  desired  to  find 
the  maximum  unit  stress  in  the  concrete  and  steel,  assuming  that  the  load  is  symmetrically 
placed  about  the  axis  XX,  Fig.  7a.  In  this  solution  the  effect  of  the  bending  moment  pro- 
duced by  the  eccentricity  of  the  load  will  first  be  considered,  after  which  the  effect  of  the  direct 
load  will  be  added. 

The  neutral  axis  is  located  by  means  of  Figs.  76  and  7c,  and  the  base  line  ef  is  drawn  in 
Fig.  7d.  The  length  eh  is  measured  off  to  represent  some  convenient  number  of  pounds  per 
square  inch,  in  this  case  400,  and  the  line  her  is  drawn.  From  the  intercepts  between  the  lines 
cf  and  cr,  the  stress  in  the  tension  steel  may  be  found.  Figs.  7e  and  7g  locate  the  resultant 
of  the  compressive  stresses.  Figs.  7/  and  7h  locate  the  resultant  of  the  tensile  stresses,  and 
the  effective  depth  is  found  to  be  14.6  in.,  from  which  656,000  in.-lb.  is  found  to  be  the  resisting 
moment  when  the  maximum  stress  in  the  concrete  is  400  lb.  per  sq.  in.  The  eccentricity  of  N 
measured  from  the  neutral  axis  is  approximately  8.25  in.,  therefore  the  load  produces  a  moment 
of  619,000  in.-lb.  Now,  if  the  resisting  moment  is  656,000  in.-lb.  when  the  maximum  concrete 
stress  is  400  lb.  per  sq.  in,,  by  proportion  the  maximum  stress  in  the  concrete  produced  by  a 
bending  moment  of  619,000  in.-lb.  will  be  377  lb.  per  sq.  in.,  shown  to  scale  as  ea  in  Fig.  7d. 

The  effect  of  the  direct  load  will  now  be  considered.  A  direct  load  applied  at  the  neutral 
axis  will  have  the  effect  of  moving  the  base  line  ef  to  the  left,  thus  increasing  the  compressive 
stresses  and  decreasing  the  tensile  stresses.  Assume  the  base  line  ef  to  be  moved  to  eji,  a 
distance  of  100  lb.  per  sq.  in.  The  increase  of  compressive  stresses  is  added  to  the  decrease  in 
the  tensile  stresses  and  found  to  be  33,600  lb.,  which  is  laid  off  to  scale  along  the  line  Cig,  thus 
locating  the  point  g.  In  other  words,  a  load  of  33,600  lb.  applied  approximately  at  the  neutral 
axis  would  move  the  base  line  ef  to  ei/i,  increasing  the  compressive  stresses  in  the  concrete  100 
lb.  per  sq.  in.  and  decreasing  the  tensile  stress  in  the  tension  steel  lOO(n)  =  1500  lb.  per  sq.  in. 
The  base  line  is  now  moved  another  100  lb.  per  sq.  in.  to  the  left,  and  the  additional  increase  in 
compressive  stresses  plus  the  decrease  in  the  tensile  stresses  is  added  to  the  33,600  lb.  already 

^  Method  as  given  by  W.  S.  Wolfe,  Instructor  in  Architectural  Engineering,  University  of  Illinois,  in  Eng.  d: 
Cont.,  April  25,  1917,  and  May  23,  1917. 


Sec.  9-36] 


BENDING  AND  DIRECT  STRESS 


407 


obtained,  making  71,400  lb.  which  is  laid  off  along  Cih,  thus  locating  h.  Again  the  base  line  is 
moved  100  lb.  per  sq.  in.  to  the  left,  reaching  the  position  63/3  and  i  is  found  to  be  out  a  distance 
of  112,400  lb.  Now  draw  the  curve  eghi  and  locate  k,  the  point  where  the  75,000-lb.  hne  cuts; 
then  draw  the  base  line  kxij,  which  shows  ax  =  587  lb.  per  sq.  in.  =  the  maximum  stress  in  the 
concrete,  and  7jd(n)  =  the  maximum  tensile  stress  in  tensile  steel.  That  is,  a  load  of  75,000  lb. 
applied  approximately  along  the  neutral  axis  will  move  the  base  line  ef  to  the  position  xy,  thus 
increasing  the  compressive  stress  in  the  concrete  210  lb.  per  sq.  in.  and  decreasing  the  tensile 
stress  in  the  steel  ijf(n)  =  210(15)  =  3150  lb.  per  sq.  in.  Now  a  slight  approximation  has  been 
made  in  assuming  that  a  load  applied  at  the  neutral  axis  moves  the  base  line  directly  to  the  left. 
This  assumption  is  exactly  correct  to  start  with,  but  as  the  base  line  moves  to  the  loft,  more 
area  comes  under  compression  and  the  position  of  the  load  must  move  slightly  toward  the  ten- 


FiG.  7. 


sion  side  of  the  beam  in  order  to  keep  the  base  lines  parallel.  This  deviation  from  the  neutral 
axis,  however,  is  only  slight  as  long  as  there  is  very  much  tension  in  the  column.  For  example, 
when  the  base  line  has  moved  to  e  1/1  the  load  should  act  through  Ci  in  place  of  through  c;  when 
the  base  line  has  moved  to  62/2  the  load  should  act  through  C2;  etc. 

As  a  graphical  check  on  the  work  the  compressive  and  tensile  stresses  in  the  column  when 
the  base  line  is  xy  are  found  and  laid  out  in  the  force  polygon,  Fig.  7j,  from  which  the  funicular 
polygon.  Fig.  7i,  is  drawn,  locating  their  resultant,  which,  of  course,  should  have  the  same 
action  line  as  the  applied  load  A^.  The  error  is  found  to  be  z,  which  is  just  about  as  large  as 
the  error  made  in  assuming  that  the  eccentricity  was  the  distance  from  the  neutral  axis  to  the 
action  line  of  N.  If  it  is  desired  to  make  a  correction  for  this  error,  add  z  to  the  eccentricity 
used.  This  will  increase  M  slightly,  which  will  increase  the  length  of  ea,  in  this  case  from  377 
to  383  and  the  maximum  stress  in  the  concrete  is  583  lb.  per  sq.  in. 

36.  Hollow  Circular  Sections. — When  the  section  of  a  reinforced-concrete  chim- 
ney, or  any  hollow  circular  section  such  as  shown  in  Fig.  8a  is  considered  as  having  an  eccen- 
tric load,  we  have  a  very  difficult  problem  as  far  as  an  analytical  solution  is  concerned. ^  How- 

1  See  analytical  method  used  in  the  design  of  chimneys,  Art.  15,  Sect.  18. 

I 


408 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  9-36 


ever,  when  the  graphical  analysis  is  applied,  we  find  that  the  solution  is  comparatively  simple, 
being  but  very  little  more  complicated  than  the  solution  of  a  solid  square  column  reinforced  on 
all  sides. 

In  Fig.  8a  the  concrete  is  divided  into  a  number  of  small  slices.  From  the  approximate 
centroids  of  a  number  of  these  slices,  on  the  compression  side,  lines  are  drawn  to  the  right  on 
which  are  shown  the  areas  of  the  various  slices,  which  areas  may  be  called  their  compression 
values.  Assuming  that  the  concrete  does  not  take  tension,  the  tension  value  of  each  of  these 
slices  would  be  zero.  From  the  steel  rods,  lines  are  also  drawn  on  which  are  marked  n  times 
the  steel  area  (assuming  n  =  15),  which  is  the  tension  value  of  the  rods  and  also  their  compres- 
sion value.  These  tension  and  compression  values  are  laid  off  in  the  regular  way  in  the  force 
polygon  Fig.  86,  from  which  the  funicular  polygon  Fig.  8c  is  drawn,  locating  the  neutral 
axis  by  the  intersection  0.    The  base  line  ef  in  Fig.  Sd  is  now  drawn,  eh  is  made  equal  to 


V 

Fig.  8. 


400  lb.  per  sq.  in.,  for  convenience,  and  the  line  bcr  is  drawn.  From  the  intercepts  between 
the  lines  her  and  ef  and,  from  the  areas  of  the  slices  and  rods,  the  compressive  forces  and  also 
the  tensile  forces  are  computed. 

At  this  point  it  is  desirable  to  make  a  check  on  the  work  which  has  been  accomplished. 
We  know  that  the  summation  of  the  compressive  forces  produced  by  a  bending  moment  should 
equal  the  sum  of  the  tensile  forces,  therefore  by  making  these  two  summations  and  comparing 
the  results  a  check  will  be  obtained.  This  has  been  done  at  the  right  of  Fig.  Sd  and  the  error 
found  to  be  less  than  }i  of  1  %,  which  is  satisfactory.  The  resultant  of  the  compressive  forces 
is  now  located  by  the  force  polygon  Fig.  Se  and  the  funicular  polygon  Fig.  8/;  also  the  result- 
ant of  the  tensile  forces  is  located  by  the  force  polygon  Fig.  Sg  and  the  funicular  polygon  Fig. 
Sh.  From  these  results  the  effective  depth  is  found  to  be  50.2  in.  and  the  resisting  moment, 
when  the  maximum  stress  in  the  concrete  is  400  lb.  per  sq.  in.,  is  computed  and  found  to  be 


Sec.  9-3c] 


BENDING  AND  DIRECT  STRESS 


409 


approximately  9,675,000  in.-lb.  The  moment  produced  by  the  eccentric  load  AT,  which  has 
been  assumed  to  act  12  in.  outside  of  the  section  and  to  have  a  magnitude  of  230,000  lb.,  is 
7,770,000  in.-lb.,  which  by  proportion  would  produce  a  maximum  stress  in  the  concrete  of  321 
lb.  per  sq.  in. 

The  effect  of  a  direct  load  of  230,000  lb.  at  the  neutral  axis  will  now  be  considered;  the  base 
line  e/ is  moved  1001b.  to  the  left,  to  the  position  ej/i,  and  eig  is  computed  and  found  to  be 
142,000  lb.,  which  is  equal  to  15  times  the  area  of  all  the  rods  times  100  lb.,  plus  the  summation 
of  the  area  of  each  and  every  slice  times  the  average  increased  compression  over  it.  The  base 
line  is  now  moved  100  lb.  farther  to  the  left,  to  the  position  62/2,  and  is  found  to  be  300,200 
lb.  In  like  manner  esi  is  found  to  be  473,300  lb.  and  the  curve  eghi  is  drawn,  k  is  now  lo- 
cated so  that  kX  =  N  =  230,000  lb.  and  the  true  base  line  is  obtained,  giving  Xa 
(the  total  maximum  stress  in  the  concrete)  =  158  +  321  =  479  lb.  per  sq.  in.  The  intersection 
of  XF  with  ad  gives  n  which  locates  the  axis  of  zero  stress.  The  maximum  stress  in  the  steel 
is  rY  =  710  X  15  =  10,650  lb.  per  sq.  in. 

As  a  graphical  check  on  the  work,  the  intercepts  between  the  lines  ad  and  XY  times  the 
various  areas  will  give  the  resisting  forces  produced  in  these  areas  by  N.  These  forces  were 
found  and  laid  off  in  the  force  polygon  Fig.  Si,  from  which  was  drawn  the  funicular  polygon 
Fig.  Sj,  locating  their  resultant  which  should  have  the  same  action  line  as  N.  The  distance 
z  shows  the  error  found. 

3c.  Solid  Circular  and  Other  Sections. — A  solid  circular  column  may  be  handled 
in  the  same  way  as  the  hollow  section  just  considered,  the  only  difference  being  that  the  areas 
of  some  of  the  slices  will  be  relatively  larger  because  of  the  absence  of  the  hole.  Also  the  con- 
struction for  sections  of  other  shapes  will  be  just  the  same  except  that  the  relative  size  and  posi- 
tion of  the  different  slices  and  rods  will  vary. 


i 


SECTION  10 


MOMENTS  IN  RIGID  BUILDING  FRAMES 

1.  Importance  of  the  Subject. — The  reinforced-concrete  building  frame  differs  from  other 
frames  particularly  in  its  rigidity  at  the  junction  of  members,  when  proper  provision  has  been 
made  for  continuity.  This  applies  not  only  to  columns  extending  from  the  basement  to  the  roof, 
and  to  beams  continuous  for  more  than  one  span;  but  more  particularly  to  the  rigidity  existing 
between  the  column  system  and  the  continuous  beams.  Many  recent  tests^  upon  completed 
structures  show  that  the  concrete  building  frame  is  a  rigid  one,  and,  if  properly  reinforced,  may 
well  be  designed  as  such.  Many  tests  also  show  that,  whether  so  designed  or  not,  the  reinforced- 
concrete  frame,  due  to  its  rigidity,  causes  column  stresses  hitherto  not  considered,  and  of  a  mag- 
nitude to  cause  more  careful  investigation  during  future  design. 

2.  Method  of  Analysis. — The  method  of  analysis  which  follows  is  that  of  slope-deflections 
developed  with  the  aid  of  the  principle  of  area  moments. 

M 

From  the  property  of  the       curve  for  beams  we  have  the  following  important  laws 

1.  The  change  in  angle  between  the  tangents  at  any  two  points  on  the  elastic  curve  of  a 
member,  which  change  is  caused  by  the  action  of  moments  on  the  members  at  those  points,  is 

M 

equal  to  the  area  on  the       diagram  of  these  moments,  included  between  the  two  points. 

2.  The  lateral  displacement  of  one  end  of  a  member,  when  that  member  is  acted  upon  by 

M  . 

moments,  is  equal  to  the  statical  moment  of  the  ^  diagram  about  the  displaced  end.  This 
is  the  principle  of  area-moments  (see  Mich.  Technic,  1910). 

1  Bulls.  64  and  84,  Eng.  Exp.  Sta.,  Univ.  of  111.;  Jour.  Am.  Cone.  Inst.,  vol.  II,  No.  6,  1914. 

»  For  any  small  portion  ds  of  a  member  (see  Fig.  A),  there  is  a  certain  value  of  x  which  may  be  designated  by 
dx.  Let  tangents  be  drawn  to  the  curve  at  the  extremities  of  the  portion  ds;  then  the  angle  between  these  tangents 
may  be  called  d<j>.  For  every  value  of  c?<^  there  is  a  corresponding  elementary  portion  dy  intercepted  on  B'B. 
This  distance  dy  is  equal  to  x  •  d4>  (since  the  curvature  is  in  reality  very  slight) ;  and,  similarly,  yi  is  equal  to 


r     r      r  Mxdx 


(See  Art.  46,  Sect.  7.) 

Suppose  that  a  curve  be  plotted  such  that  the  ordinate  at  any  point  represents  the  bending  moment  at  the 
corresponding  point  in  the  member,  divided  by  EI.    Thus,  for  any  point  P, 

Mp  M 
the  ordinate  to  the  curve  is  The  area  under  this      curve  for  a  distance 

M 

dx  along  its  axis  (shaded  in  the  figure)  is  equal  to-^j  •  dx;  likewise,  under  the 
whole  curve  it  is 

Mdx 
EI 


C  — 
J  A  EI 


But  this  is  the  expression  for  the  change  of  slope  4>  of  the  tangent  at  A 
with  respect  to  the  tangent  at  B;  hence  the  first  law  is  evident. 

The  shaded  area  in  Fig.  A  has  a  moment  about  the  end  B  equal  to 

^jdx  'X.    This  is  seen  to  be  the  value  of  dy.    The  moment  about  B  of  the 
M 

total  area  under  the      curve  is 


Fig.  a. 


i: 


Mxdx 


U  EI 

which  is  the  value  of  y,  the  linear  deflection  of  one  end  normal  to  the  original  position  of  the  member.  The  second 
law  then  follows. 

411 


412 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  10-2 


Before  proceeding  with  the  appUcation  of  these  laws  or  principles,  it  is  necessary  to  estab- 
lish rules  concerning  the  signs  of  moments  and  deflections. 

The  moment  at  the  end  of  any  member  will  be  considered  positive  if  the  external  moment 
at  that  end  acts  in  a  clockwise  direction.  The  subscript  of  the  moment  will  determine  the  mem- 
ber and  end  in  question;  thus  Mab  is  the  moment  at  the  end  A  of  the  member  AB. 

The  change  in  slope  of  the  tangent  to  the  elastic  curve  of  a  member  will  be  considered  posi- 
tive when  the  tangent  has  turned  in  a  clockwise  direction. 

The  deflection  of  any  point  in  the  member  will  be  measured  normal  to,  and  away  from,  the 
base  line  or  line  of  original  position.  The  sign  of  the  deflection  will  be  considered  positive  when 
measured  in  the  same  direction  from  the  base  line  as  are  positive  slopes. 

M 

diagrams  will  be  plotted  on  the  tension  side  of  the  member. 

In  Fig.  la  there  is  shown  a  member  AB  acted  upon  by  moments  and  shears  at  the  ends. 
Let  AB'  be  the  original  position  when  considering  the  member  AB,  and  A'B  the  original  posi- 
tion when  considering  the  member  BA.    The  angles  6 a 
I  and   Ob  are  negative,  as  is  also  d.    According  to  the 

^    scheme  of  signs,  the  moments  at  both  ends  are  positive. 

However,  when  the      diagram  is  plotted  with  respect  to 

the  member,  as  indicated  above,  there  is  seen  to  occur 

I  ^.rtTTTTTIlTll  '^aA       ^  point  of  inflection.    Fig.  Ih  is  the       diagram  for  the 

•^'iili^^  member  under  the  loading  shown. 

£Z  Since  the  end  A  is  not  fixed,  the  total  deflection  d  of 

B  is  due  partly  to  the  change  in  slope  at  A  and  partly 
Fig.  1.  to  the  flexure  of  the  member.    Thus,  the  distance  d  — 

BjJ,  is  the  deviation  due  to  flexure,  and  is  equal  to  the 

statical  moment  of  the      diagram  about  B.    The  area  of  the  ^  diagram  is  seen  to  be  the 

algebraic  sum  of  the  areas  a' ah  and  a'hh' ;  whence 

The  change  in  slope  of  the  member  from  5  to  A  is  0^  —  Qb^  and  is  equal  to  the  area  of 
the  ^  diagram,  or 

Qa  -  Qb  =  2^  {Mab  +  Mba) 
Eliminating  Mba  from  the  two  equations  above,  there  results 

Substituting  K  for  ^  and  R  for 

Mab  =  2EK{2dA  +  Ob  -  SR)  (1) 
Mba  =  2EK{2dB  +  Oa  -  SR)  (la) 
This  is  the  general  equation  for  moment  at  one  end  of  a  member  carrying  no  transverse  load, 
in  terms  of  the  relative  changes  in  position  of  the  ends.^ 

When  there  is  a  transverse  load  upon  the  member  an  expression  similar  to  equation  (1) 
may  be  derived.    Consider  the  member  shown  in  Fig.  2a.    The  deflection  of  B  from  the  tan- 

M 

gent  at  A  is  d  —  6aI  and  equals  the  moment  of  the        diagram  about  B  (see  Fig.  2b). 

1  The  above  method  for  the  general  treatment  of  rigid  frames  first  appeared  in  Bulletin  1,  University  of 
Minnesota,  "Secondary  Stresses  and  other  Problems  in  Rigid  Frames,"  by  G.  A.  Maney,  March,  1915.  The 
method  was  applied  to  the  special  case  of  wind  stresses  in  office  buildings,  Bulletin  80,  University  of  Illinois,  by 
W.  M.  Wilson  and  G.  A.  Maney  (June,  1915).    The  notation  here  used  is  from  the  latter  bulletin. 


Sec.  10-2] 


MOMENTS  IN  RIGID  BUILDING  FRAMES 


413 


This  diagram  is  similar  to  that  shown  in  Fig.  16,  except  that  the  area  caused  by  the  load  is 
added  to  the  diagram  of  the  other  moments  at  A  and  B. 

\MabI      MbaI  ^  Pab 
El\_    Z     ^  & 

M 


The  difference  in  slope  between  the  two  ends  is  (Oa  —  Ob),  and  is  equal  to  the  area  of  the 


diagram. 


0  = 


I 

2EI 


(^Mab  +  Mba  +  ^) 


EI 


From  these  two  equations  Mba  may  be  eliminated,  whence 


Mab  =  2EK{2dA  +dB  -  SR) 


(2)  si^:::------ 


Similarly 

Mba  =  2EK{2dB  -\- Oa  -  ZR)  +  ^        (2a)  ^Jl^A 

If  the  transverse  load  on  the  member  is  symmetrical,  then  ' 
equation  (2)  reduces  to 


Mab  =  2EK{2dA  +  Ob  -  3  R) - 
Mba  =  2EK(2dB  +  Oa  -  SR)  + 


(3)  ^ 
Ell 


(3a) 


in  which  F  is  the  area  of  the  moment  diagram  for  the 
given   svmmetrical   loading   on  a  simple  span.^  For 

F 

different  types  of  symmetrical  load  the  values  of  y  are  given  below: 


Values  of  7",  Moment  Factor  for  Symmetrical  Loads* 


Loadinc 


1 


P  P 


K/-4-#4-?-H 
f  \ 


"p  ^  'p 

V  -  ^  ---4 


.p  «p  >p  ■ 


Ib.perff. 


I*  £7 -  ■>)<■•  i  ■  ■>|<-(7 

I  w  Ib  perffy  I 


f lb  per -ft-.  '  f 


Moment  diagram 


.Pa 


Tp^ 


wa'- 
'2 


Moment  factor 


8 


—  P£ 


wa' 
17 


*  Prepared  from  a  fable  by  rE.Richarfj  Masfers  Thesis,  I9IS,  UnuoflU 

It  should  be  noted  that  in  equations  (2)  and  (3)  the  sign  of  the  last  term  is  negative. 
In  equations  (2a)  and  (3a)  the  sign  of  the  last  term  is  positive.    A  general  rule  results : 

1  The  last  term  of  equations  (2)  and  (3)  is  the  moment  at  the  end  of  a  fixed  beam  loaded  similarly  to 
member  AB. 


414 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  10-3 


If  the  load,  independent  of  the  member,  tends  to  rotate  around  the  joint  under  considera- 
tion in  a  clockwise  direction,  the  sign  of  the  last  term  of  equations  (2)  and  (3)  is  negative.  If 
the  load,  independent  of  the  member,  tends  to  rotate  around  the  joint  under  consideration  in 
a  counter-clockmse  direction,  the  sign  of  the  last  term  of  equations  (2)  and  (3)  Is  positive,  as 
in  equations  (2a)  and  (3a). 

By  comparison  of  equations  (1)  to  the  succeeding  ones,  the  last  term  in  equations  (2) 
and  (3)  are  noted  to  be  ''load  terms";  that  is,  they  are  the  modifying  factors  of  the  equations 
due  to  the  presence  of  the  loads. 

A  number  of  special  equations  arise  from  those  in  (1),  (2)  and  (3)  when  various  end  re- 
straints are  imposed  upon  the  member.  These,  for  convenience,  have  been  tabulated  below. 
The  above  statement  concerning  signs  applies  here  also. 


Member  and  loading 

e 

Mba 

Eq-No. 

^  d) 

Zero 

lb 

 ^) 

Ic 

¥  1) 

Id 

 ^) 

^A  '^B 

6EH9b 

Je 

Zero 

3EKe^i-^(Uci) 

2b 

4EKe^'i-^ 

2c 

1^  Symmehical  load 

^\ ^ 

-Zero 

3EKe^^\^ 

3b 

^A^'^B 

BEKe^i-j- 

3c 

^^Symmefrical  lead  ^ 

4EKeg+-j 

3d 

3.  Application  of  Method  of  Analysis  to  Simple  Cases. — 1.  Let  it  be  desired  to  determine  the 
moment  at  the  central  support  of  the  beam  shown  in  Fig.  3. 

Referring  to  equation  26  in  the  above  table  of  special  moment  equations. 


Mba  =  3EKidB  +  ^  (h  +  a) 


2h^ 
K. 


t^.  JJ.....M...Lj 

r       '        T  T  and  from  equation  16, 

Fia.  3.  Mbc  =  ZEKt^b 

Since  the  summation  of  moments  around  the  joint  B  must  equal 

zero  for  equilibrium, 

Mba  +  Mbc  =  0 
{3EKi  +  SEK,)eB  +  ^(^1  +  a)  =  0 


Ob  = 


SEKi  +  3EK, 


[ga:  +  a)] 


Sec.  10-3] 


MOMENTS  IN  RIGID  BUILDING  FRAMES 


415 


whence 


Pah 


(^1  + 


either  of  which  equations  gives  tension  at  the  top  of  the  beam  over  the  support  B. 
If  Ki  =        and  li  =  h, 


Mbc  =  -  Mba  =  - 


Pab 

4/i2 


(^1  +  a) 


2.  Let  it  he  desired  to  find  the  moment  at  the  top  of  the  lower  column  in  the  frame  shown  in 
Fig.  4.    Let  the  values  of  K  for  the  column  he  the  same,  and  let  K  for  the  girders,  also,  be  alike. 
From  equation  Sd  in  the  above  table, 

F 

Mba  =  4EKidB  +  y  (o) 

From  equation  Id, 

Mbd  =  Mbe  =  4EK2dB 

and 

Mbc  =  4:EKidB 

Since  the  sum  of  the  moments  around  the  joint  B 
must  equal  zero, 


Mba  +  Mbc  +  Mbd  +  Mbe  0 
{SEKi  +  SEK2)dB  +7  =  0 
1  F  1 


^  ^  wl^ 

SEKi  +  SEKo '  I         SEKi  +  SEK2 '  12 

Substituting  into  the  above  equations  there  results 


D 

n  lb  per  ft 

wmm. 

B  K, 

E 

7/ 

(") 

Y 

Momenf  Diacpvm 

Fig.  4. 


Mbd  =  Mbe 
Mbc 


wP 
12 


/K^  +  2K2  \ 
=  \2Kr  +  2K2I 

\2Ki+  2K.J  12 

\2Ki  +  2K2)  12 


If  K2  =  0,  that  is,  a  simple  support  replaces  the  columns  at  B, 
Mba  -  -  Mbc 


wl^ 
24 


which  is  the  moment  at  the  central  support  of  a  continuous  girder  with  fixed  ends  loaded  on  one 
span  with  a  uniform  load. 

4.  Conception  of  Rigidity  of  Building  Frames. — Suppose  a  point  in 
space  to  be  held  to  some  infinitely  rigid  body  by  several  elastic  members, 
each  of  which  is  fixed  at  the  end  farthest  from  the  point  in  question. 
Thus,  in  Fig.  5,  the  point  A  is  the  rigid  junction  of  the  members.  The 
members  1  to  5  are  fixed  at  points  a,  h,  c,  d  and  e,  and  are  rigidly  con- 
nected to  each  other  at  A.    Let  AB  be  a  loaded  member,  tending  to 
turn  point  A  in  a  clockwise  direction.    If  the  members  1  to  5  are  infinitely 
rigid  or  any  one  of  them  is  infinitely  rigid,  the  slope  of  the  tangent  to 
AB  at  A  will  remain  in  a  fixed  position  throughout  loading,  and  AB 
would  be  said  to  be  fixed  at  A.    Again,  if  the  members  1  to  5  were  not 
at  all  rigid,  A  would  turn  and  there  would  be  no  bending  restraint  upon  AB,  through  the 
members  meeting  at  point  A.    If  there  is  no  load  acting  upon  members  1  to  5,  there  are  two 
limiting  conditions  of  rigidity  at  the  joint  A — namely:  (1)  zero  restraint  and-  (2)  fixity,  due, 


416 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  10-5 


respectively,  to  whether  the  members  1  to  5  have  zero  stiffness,  or  have  infinite  stiffness.  It 
is  evident,  since  the  sum  of  the  effects  of  each  of  the  members  is  the  total  effect  of  all  of  the 
members  in  restraining  the  rotation  of  point  A,  that  the  effect  of  all  together  may  be  thought 
of  as  the  effect  of  but  one  member  capable  of  giving  the  same  restraint. 

In  a  building  frame  of  reinforced  concrete,  any  beam  is  restrained  a  certain  amount  at 
each  end,  due  to  the  rigid  connection  existing  between  it  and  the  columns  above  and  below, 
and  the  girder  beyond.  The  restraint  causes  negative  moments  in  the  ends  of  the  beam,  and 
in  turn  the  load  on  the  beam,  in  causing  a  tendency  for  a  rotation  of  A,  causes  flexural  stresses 
in  the  restraining  members. 

Fig.  6  shows  a  uniform  load  over  one  span  in  a  building  frame,  and  the  deformations  caused. 
The  members  radiating  from  A  and  B  are  restrained  at  their  outer  ends  to  an  extent  varying 
between  a  hinged  and  a  fixed  condition.  If  loads  were  put  on  aA  and  Bd,  the  deflections  in 
the  columns  at  A  and  B  would  be  practically  removed,  and  AB  would  be  practically  fixed. 
Suppose,  however,  that  instead  of  this  the  spans  beyond  a  and  d  were  loaded.    This  would  add 

to  the  deflections  shown.  Further  deformation  could  be 
obtained  by  loading  alternate  panels  in  all  directions. 

A  different  effect  could  be  obtained  by  loading  the 
panels  above  and  below  AB.  This  would  develop  a  point 
of  contraflexure  in  the  column,  but  would  give  a  constant 
moment  in  the  unloaded  girders.  By  loading  alternate 
bays  the  maximum  effect  of  this  kind  would  be  obtained. 

It  will  be  possible  to  remove  the  portion  ahcdef  of  the 
frame,  and  impose  upon  the  extremities  of  the  members 
such  moments  as  will  imitate  any  condition  of  full  or  partial 
loading.  It  will  be  assumed  in  these  cases  that  the  three 
girders  have  equal  K's;  that  the  lower  columns  have  equal  K's;  and  that  the  upper  columns 
have  equal  K's.  This  will  be  recognized  as  a  common  condition;  and  though  cases  may  arise 
which  are  different,  this  case  will  aid  the  judgment  of  the  designer. 

5.  Moments  at  Interior  Columns  in  Beam-and-girder  Construction. 

6a.  All  Terminals  Hinged  (Case  I). — From  the  fact  that  the  frame  is  symmet- 


b  ....  c 

a  

d 

A—-'B 

e 

Fig.  6. 


9c 


K 
Ho  ^ 


tiomenf  diagram 


rically  loaded  and  is  symmetrically  rigid  6 a  =  —  Qb]  hence,  from  equation  3c, 

F 


From  equation  16, 


Mab  =  2EKidA  - 
MAf  =  SEKoOa 

MAa  =  SEKidA 

MAb  =  SEKzdA 


But  for  equilibrium, 

Ma/  +  MAa  +  MAb  +  Mab  =  O 
Substituting  and  solving, 

_  F   1 


Sec.  10-56] 


MOMENTS  IN  RIGID  BUILDING  FRAMES 


417 


I 


Substituting  this  value  into  the  above  moment  equations, 

I  ISKo  +  5Ki  +  SK,i 

_  FT  SKo  1 

I  IsKo  +  5Ki  +  ^K^] 

5b.  All  Terminals  Fixed  (Case  II). — As  in  the  preceding  development, 


do) 

(lb) 


Symhad! 


f 

i  i 

From  equation  Id, 


Since 


it  is  found  that 


By  substitution, 


Mab  =  2EKidA 


Ma/  =  ^EKodA 

MAa  =  ^EK.dA 

MAb  =  ^EKsdA 


Ma/  +  MAa  +  MAb  +  Mab  =  O 


dA  = 


I     4Ko  +  6Ki  +  4K, 


I  l2Ko  +  SKi  +  27^:3] 


(Ila) 
(116) 


Equation  (Ila)  could  have  been  derived  from  (la)  by  replacing  the  SK  of  each  outstanding 
member  by  4:K,  as  would  be  clear  from  a  study  of  equations  16  and  Id 

From  these  two  cases,  Diagram  1  on  page  421  was  prepared.    Instead  of  plotting  the  values 

K  K 

of  K  directly,  the  ratio  of  each  K  to  Ki  was  plotted.    Thus  Ko'  =       and  K/  =  The 

diagram  shows  clearly  the  small  difference  in  the  negative  moment  at  the  end  of  the  loaded  girder 
between  hinged  and  fixed  terminals.  When  Ks^  =  0  there  are  no  upper  columns,  as  is  the  case 
in  a  viaduct  bent,  or  a  one-story  deck  structure.  When  K3'  =  Ko'  =  0,  the  girder  becomes  one 
on  simple  intermediate  supports. 

If  a  structure  of  two  stories  in  height  were  extended  indefinitely  in  either  direction  and 
alternate  spans  were  loaded,  Cases  I  and  II  would  be  modified  by  giving  the  two  outside  girders 
a  constant  moment  over  their  length,  and  having  their  terminals  neither  fixed  nor  hinged. 
Expressions  for  Mab  and  Ma/  for  each  case  follow. 
27 


418 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  10-5c 


6c.  Columns  Hinged.    Outer  Girders  with  Constant  Moment  (Case  III).- 


5d.  Columns 


Mab 

Mas 
Fixed. 

f<3 


3Xo  +        +  3K3I 
3A^  1 


Outer   Girders  with  Constant  Moment 


(Ilia) 

(III6) 
(Case  IV).— 


If 


BK, 


2Ko  +  2A'i  +  2/^. 


(IVa) 


(1V6) 


Equations  (Ilia)  and  (IVa)  are  plotted  on  Diagram  2.  It  indicates,  as  before,  the  small  dif- 
ference in  the  value  of  Mab  between  fixed  and  hinged  columns. 

A  third  condition  which  will  develop  high  stresses  in  the  columns,  and  which  will  give  a 
high  degree  of  rigidity  to  joints  A  and  B,  is  a  case  of  loading  in  which  alternate  bays  are  loaded, 
and  all  the  spans  of  one  bay  for  the  full  height  of  the  structure  are  loaded.  When  all  panel 
loads  are  the  same,  or  when  the  loads  are  such  as  to  give  the  same  rotation  at  each  joint,  the 
point  of  inflection  will  be  at  the  center  of  the  column.  The  girders  may  have  their  extremities 
either  hinged  or  fixed,  or  the  outer  girders  may  have  constant  moments  over  their  length. 
Each  of  these  conditions  is  treated  in  a  following  case. 

be.  Point  of  Inflection  at  Center  of  Columns.    Outer  Girders  Hinged  (Case  V). — 


a  ff,  A 


1. 


Mab 


Mas  = 


1 

f 

.TTTTTTiTl^ 

^  i 

II6K0  +  5Ki  +  6i^3. 


(Va) 


r.] 


6/.  Point  of  Inflection  at  Center  of  Columns. 


Outer  Girders  Fixed  (Case  VI) 


(Vb) 


K,  A. 


1 

f 

i  i 

Sec.  10-5^] 


MOMENTS  IN  RIGID  BUILDING  FRAMES 


419 


Mab  = 

Ma/  = 


F  rSKo  +  2K,  +  SK, 


ii 


3Ko  +  SKi  +  SK, 


5g.  Point  of  Inflection  at  Center  of  Columns. 
Moment  (Case  VII).— 


I  (Via) 
(VI6) 

Outer  Girders  with  Constant 


^3 


■p.  I 


Mab 
Mas 


e 


f 

llllllllllll^ 

3Ko  +  Ki   +  SK 


l  ISK 


SKo  +  2Ki  +  3A' 


+  2Ki  +  3^3. 


(Vila) 
(VII6) 


Equations  (Va),  (Via)  and  (Vila)  have  been  plotted  in  Diagram  3.  It  should  be  noted,  ac- 
cording to  Diagrams  2  an^  3,  that  the  effect  of  the  constant  moment  along  the  outer  girders  is 
to  cause  a  rotation  in  addition  to  that  caused  normally  by  the  load;  and  that  this  additional 
rotation  causes  a  decrease  in  negative  moment  in  the  girder  AB  from  what  it  would  have  been 
had  the  girders  been  either  hinged  or  fixed  at  their  outer  ends.  This  is  consistent  with  the 
fundamental  conception  of  rigidity. 

Diagram  4  has  been  plotted  to  show  comparatively  the  results  of  the  foregoing  cases. 
Since  both  Ko'  and  Ks'  have  the  same  coefficients  in  the  foregoing  expressions  for  Mab,  Diagram 
4  is  plotted  between  the  moment  and  the  sum  of  Ko'  and  Ks'.  The  resulting  curves  are  identical 
with  those  for  Kz'  =  0  in  Diagrams  1  to  3. 

F 

The  variation  of  moment  is  for  nearly  all  cases  not  over  10%  of  the  load  factor  y  For 

values  of  (Ko'  +  K/)  >  5,  the  moment  is  proportional  to  the  value  of  (Ko'  +  K/).  The  small 
difference  in  moments  between  hinged  and  fixed  terminals  is  again  emphasized.    All  cases 

F 

approach  a  moment  Mab  =  y  as  a  maximum  limit. 

On  the  first  floor  there  may  arise  a  condition  in  which  the  first  tier  of  columns  may  be 
hinged  or  fixed,  while  the  second  tier  of  columns  may  have  a  central  point  of  inflection.  Since 
the  greatest  stress  will  arise  from  fixity  of  the  lower  tier,  rather  than  from  a  hinged  condition, 
it  will  be  investigated.    The  outer  girders  will  be  located  as  in  Cases  V  to  VII  above. 

6h.  Point  of  Inflection  at  Center  of  Upper  Columns.    Lower  Columns  Fixed. 
Outer  Girders  with  Constant  Moment  (Case  VIII). — 


— ^Kjllllllllli 


_  _F  \2Ko  -\-  K,  +  ZK{\ 
'^^^  I  l2Ko  +  2Ki  +  3A3J 


M, 


F  V  SK,   1 

I  l2Ko  +  2Ki  +  3X3J 


(Villa) 
(VIII6) 


5i.  Point  of  Inflection  at  Center  of  Upper  Columns.    Lower  Columns  Fixed. 
Outer  Girders  Hinged  (Case  IX).— 


420 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  lo-sy 


i7* 


d  K,  A 


*7V 


Mab 


Mai, 


F  V4:K^  +  3Xi  +  eiiCsl 
Z  L4i^o  +  SXx  +  6K3J 

rL4Ko  +  5^1:1  +  6X31 


(IXa) 


(1X6) 


6j.  Point  of  Inflection  at  Center  of  Upper  Columns.    Lower  Columns  Fixed. 
Outer  Girders  Fixed  (Case  X).— 


^/r:  Ai 

Mab  = 
= 


Ho  Ka 


Z  L2/^o  +  3/^1  +  3X3] 
3X3  1 


f[ 


2Ko  +  3Ki  +  3/!:= 


(Xa) 
(X6) 


The  moment  Mab  as  given  by  each  of  the  above  three  cases  is  plotted  in  Diagram  5.  There 
is  little  difference  between  the  moments  on  this  diagram  and  those  on  Diagram  3,  for  corre- 
sponding Kz. 

A  review  of  the  foregoing  ten  cases  shows  that  the  negative  moments  in  the  loaded  girders 
cannot  in  any  way  exceed  those  for  a  continuous  girder  whose  ends  are  similarly  restrained. 
It  is  justifiable,  therefore,  to  design  the  girders  as  continuous,  so  far  as  negative  moments  are 
concerned;  and  for  either  positive  or  negative  moments  the  recommendations  of  the  Joint 
Committee  (see  Art.  45,  Sect.  7)  are  entirely  adequate  as  a  basis  of  computation. 

The  effect  on  the  columns  of  unbalanced  floor  load  is  shown  for  each  of  the  ten  cases  on 
Diagrams  6  to  9  inclusive.  The  greatest  moment  in  the  interior  columns  is  found  at  either 
end  of  the  second-tier  columns  when  the  first  tier  has  fixed  bases  (Case  VIII,  Diagram  9). 

F 

The  value  of  this  moment  is  shown  on  Diagram  10.    Very  rarely  will  it  exceed  60%  of  y> 

which  for  uniform  loads  gives  0.05  wl"^. 

6.  Moments  at  Exterior  Columns  in  Beam-and-girder  Construction. — Since  exterior 
columns  must  resist  all  the  moment  in  the  end  of  the  joining  beam,  the  moments  will  be  liable 
to  be  somewhat  higher  than  in  interior  columns,  where  the  girder  beyond  takes  its  share  of  the 
moment. 


Syjnmefrical 


It  has  already  been  shown  (page  418)  that  when  moments  are  applied  at  a  and  h  such 
that  points  of  inflection  are  caused  at  the  mid-height  of  the  columns,  the  columns  more  firmly 
retard  the  rotation  of  the  joint  A.  The  moment,  therefore,  is  greater  in  the  columns  when 
the  moments  at  a  and  h  are  thus  applied.    The  condition  of  restraint  of  B  may  vary  from 


Sec.  10-6] 


MOMENTS  IN  RIGID  BUILDING  FRAMES 
Diagram  1 


100 

% 
t 

Cu.|r- 

o 

.1  60 
^  50 

1  1   1  1  1  1  1  1  1  1  1  1   1  1   1  1  1 

'Mill  1  '  t'  ,,.  '\ 

c 

ur 

ve 

s 

*  V 

ah 

>  or 

r1 

— 

- 

- 

— 

— 

- 

-< 

/ 

K3 

negative  moment  at 
ends  of  airder  AB 

/ 

'  Columns  and  qinders 

7 

•        hinged  at  ends-  -  Case  I 

-                            — columns  ana  giraers 

^=k;    fixed  at  ends-  Case  U 

e  3 
Values  of       (Lower  column) 

Diagram  2 


100 


90 


c 

K 

c 

(y^  70 

il 


I 

Z 


60 


-50 


-  K, 

Sym. 

K, 

A 
Ko 

Negative  moment 
at  ends  of  girder  AS 


at  ends  Case  III 

 Columns  fixed 

^=K'  at  ends  Case  lY 


z 


60 


50 


Values  of  Ko  (Lower  columin) 
Diagram  3 

TTT 


jS^^  Negative  moment  M*© 
•<fKq  \     at  ends  of  girder 


'ex- 

^        ^.       treme  ends  CaseV 

K.       K.   Girders  fixed  at  ck- 

V   K     .    treme  ends.-  CaseYI 

—•-k;   ^»k;  Girders  with  con - 

stent  moments.  Case TH 


Values  of  Ki  (Lower  column) 


422  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  10-6 


Diagram  4 


0  2  4  6  8  10      ,   12  14  16  18  20 

Values  of  (k:  +  KJ 


Diagram  5 


1  1  1  1  1 

1 

1 

L 

Vc 

jes 

pf 

H 

i 

1 

ST 

■ 

£01 

n 

g.  90 

11 

S  i- 

80 

A 

J" 

y 

/ 

/ 

/■ 

w 

K3 

Necrative  momerrT  m^b 

Negative 
of 

/ 

I 

Ki 

K, 

-  rtirders  with  cons-forrf 

A 

K. 

B 

Ke 

Ko 

moments  - 

-Case  YIU 

? 

-  Girders  hinged-Case  IX 

K, 
K 

-  Girders  f  ixec 

- 

CaaeX 

= 

0  I  2  3  4  5 

Values  of  Kq  (Lower  column) 


Diagram  6 


Values  of  K3  (Upper  coluTnn) 


Sec.  10-6] 


MOMENTS  IN  RIGID  BUILDING  FRAMES 
Diagram  7 


423 


100 


c 

O  O  80^*- 


•^=k;  -^  =  k;  fixed  Case  VI 


5ym 


K3      Moment  MAf 


 Columns 

hinged  ••  Case  HI 
- —  Columns 


Values  of  K3  (Upper  column  ) 

Diagram  8 


100 


80 


P 


20 


"5  ^ 
I  0 


Moment  M^^f 


  Girders  hinged-Case^ 

 Girders  with  con 

stanf  momen+  CaseYI 

^  =  k;    ^-Ka  Girders  fixed-Case-ra 


Values  of  K3  (upper  column) 
Diagram  9 


.  < 


100 


Moments  in  second 
tier  columns 

 Outer  girders  with 

constant  moments-Case  YlII 

 Outer  girders 

hinged  Case  IX 

K.        K.  ^,<   Outer  girders 


Values  of  KJ,  (Lower  column) 


424 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  10-6 


Diagram  10 


l.O  ,  1.5 
Values  of 


Diagram  11 


Moments  in 
exterior  columns 

K3  Jm}oad^ 


Values  of  '^X^j 


Sec.  l(H6al 


MOMENTS  IN  RIGID  BUILDING  FRAMES 


425 


fixity  to  a  hinged  support.    It  will  be  assumed  that  A  and  B  do  not  receive  translation  during 
the  loading  of  the  frame.    The  following  moments  at  the  head  of  the  lower  column  result: 
6a.  Inner  End  of  Girder  Hinged  (Case  XI). — 

66.  Inner  End  of  Girder  Fixed  (Case  XII).— 

Diagram  11  was  plotted  from  these  two  cases.  Case  XI  gives  an  increase  in  moment 
of  approximately  40%  over  Case  XII,  and  this  shows  the  greatly  undesirable  result  of  putting 
an  expansion  joint  in  the  girder  system  only  one  span  from  the  exterior  columns.  If  the  girders 
are  continuous  past  the  second  column  from  the  end,  few  cases  will  arise  in  which  the  moment 

at  the  head  of  the  lower  exterior  column  (MAb)  will  exceed  60%  of  the  load  factor  ^0  ,  which 

for  a  uniform  load  over  AB  gives  0.05  wP. 

7.  Moments  in  Columns  in  Flat-slab  Construction. — In  flat-slab  construction,  it  is  neces- 
sary to  estimate  the  stiffness  of  the  floor  before  it  is  possible  to  compute  the  moments  at  the 
heads  of  the  column.  This  may  be  done  by  replacing  the  floor  slab  by  an  "equivalent  girder." 
Just  what  portion  of  the  floor  slab  may  be  considered  as  a  girder  resisting  deformation  in  the 
columns  depends  upon  the  type  of  reinforcing  employed. 

Consider  a  flat-slab  structure  in  which  four-way  reinforcing  has  been  employed.    If  one 
column  is  submitted  to  a  bending  moment,  the  rigidity  of  the  joint  at  its  end  depends  upon  the 
rigidity  of  the  column  beyond  and  upon  the  stiffness 
of  the  floor  slab.    The  moment  taken  by  the  flat 
slab  may  be  taken  partially  by  the  diagonal  system  ^ 
of  reinforcement  to  columns  lying  diagonally  across     ^  a,>^Nil/'x,c 


the  panel  from  the  column  in  question,  and  partly  i  |  a 

by  the  rectangular  system  to  columns  in  the  same  (jT—. 2>^^|^4^^^f!m) 
bent  as  the  column  in  question.    If  this  same  struc-  ^ 
ture  is  loaded  on  its  floor  in  alternate  panels,  the  Fig.  7. 

moment  caused  in  the  slab  will  be  carried  to  the 
columns  by  the  two  systems  of  reinforcement. 

Consider  now  an  exterior  column  as  shown  in  Fig.  7.  Let  two  adjacent  spans  be  loaded 
.with  a  uniform  load.  Moment  is  brought  to  the  column  by  the  three  bands  of  reinforcement 
a,  b,  and  c.  As  the  structure  is  loaded  symmetrically  to  the  right  and  to  the  left  of  band  6, 
the  moments  brought  by  the  bands  a  and  c  will  be  equal.  The  proportion  of  moment  carried 
by  bands  a  and  c  to  that  carried  by  band  b  depends  upon  the  rigidity  of  the  two  systems  of 
paths. 

Suppose  there  exist  no  diagonal  bands  a  and  c.  The  reinforcement  would  now  follow  a 
two-way  system  and  reinforcing  for  the  central  portions  of  the  panel  would  cross  over  the  bands 
of  reinforcing  between  columns.  If  in  this  system  the  load  is  applied  symmetrically  with  re- 
spect to  the  band  &,  the  moment  of  the  load  carried  to  A  would  reach  A  largely  through  the  beam 
action  of  the  bands  of  reinforcing  extending  bet\veen  columns.  It  is  here  assumed  that  the 
band  6  has  a  width  equal  approximately  to  the  width  of  the  depressed  head. 

Whereas,  in  the  case  of  the  four-way  reinforcement  a  considerable  amount  of  moment 
is  brought  by  bands  a,  b  and  c  to  column  A,  which  in  the  two-way  reinforcement  would  have 
reached  the  column  A  through  the  band  b  and  through  the  band  along  the  outer  wall,  it  will 
be  assumed  for  purposes  of  estimation  that  the  amount  of  moment  brought  to  A  may  be  deter- 
mined by  assuming  a  beam  action  of  the  rectangular  reinforcement 


426 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  10-8 


It  will  be  considered  first  that  the  stiffness  between  columns  A  and  B  is  furnished  by  a 
strip  of  floor  slab  the  width  of  band  b.  Later  a  discussion  concerning  the  error  involved  in  this 
assumption  will  be  undertaken. 

The  moment  brought  to  the  head  of  the  column  will  be  estimated  by  considering  a  load 
over  the  area  between  A  and  B  having  the  width  of  one  panel.  The  frame  in  sectional  view 
appears  on  page  420.  The  moment  Mab  is  given  under  Case  XII.  It  will  be  sufficient  in  com- 
puting the  value  of  Ii  for  Ki  to  consider  only  the  concrete  area,  neglecting  the  cross-section 
of  the  reinforcement.  In  the  columns,  however,  the  reinforcement  should  be  considered  in 
computing  the  moment  of  inertia.  Having  solved  for  the  moment  by  formula  (XII),  the  neces- 
sary flexural  reinforcement  at  the  ends  of  the  column  may  be  computed.  The  moments  in  the 
various  bands  in  the  slab  are  found  in  the  computations  on  flat  slab  floors  (see  Art.  20,  Sect. 
11). 

Concerning  the  portion  of  the  slab  between  columns  A  and  B,  it  has  been  assumed  above 
as  having  a  width  equal  to  the  width  of  the  band  b.  It  should  be  noted  that  the  moment  of 
inertia  Ii  of  the  cross-section  of  this  strip  varies  directly  with  its  width.  Hence  Ki  also  varies 
directly  with  its  width.  An  examination  of  formula  (XII)  indicates  that  considering  the  values 
Ko  and  Ks  as  constants,  the  moment  is  decreased  by  an  increase  in  Ki,  that  is  to  say,  by  an  in- 
crease of  the  width  of  the  strip.  Just  how  extensive  this  variation  may  be  can  readily  be  deter- 
mined from  Diagram  11. 

8.  Criteria  for  Maximum  Combined  Stresses  in  Columns. — Maximum  stresses  in  columns 
may  occur  from  two  sources:  first,  from  a  maximum  bending  moment  and  direct  stress;  and, 
secondly,  from  a  maximum  deflection  of  the  column  together  with  direct  stress.  Maximum 
deflection  of  the  column,  and  maximum  moment  in  the  column  occurring  from  moment  intro- 
duced into  the  column  from  the  girder,  do  not  occur  simultaneously.  Although  it  is  not 
always  true,  it  is  usually  the  case  that  the  maximum  moment,  together  with  the  combined 
stress,  will  give  the  greatest  fiber  stress  in  the  column. 

It  may  be  necessarj^  to  design  certain  columns  for  a  given  static  load,  or  it  may  be  necessary 
to  investigate  columns  for  special  loading  in  a  given  panel  or  panels.  For  that  reason  the 
following  criteria  are  given. 

8a.  Interior  Columns. — Maximum  moments  are  caused  by  loading  the  bay 
adjacent  to  the  column  in  question  for  the  full  height  of  the  structure,  and,  where  possible,  by 
loading  alternate  bays  in  both  directions  from  that  bay.  The  maximum  moment  will  be  found 
in  the  second-tier  columns.  The  maximum  stress  in  these  columns  will  be  found  by  combining 
the  stress  caused  by  this  maximum  moment  with  the  axial  stress  produced  by  the  load  on  the 
floors  above  the  first  floor. 

Maximum  deflections  may  be  caused  in  the  interior  columns  by  loading  spans  alternate  in 
all  directions.  In  the  case  of  very  slender  columns,  the  deflection  may  add  a  moment  caused 
by  the  direct  load  to  that  moment  causing  the  deflection.  The  stress  thus  produced,  when  com- 
bined with  the  dead  load  and  such  live  load  as  is  transmitted  to  the  column  in  question  will 
produce  the  maximum  fiber  stress  for  that  case  of  loading. 

8b.  Exterior  Columns. — ^Loading  to  produce  the  maximum  stress  due  to  moment 
in  the  exterior  columns  is  the  same  as  that  for  interior  columns.  Likewise  the  loading  causing 
the  maximum  deflection  in  the  exterior  column  is  applied  in  the  same  manner  as  the  loading 
causing  the  maximum  deflection  in  the  interior  columns.  Exterior  columns,  however,  will 
receive  more  moment  than  interior  columns  because  of  the  fact  that  the  columns  are  not  assisted 
by  a  girder  beyond  in  restraining  the  moment  generated.  Whatever  negative  moment  there  is 
in  the  end  of  the  girder  in  the  exterior  bay,  it  must  be  balanced  by  a  moment  in  the  exterior 
column  above  and  below  that  girder.  The  stresses  due  to  this  moment  combined  with  the 
stresses  due  to  axial  loading  will  cause  the  maximum  fiber  stress  in  the  column. 

A  very  important  consideration  in  the  exterior  columns  is  the  moment  caused  in  the  corner 
columns.  When  the  floor  is  constructed  of  slabs  and  beams,  the  moment  may  be  considered 
as  being  introduced  into  the  column  by  the  two  girders  meeting  at  right  angles  to  each  other, 


Sec.  10-9] 


MOMENTS  IN  RIGID  BUILDING  FRAMES 


427 


and  these  moments  may  then  be  combined  to  give  a  diagonal  resulting  moment.  The  column 
in  such  construction  is  usually  square,  and  there  will,  therefore,  be  a  change  of  axes  for  this 
resultant  bending.  When  the  floor  is  a  flat  slab,  moments  are  brought  into  the  corner  column 
from  three  sources  (in  four-way  reinforcing  systems),  from  the  lintel  beams  and  from  the 
diagonal  band  of  reinforcing  that  crosses  the  corner  panel.  It  has  been  found  from  tests  on 
buildings  that  this  diagonal  band  carries  extremely  high  stresses  in  the  reinforcing  and  that  these 
high  stresses  introduce  into  the  corner  columns  very  large  moments.  An  estimate  of  the  mo- 
ment in  the  corner  column  can  be  made  by  considering  an  equivalent  beam  action  (see  page  425) 
to  replace  this  diagonal  band.  The  negative  moment  at  the  extremity  of  this  equivalent  beam 
may  be  computed  and  this  moment  may  then  be  combined  with  the  resultant  moment  of  the 
moments  at  the  ends  of  the  lintel  beams.  It  should  be  here  noted  that  the  length  of  the 
equivalent  girder  is  the  length  of  the  diagonal  across  the  panel.  If  the  corner  column  is  not 
round,  the  transfer  of  axes  is  necessary  before  computing  maximum  fiber  stress. 

9.  Wind  Stresses  in  Building  Frames. — It  is  often  necessary  to  determine  the  stresses  set 
up  in  a  large  building  frame  by  wind  pressure  on  some  exposed  face  of  the  building.  Exact 
methods^  of  the  analysis  of  these  stresses  are  very  long  and  tedious,  and  some  of  them  are  so 
laborious  that  it  is  impracticable  if  not  impossible  to  apply  them  to  a  building  of  any  consider- 
able height. 

An  exhaustive  study  of  stresses  due  to  wind  pressures  in  buildings  has  been  made  in  Bulletin 
80  of  the  Engineering  Experiment  Station  of  the  University  of  Illinois  by  Prof.  W.  M.  Wilson 
and  G.  A.  Maney.  In  this  bulletin  a  number  of  approximate  methods  have  been  studied  with 
a  view  to  the  determination  of  their  accuracy,  and  a  comparison  of  exact  methods  has  been  made 
to  determine  their  applicability,  after  which  the  writers  of  the  bulletin  present  an  original 
procedure  for  exact  analysis  by  slope-deflections. 

Tall  building  frames  which  are  not  symmetrical  about  a  vertical  center  line  or  which  have 
a  considerable  variation  in  the  sizes  of  adjacent  members  should  be  analyzed  by  some  one 
of  the  exact  methods,  of  which  that  of  slope-deflections  is  probably  the  most  usable. 

For  bents  of  a  given  building  frame  having  practically  equal  spans  and  equal  column 
sections,  an  approximate  method  based  on  the  following  assumptions  has  been  found  to  give 
quite  accurate  results.^ 

1.  Points  of  inflection  in  columns  are  located  at  their  mid-height. 

2.  The  point  of  inflection  of  each  girder  is  at  its  mid-length. 

3.  The  shear  on  each  interior  column  is  equal,  and  the  shear  on  each  exterior  column  is 
equal  to  one-half  the  shear  on  any  interior  column. 

The  wind  is  considered  as  being  applied  at  each  floor  level.  If  W  represents  the  total  wind 
force  applied  to  the  structure  above  a  given  floor,  then  according  to  assumption  (3),  the  shearing 
force  W  is  distributed  among  the  several  columns  just  above  this  floor  in  such  a  manner  that 
each  interior  column  takes  an  equal  amount  and  each  exterior  column  takes  half  of  the  amount 

W 

taken  by  an  interior  column.    Thus  if  n  is  the  number  of  panels,  —  is  the  amount  taken  by 
W 

each  interior  column,  and      is  the  amount  taken  by  each  exterior  column. 

The  direct  stresses  in  the  girders  are  relatively  small  and  are  usually  neglected.  The 
direct  stresses  in  the  columns  are  important  in  very  tall  narrow  buildings  and  may  be  com- 
puted by  considering'  the  frame  of  the  building  to  act  as  a  cantilever  beam  with  its  fixed 
end  at  the  ground.    The  direct  stress  in  any  given  column  will  be  proportional  to  the 

1  The  reader  is  referred  to  the  following  articles,  any  one  of  which  gives  an  exact  solution  of  the  problem: 
"Wind  Stresses  in  the  Frames  of  Office  Buildings,"  by  Albert  Smith,  Journal  Western  Society  of  Engineers, 

vol.  20,  No.  4,  p.  341. 

"Stresses  in  Tall  Buildings,"  by  Cyrus  A.  Melick,  Bull.  8,  College  of  Engineering,  University  of  Ohio. 

"The  Theory  of  Frameworks  with  Rectangular  Panels  and  its  Application  to  Buildings  Which  Have  to 
Resist  Wind,"  by  Ernst  F.  Johnson,  Trans.  Am.  Soc.  C.  E.,  vol.  55,  p.  413. 

"Wind  Stresses  in  the  Steel  Frames  of  Office  Buildings,"  Bull.  80,  Engineering  Experiment  Station,  Uni- 
versity of  Illinois. 

2  "Wind  Stresses  in  Frames  of  Office  Buildings,"  by  Albert  Smith  of  Purdue  University,  Journal  of  Western 
Society  of  Engineers,  vol.  20,  No.  4,  p.  341, 


428 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  10-10 


77 


Fig.  8. 


distance  of  the  column  from  the  center  line  of  the  building.    To  be  able  to  find  these  direct 

stresses,  the  moment  of  the  total  wind  pressure  about  a  given 
floor  level  must  be  placed  equal  to  the  moment  of  the  direct 
stresses  in  the  columns  about  the  center  line  of  building.  The 
direct  stress  in  a  column  due  to  wind  should  be  combined  with 
the  stress  due  to  vertical  loading. 

Since,  according  to  assumptions  1  and  2  above,  points  of 
inflection  occur  at  the  center  of  each  column  and  at  the  center 
of  each  girder,  a  single  joint  may  be  removed  as  a  free  body- 
as  in  Fig.  8.  The  moments  in  ^the  members  about  the  joint 
may  readily  be  found  from  such  a  figure. 
The  couple  caused  by  the  shears  on  the  columns  must  be  resisted  by  the  shears  on  the 
girders.    The  girders  are  assumed  as  having  the  same  length.  Then 


2ln 


(1) 


assuming  a  and  b  to  refer  to  two  adjacent  stories.  It  is  sufficiently  exact  in  making  com- 
putations by  this  method  and  in  keeping  with  the  assumption  of  equal  column  sections  to 
consider  Wa  and  h2  as  equal  to  Wb  and  hi  respectively. 

Wbhi 

The  moment  at  the  base  of  the  upper  column  is  equal  to       ?        that  at  the  top  of  the 

lower  column,  The  moment  at  the  end  of  either  girder  due  to  the  wind  is 

For  an  exterior  panel  (Fig.  9)  the  value  of  V  is  given  by  yy. 
equation  (1).    The  moment  at  the  base  ot  the  upper  column  is  2/? 

equal  to        5  at  the  top  of  the  lower  column,         ]  and  at  the 

J    ^  ^  .J 
end  of  the  girder,  -y* 

10.  Roof  Frames. — It  would  be  impractical  to  give  here  a 
complete  set  of  formulas  for  the  large  range  of  possible  roof 
frames.  It  will  be  of  use,  however,  to  give  some  of  the  more 
common  types  of  frames. 


Type  I 


7-^ 


■Case  I. 


> 

Fig.  9. 


Va  = 


H 


r 

ho 

wl^  R(3ho  +  5h) 

64  ■   ho^S  +  R(3hoh  +  hi^) 


S  =  ^ 


%wl 


Case  11. 


A 


■4" 


Type  n— Case  /. 


♦unTTiunTrn 


Hb 
Ha 

h 

h, 
Va 

H 


V_VWh,{S  +3R)  +  bhi^R{3ho+h)  +  5ho^hS-{- WR{ho+ h)' 
16L  ho^S  +  R{3hoh  +  hi^) 

Vh  -  Hb 


wl 
2 


R(l  +  A;) 


=  S 


wl 


ShilSd  +  k^)  +  R(l  -j-k 


-hk^)] 


Sec.  10-11] 


MOMENTS  IN  RIGID  BUILDING  FRAMES 


429 


Case  II. 


Hb 


phiV         5S  +  R{4: -\- 2k)  1 
8  U(l  +k')  +R{1  +  k  +  k^)j 

7^   Ha  =  phi  -  Hb 


Case  III. 


Hi 


I 


_Pkr         2k^S  +  R{1  +  2k)  1 
2  L'S^Cl  +/c3)  +72(1  +k-\-k^)\ 


P  -  H. 


Type  III.— Case  /. 


r 


21 

wlx^  4l,R  +  S(l  +  Uj) 
8lh'         R  -\-  S 


S  = 


Ii 


Case  II. 


Va 


Hb 


^  21 

ph  4I2R  +  Sjh  +  5I2) 
81'  R  +  S 


11.  L-frames. — The  L-frame  may  occur  either  with  a  fixed  or  hinged  column  base;  or  with 
a  fixed  or  hinged  girder-end.  In  the  four  cases  which  follow,  the  girder-end  is  fixed  and  the 
column  base  hinged.  The  frame  may,  with  its  loading,  be  revolved  through  90  deg.  to  suit  the 
reverse  of  the  cases  shown.  Frames  of  this  nature  which  are  fixed  at  both  extremities  seldom 
occur  in  practice  as  a  separate  structure,  and  hence  are  not  given  here. 


Case  I. 


R  = 


Ha  = 


SPam^ 


Va 


Rh^  {SR  +  ^S) 

2S  (a  +  26)  +SR(b  +  2a) 


{3R  +  4S) 
Mb  =  -  HaK    Mc  =  -  HAh  +  VaB 


Pri 


-  HAh  +  VAa 


430 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  10-11 


Case  II. 


wb 


A' 


mmmmc 

<.t.....^..::-^...>i 


Mx,,  (max.)  = 


2w 


Case  III. 
B 


1  

i 

Case  IV. 


A 


Ha 
Va 


SPa  [2h^S  -  aS  (26  +  m)] 
'  Rh^{SR  +  4:S) 

2P  [ISRh^  +  a^Si2b  +  m)] 


Havi 


{SR  +  4^') 

Mb  =  HAh 


Pa 


Mc  =  Mb  +  VAb 


Ha  = 


Sph  (R  +  S) 


V  -  2p 

A  very  common  form  of  the  L-frame  is  the  one  which  is  hinged  at  both  extremities.  It  is 
not  uncommon  for  the  beam  to  have  some  slope  other  than  horizontal.  Both  cases  follow 
briefly: 

Mac  =  ZEKxQa  -  N 
Mae  =  3EK2dA 
Mas  =  —  Mac 
Mab 


A 

5« 


Load 


Oa 


SEK, 


Mab 
Mac  =  -Fr—  '  Ki 


N  =  -  MAi 


K2 


N 


Mac 


NK2 


Pah 
21^ 


Suppose  the  "load"  to  be  a  concentrated  load  P,  placed  a  distance  a  from  C.  Then  = 
(I  +  a).    If  the  "load"  is  a  symmetrically  placed  load,  with  respect  to  the  member  AC, 


N 


=  y,  the  moment  at  the  end  of  a  fixed  beam  which  carries  that  particular  loading  (see  page 


41.3  for  values  of  j  for  various  loads). 

When  the  beam  is  not  horizontal,  but  slopes  upward  to  the  end  C,  the  solution  of  the 
fram^  may  be  obtained  by  letting  h  in  Type  II  of  "Roof  Frames"  become  zero. 


SECTION  11 


BUILDINGS 
FLOORS— GENERAL  DATA 

1.  General  Types  of  Concrete  Floors. — There  are  four  general  types  of  concrete  floors: 
(1)  monolithic  beam  and  girder  construction,  (2)  flat-slab  construction,  (3)  unit  construction 
and  (4)  steel-frame  construction  with  concrete  slabs.  In  the  fourth  type  mentioned,  the  beams 
and  girders  are  usually  covered  with  concrete  for  fire  protection. 

2.  Floor  Loads. — The  following  extract  from  the  Seattle  Building  Code  illustrates  good 
practice : 

All  floors  shall  be  constructed  to  bear  a  safe  live  load  per  superficial  square  foot  of  not  less  than  the  following 
amounts. 

Pounds 


Public  buildings     100 

Detention  buildings,  in  cells  or  wards   60 

Churches,  chapels,  theatres,  assembly  halls  or  court  rooms  with  permanent  seats   80 

Lobbies,  passageways,  corridors  and  stairways  of  the  same   100 

Assembly  halls  with  movable  seats   100 

Halls  used  for  dancing,  or  roller  skating   150 

Lobbies,  passageways,  corridors  and  stairways  of  the  same   100 

Stables   80 

Dwellings,  apartment  houses,  flat  buildings  and  lodging  houses   50 

Class  rooms  in  schools   60 

Assembly  rooms  in  schools   80 

OflBce  buildings  and  hotels,  ground  floor   125 

For  floors  above  the  ground  floor   75 

Store  buildings  for  light  merchandise,  ground  floor   125 

For  floors  above  the  ground  floor   100 

Store  buildings  for  heavy  merchandise,  such  as  grocery  stores  or  hardware  stores   150 

Warehouses   200 

Factories  and  workshops,  when  the  nature  of  the  work  is  general   125 

Machine  shops,  armories,  drill  rooms  and  riding  schools   250 


Floors  in  a  building  to  be  used  for  the  sale,  storage  or  manufacture  of  heavy  machinery,  shall  be  propor- 
tioned to  the  load  they  may  have  to  carry. 

In  addition  to  specifying  minimum  floor  loadings  for  which  the  various  types  of  buildings 
must  be  designed,  the  Rochester  Building  Code  requires  also  the  following : 

The  weight  placed  on  the  floors  of  any  building,  now  or  hereafter  constructed,  shall  be  safely  distributed 
thereon.  The  bureau  may  require  the  owner  or  occupant  of  any  building  or  portion  thereof  to  redistribute  the 
load  on  any  floor,  or  to  lighten  such  load  when  deemed  necessar.y,  even  if  not  greater  than  the  minimum  in  this 
section  prescribed. 

To  prevent  overloading  in  all  warehouses,  storehouses,  factories,  workshops  and  stores,  now  or  hereafter 
constructed,  where  heavy  materials  are  kept  or  stored,  or  machinery  introduced,  the  weight  that  each  floor  will 
safely  sustain  upon  each  square  foot  thereof,  or  upon  each  varying  part  of  such  floor,  shall  be  estimated  by  a 
competent  person  employed  by  the  owner  or  occupant,  or  the  bureau  may  make  such  estimate,  and  said  estimate 
shall  be  placed  permanently  on  a  stone  or  metal  tablet  in  a  conspicuous  place  in  the  hallway  of  each  story  or  vary- 
ing parts  of  each  story  of  the  building  to  which  it  relates. 

No  person  shall  place  or  permit  to  be  placed  on  the  floor  of  any  building,  now  or  hereafter  constructed,  any 
greater  load  than  the  safe  load  thereof  as  correctly  estimated  and  ascertained  as  herein  provided. 

The  working  stresses  usually  employed,  and  those  recommended  by  the  Joint  Committee 
are  intended  to  apply  to  static  loads  only.    Proper  allowance  for  the  dynamic  effect  of  the  live 

431 


432 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-3 


load  should  be  taken  into  account  by  adding  the  desired  amount  to  the  live  load  to  produce  an 
equivalent  static  load  before  applying  the  unit  stresses  in  proportioning  parts.  An  allowance 
for  impact  will  be  necessary  only  in  special  cases,  as  in  the  case  of  floors  supporting  heavy  ma- 
chinery. The  amount  to  add  to  the  live  load  because  of  impact  will  vary  all  the  way  from  25 
to  100%  depending  upon  the  proportion  of  the  specified  live  load  which  may  be  subject  to 
motion. 

The  dead  load  of  any  floor  may  be  estimated  from  the  following  approximate  data — weights 
are  per  square  foot  of  floor  surface: 

Wooden  wearing  surfaces,  4  to  6  lb.  Plaster,  5  lb. 

Screeds  or  nailing  strips,  2  lb.  Suspended  ceiling,  10  lb. 

Cinder-concrete  filling  (2  in.  thick),  15  lb.  Cinders,  7  lb. 

Hollow  tile,  see  Art.  12. 

3.  Economic  Considerations. — The  size  of  floor  bays  depends  upon  the  loading,  the  uses 
to  which  the  building  is  to  be  put,  and  the  size  and  shape  of  the  ground  area.  In  a  large  build- 
ing it  is  frequently  worth  while  to  make  several  comparative  estimates  with  different  layouts 
of  the  beams,  girders  and  columns,  so  as  to  obtain  the  most  economical  arrangement  under 
the  given  conditions. 

The  cost  of  changing  forms  to  meet  changes  in  size  of  beams  and  columns  in  different  stories 
must  be  kept  constantly  in  mind.  It  is  more  economical  to  vary  the  depths  of  beams  from  floor 
to  floor  than  the  widths,  on  account  of  the  slab  panels ;  and  to  vary  square  columns  in  one  dimen- 
sion rather  than  in  two,  both  on  account  of  the  columns  themselves  and  the  beams  which  frame 
into  them.  It  is  not  advisable  to  change  the  size  of  members  from  floor  to  floor  for  small  differ- 
ences in  computed  dimensions;  nor  is  it  advisable  on  any  floor,  if  simplicity  in  field  work  is 
desired,  to  make  slight  changes  in  the  sizes  of  beams  and  in  the  thicknesses  and  reinforcement 
of  the  slabs,  unless  such  variations  occur  over  large  areas.  When  slabs  of  considerable  variation 
in  span  alteFn,^irej  it  is  better  to  vary  the  thickness  and  keep  the  reinforcement  the  same,  than 
to  vary  the  reinforcement  and  use  the  same  thickness  of  slab.  Although  slight  differences  in 
dimensions  are  not  desirable,  the  designs  made  should  be  considered  carefully  in  every  detail. 

4.  Floor  Surfaces. — A  concrete  floor  usually  has  a  mortar  or  granolithic  finish  as  wearing 
surface.  Such  a  surface  if  not  allowed  to  set  rapidly  is  hard  and  practically  impervious  to 
water. 

^he  usual  proportions  for  granolithic  finish  are  1  part  Portland  cement,  1  part  sand,  and 
^j^t  crushed  stone  which  passes  through  a  K-in.  mesh  screen.  This  mortar  surfacing  is  laid 
^^ff  the  concrete  slab  and  troweled  to  a  hard  finish.  If  placed  before  the  concrete  below  has 
^t,  it  may  be  from  to  1  in.  thick  but  where  the  concrete  of  the  slab  becomes  old  before  the 
granolithic  finish  is  laid,  the  thickness  should  be  at  least  2  in. 

Granolithic  finish  is  screeded  to  grade  with  a  straight-edge,  smoothed  with  a  wooden 
float,  and  finished  with  a  steel  trowel.  It  is  often  marked  off  into  blocks,  or  sections,  of  suitable 
size  by  shallow  grooves.  The  object  in  dividing  the  surface  into  panels  is  purely  ornamental, 
since  reinforcement  against  shrinkage  cracks  is  provided  in  the  lower  portion  of  the  concrete 
slab. 

For  a  complete  treatment  of  concrete-floor  surfaces,  see  Sect.  4. 

Some  engineers  prefer  to  lay  a  cinder-concrete  base,  not  less  than  2  in.  thick,  before  placing 
the  cement  finish.  The  advantage  of  this  method  is  that  should  there  be  any  reason  for  remov- 
ing a  section  of  the  finished  floor,  it  can  be  accomplished  without  injury  to  the  reinforced-con- 
crete  slab.  On  account  of  the  porosity  of  the  cinder  concrete  it  is  difficult,  however,  to  obtain 
a  satisfactory  cement  finish  if  the  same  is  placed  before  the  cinder  concrete  base  has  set. 

If  a  wood  floor  is  desired,  2  by  3-in.  or  2  by  4-in.  sleepers  are  usually  laid  on  top  of  the 
rough  concrete  slab,  and  cinder  concrete  or  stone  concrete  poor  in  cement  is  run  between  these 
nailing  strips.  For  ordinary  cases,  %  to  13^ -in.  maple  flooring  nailed  to  2  by  3-in.  sleepers,  16  in. 
apart,  is  found  satisfactory.  The  proportions  of  cinder  concrete  specified  vary  considerably — 
average  proportions  are  1 :  3  :  6.   The  sides  of  sleepers  are  usually  beveled,  but  this  does  not 


Sec.  11-5] 


BUILDINGS 


433 


prevent  them  from  becoming  loose  if  the  wood  shrinks.  The  best  method  of  holding  the  sleepers 
in  place  is  to  drive  40d.  nails  in  the  sides  of  the  sleepers  at  intervals  of  3  ft.  on  alternate  sides. 
These  nails  key  with  the  concrete  and  prevent  movement  of  the  sleeper. 

There  has  been  much  dissatisfaction  with  the  above  method  of  constructing  wooden  floor 
surfaces  on  account  of  the  liability  of  the  sleepers  to  decay  by  dry  rot.  To  lessen  decay  the 
sleepers  should  be  well  seasoned  and  might  advantageously  be  impregnated  with  preservative 
of  some  sort,  and  care  should  be  taken  to  permit  no  moisture  to  reach  them  even  after  the  top 
flooring  is  in  place.  Sufficient  time  should  be  allowed  the  concrete  to  dry  out  before  the  finished 
flooring  is  laid.  Dry  rot  is  a  fungus  disease  of  wood  that  thrives  in  the  presence  of  moisture 
and  absence  of  circulating  air.  It  makes  little  difference  in  result  whether  the  moisture  is  the 
sap  of  the  green  wood,  or  water  that  soaks  into  the  wood  after  it  has  been  dried. 

Sleepers  are  sometimes  laid  in  dry  cinder  fill.  In  such  construction  the  chance  of  dry  rot 
is  probably  small,  since  there  is  some  opportunity  for  air  circulation  through  the  porous  cinders. 
Cinders  also  tend  to  absorb  moisture. 

A  sand-and-tar  base  for  plank  flooring  on  reinforced-concrete  floor  slabs  has  been  employed 
to  some  extent  to  avoid  any  danger  from  dry  rot.  A  layer  of  sand  mixed  with  coal  tar  is  spread 
about  in.  thick  on  the  floor  slab  and  leveled  while  still  warm  and  soft  with  a  straight-edge. 
On  this  layer  is  then  placed  first  a  layer  of  2-in.  plank,  then  %-in.  roiigh  pine  board,  and  finally 
a  wearing  surface  of  %  to  13^:^-in.  maple.  The  different  layers  of  planking  should  be  placed  in 
different  directions. 

The  following  construction  has  been  used  in  schoolhouse  floors  with  satisfactory  results: 
At  the  completion  of  the  floor  slab,  a  1-in.  footing  of  sand  is  placed  on  top  of  the  same  and  brought 
to  a  true  level  by  screeding.  On  top  of  the  sand  are  placed  13'^-in.  boards  laid  diagonally  and 
nailed  together  at  the  edges.  The  form  lumber  used  for  centering  is  generally  employed  for 
this  work.  On  top  of  the  l^-^-in.  boards  is  then  placed  building  paper,  which  in  turn  is  covered 
by  the  finished  flooring. 

So-called  "nailable  concretes"  have  been  attempted  but  without  substantial  success. 
They  are,  in  effect,  poor  concretes,  made  from  cinders  and  sand  with  a  small  amount  of  asbestos 
or  like  substance,  into  which  flooring  nails  may  be  driven.  Their  prolonged  retention  of  water, 
generation  of  acid  from  wet  cinders  and  faulty  hold  on  nails  has  prevented  their  extensive  use. 

In  hotels  and  similar  establishments,  linoleum  or  carpeting  over  a  fairly  smooth  cement 
base  seems  to  give  satisfaction.  If  the  floor  is  very  wet  and  alkaline,  saponification  may  take 
place,  with  destruction  of  the  linoleum.  A  thoroughly  good  cement  is  insurance  against  such 
occurrences.    Sodium  silicate  should  not  be  used,  as  it  liberates  free  sodium. 

Flat  tiles  are  sometimes  employed  as  a  floor  surface  in  reinforced-concrete  construction. 
The  most  durable  and  sanitary  tile  is  the  vitreous-clay  tile.  The  ceramic  tile  is  perhaps  the  most 
often  used  and  is  a  vitreous-clay  tile  manufactured  in  square,  hexagonal,  and  round  shapes.  The 
squares  range  in  size  from  }^  to  in.  and  the  hexagonal  shapes  from  to  1  in.  Tiles  are 
laid  some  little  time  after  the  floor  slab  is  poured  and,  if  set  in  Portland-cement  mortar,  should 
be  embedded  in  a  layer  not  less  than  2  to  in.  thick  in  order  to  prevent  curling  of  the  tile  due 
to  shrinkage  of  the  base.  There  are  now  on  the  market,  however,  some  patented  bases  which 
seem  satisfactory  and  which  will  allow  a  bedding  thickness  of  only  1  in.  over  and  above  the 
thickness  of  the  floor  slab  proper. 

5.  Small  Floor  Openings. — The  methods  of  arranging  slab  reinforcement  around  small 
openings,  such  as  for  chimneys  and  ventilators,  needs  some  consideration.  Both  a  wrong  and 
a  right  method  are  shown  in  Fig.  1.  The  openings  are  shown  against  a  wall,  and  the  floor 
slab  is  reinforced  in  only  one  direction. 

The  method  shown  of  placing  the  reinforcing  rods  parallel  to  the  opening  makes  a  neat 
looking  job,  but  it  should  be  evident  that  no  proper  provision  is  necessarily  made  to  carry  the 
load  which  would  ordinarily  come  on  the  wall  at  the  openings.  The  right  method  shown  is 
less  artistic,  but,  as  a  general  rule,  is  vastly  more  efficient.  The  cross  rods  serve  only  to  rein- 
force the  slab  locally.  All  such  designs  should  be  carefully  studied  to  make  sure  that  the 
28 


434 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-6 


m// 

trr 


I  I 

nil 
1 1 1 1 

LLLL'i 


TT 


mm 
ii  1*1 

II  Mil 

Oil 

I I I  1 1 
Mill 

1 1 1  1 

I'l  l 
iliiil 

II!'" 


I  .  I 


mm 


f 

/II 


I 

1^1 


required  strength  is  secured  at  all  points.  Slab  rods  should  never  be  curved  horizontally  to 
dodge  floor  openings  as  a  curved  rod  will  tend  to  rotate. 

Wrought-iron  and  galvanized-iron  sleeves  are  built  into  the  construction  work  for  all 
steam,  return,  sprinkler,  sewer,  gas,  and  similar  pipes.  All  floor  sleeves  should  be  flush  with 
the  ceiling  line  and  should  extend  about  2  in.  above  the  floor  line.  Pipe-risers  should  not  be 
allowed  to  come  up  through  columns  as  repairs  and  alterations  are  difficult,  if  not  impossible, 
under  such  an  arrangement;  electric  conduits,  however,  form  an  exception  to  this  rule.  Special 

shafts  with  fireproof  walls  are  sometimes 
used  for  plumbing  and  vent  pipes,  and  this 
practice  has  much  to  commend  it  since  a 
floor  to  be  a  perfect  fire  cutoff  should  be 
solid  from  wall  to  wall,  with  stairways, 
elevators,  and  all  openings  enclosed  in  ver- 
tical fireproof  walls. 

6.  Provision  for  the  Attachment  of 
Shaft -hangers  and  Sprinkler  Pipes. — There 
are  many  different  methods  of  attaching 
shafting,  sprinkler  pipes,  and  machinery  to 
the  under  side  of  a  concrete  floor.  The 
method  adopted  should  be  as  flexible  as 
possible  in  order  to  accommodate  future 
changes  in  the  line  of  shafting,  additions,  or 
improved  machinery.    All  bolts  and  sockets 


1 

JJl 


3ecr/7?  ••' 

Wrong  Method 


Fia.  1. 


Sea/7?- 

Right  Method 

Method  of  placing  reinforcement  around  small 


floor  openings. 


should  be  placed  before  the  concrete  is  run,  as  drilling  is  expensive  and  reinforcing  bars  are 
liable  to  be  encountered,  which  would  cause  more  or  less  difficulty,  and  might  lead  to  serious 
trouble  if  cut  off. 

A  convenient  method  is  to  place  suitable  bolts  at  intervals,  usually  4  ft.  on  centers,  with 
their  threaded  ends  projecting  from  the  concrete.  By  means  of  these  projecting  bolts,  timbers 
may  be  fastened  wherever  desired  and  the  shaft-hangers  lag-screwed  in  place. 


—•  Stirrups  

 Han^r ^ItSj--^.^ 


Shaft  hanger  ... 
hcf  scretyecf  "" 


Section, 


Elevation 


Fig.  2. 


The  heads  of  bolts  projecting  into  concrete  should  be  enlarged  or  bent  so  that  the  bolt 
will  not  tear  out.  If  desired,  a  washer  or  plate  may  be  employed  for  this  purpose  underneath 
the  head  of  the  bolt.  Figs  2  and  3  illustrate  the  use  of  large  washer  nuts.  These  are  tempo- 
rarily held  in  position  by  a  thin  iron  tube  resting  on  the  centering  and  by  a  bolt  projecting 
through  the  hole  in  the  bottom  of  the  beam  box.  The  washer  nut  is  tightened  down  to  the  top 
of  the  tube  which  secures  it  firmly  in  an  upright  position  (see  detail  shown  in  Fig.  4).  When 
the  beam  boxes  or  centering  are  removed,  the  bolts  are  easily  unscrewed  from  the  nut,  leaving 
a  clear  passage  through  the  concrete  to  the  nut  above.  The  stirrups  shown  are  to  prevent 
excessive  deformation  in  the  beam.  By  the  method  shown  in  Fig.  3,  the  shaft-hangers  may 
be  securely  fastened  by  bolts. 


Sec.  11-6] 


BUILDINGiS 


435 


When  projecting  bolts  are  used,  it  is  seldom  that  all  are  made  use  of,  and  those  not  used 
present  an  unsightly  appearance.  This  is  the  main  objection  to  the  scheme  shown  in  Fig.  5. 
Saddles  and  check  nuts  serve  to  hold  the  long  bolts  in  position. 

The  Unit  socket  is  shown  in  Fig.  6.  This  device  serves  also  as  a  support  and  spacer  for 
the  beam  rods,  keeping  them  all  properly  spaced  from  each  other  and  from  the  beam  box  or 
centering. 

A  form  of  adjustable  socket  for  use  in  beams,  principally,  is  shown  in  Fig.  7.  These  castings 
are  made  in  convenient  lengths  and  the  slot  in  the  bottom  makes  it  possible  to  place  hangers 


\^-5tirrups 

Holes  punched 
J)oJts  cfh^pecf 
through  before  Cis 
bolted  to  beam, 


d  and  \  \ 


Section 


Elevation 


Fig.  3. 


or  bolts  at  any  desired  location  along  the  length  of  the  insert.  The  casting  can  be  anchored 
as  securely  in  the  concrete  as  may  be  necessary  by  the  use  of  stirrups  passed  through  the  open 
spaces. 

Figs.  8  and  9  illustrate  two  other  methods  used  for  attaching  shaft-hangers  to  beams. 
Fig.  8  is  what  is  known  as  a  pipe-slot  hanger.  Fig.  9  can  be  made  a  strong  and  serviceable 
support  for  motors  and  machinery. 

The  schemes  shown  in  Figs.  10  and  11  have  been  used  quite  extensively  by  the  Turner 
Construction  Co.  of  New  York  City. 

Fig.  12  shows  a  hanger  socket  mainly  for  use  in  slabs.  The  casting  varies  in  length  with 
the  depth  of  the  slab  and  is  made  smaller  at  the  tapped  end  than  at  the  top,  so  there  will  be  no 
possibility  of  the  binding  of  the  tap-screw 
when  screwed  in.  The  cross-pin  shown 
passes  transversely  through  a  cored  hole  in 
the  upper  end  of  the  casting.  Fig.  13 
shows  a  somewhat  similar  type  of  socket. 
A  bolt  through  a  hole  in  the  form  secures 
it  in  position  during  concreting.  Figs.  14 
and  15  show  two  other  methods  used  for 
slabs  between  beams. 

A  flexible  method  of  attachment  is 
shown  in  Fig.  16 — a  method  used  in  the 
shops  of  the  United  Shoe  Machinery  Co., 
Beverly,  Mass.  The  anchor  bolts  were 
spaced  3  ft.  on  centers  in  all  transverse 

floor  and  roof  girders.    A  transverse  line  of  bolts  alternately  spaced 
was  also  built  in  the  middle  of  each  floor  and  roof  panel. 


2".  3\  fP/.  ffappecf) 


Fig.  4. — Detail  of  socket  and  bolt. 


1  ft.  and  6  ft.  centers 
In  the  girder  arrangement,  the 
nuts  on  the  lower  ends  of  the  anchor  bolts  engage  cast-iron  saddles  which  clamp  against 
pairs  of  angles  with  wood  fillers.  Fig.  16  shows  how  the  "T  "-headed  attaching  bolts  may 
move  freely  along  the  slot  formed  by  the  angles.  In  the  floor  panels,  the  bolts  have  simple 
heads  or  nuts  upon  the  upper  ends  which  bear  upon  flat  washers.  In  thin  slabs  the  heads  bear 
upon  washer  plates  in  the  upper  surface  of  the  slab  (Fig.,  16). 


436 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-6 


\  Harcf  P/ne 


^^"niy  Bent  bar 


"^S? — 
Fig.  5. 


Fig.  6. 


1 

liol 

-<• 

1 

\-Slof 


Fig.  7. 


bolt 

Fig.  8. 


Fig.  9.  Fig.  10.  Fig.  11. 


Sec.  11-7] 


BUILDINGS 


437 


It  is  not  good  practice  to  depend  upon  reinforcing  rods  for  direct  support  of  shaft-hangers, 
as  thereby  too  great  a  strain  is  placed  locally  on  the  rods  and  the  concrete  under  them  will 
become  loosened  from  the  continuous  pull  and  vibration  of  the  shafting. 


A'Pin.fZ'hn^ 


Washer 


Fig.  12. 


Elevgiiior>  Plan 

Fig.  13. 


,4W^  f  yyasher 


Fia.  16. 


7.  Bedding  Machinery. — Machines  can  readily  be  connected  to  the  concrete  by  drilling 
small  holes  in  the  floor  at  the  proper  points  and  setting  lag-screws  or  through-bolts.  If  through- 
bolts  are  required,  the  holes  should  be  located  before  the  floor  is  concreted.  A  permanent 
level  base  may  be  obtained  by  leveling  the  machine  an  inch  or  two  above  the  foundation  proper 
and  grouting  it  in  place.    A  dam  of  sand  is  first  built  around  the  machine.    Then  the  grout, 


438  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  11-8 

in  proportions  1  part  cement  to  1  or  2  parts  of  sand  mixed  to  the  consistency  of  thick  cream, 
is  poured  so  as  to  run  under  the  casting.  As  the  mortar  sets  it  is  rammed  with  a  rod  to  prevent 
shrinkage. 

In  most  cases  machinery  runs  better  and  lasts  longer  if  placed  on  solid  foundations,  but 
there  are  exceptional  cases  where  machines  seem  to  require  more  or  less  give  on  their  bases,  as 
in  certain  textile  mills.  In  such  cases  a  wood-finished  floor  can  be  laid  or  wooden  timbers 
fastened  to  the  concrete  floor.  Sheet  cork  and  linoleum  carpet  have  also  been  used  for  this 
purpose. 

8.  "Waterproof  Floors. — In  case  of  fire,  a  water-tight  floor  in  factory  buildings  prevents 
damage  from  water  to  the  machinery  or  materials  in  the  stories  below.  According  to  Insurance 
Engineering,  the  damage  from  water  after  a  fire  in  fireproof  factory  buildings  is  much  greater 
than  that  from  the  fire  itself.  A  concrete  floor  with  granolithic  surface  is  practically  impervious 
to  water  but  unless  a  floor  is  made  self-draining,  water  will  get  down  through  the  floor  open- 
ings. Raised  sills  should  be  provided  around  all  openings,  whether  or  not  a  cement  finish  is 
used,  and  scuppers  of  ample  size  should  be  placed  in  the  outside  walls  to 
carry  water  [from  the  floors  to  the  outside  of  the  building.  Fig.  17  is  a 
/7  ^'^^^l  detail  of  wall  scuppers  used  in  the  Liberty  Silk  warehouses.  New  York 
City.  The  waterproofing  of  floors  may  be  accomplished  by  using  an 
impervious  finished  flooring  or  by  using  an  undercoating  of  asphalt  felt 
laid  in  hot  asphalt. 

9.  Tests. — Within  the  last  few  years  full-sized  floor  panels  of  both 
the  monolithic  beam  and  girder  and  the  flat-slab  types,  have  been 
tested  for  the  elastic  deformation  of  the  concrete  and  the  steel  under 
increasing  loads.  The  tests  consisted  in  loading,  with  an  increasing 
load,  a  number  of  consecutive  panels  of  a  reinforced-concrete  build- 
ing, and  of  observing  the  exact  contraction  or  expansion  of  certain 
portions  of  the  steel  and  of  the  concrete  by  means  of  delicate  instru- 
ments. In  order  to  make  such  observations,  the  concrete  was  re- 
moved from  the  steel  in  given  places,  and  drill  holes  were  made  in  the 
steel  thus  uncovered.  Into  these  holes  the  extensometer  points  were  placed.  Small  holes 
were  also  drilled  in  the  concrete  for  the  same  purpose.  From  the  elastic  deformations  ob- 
tained for  moduli  of  elasticity  of  the  steel  and  concrete,  the  stresses  in  the  members  were 
computed  and  the  results  compared  with  those  for  which  the  building  was  designed.  Much 
valuable  data  pertaining  to  proper  methods  for  design  have  been  obtained  from  these 
tests. 

10.  Basement  Floors. — A  basement  floor  in  dry  ground  is  usually  made  of  1 :  3:5  concrete, 
3  or  4  in.  thick.  Usually  no  wearing  surface  is  needed  other  than  the  ordinary  concrete  troweled 
to  a  hard  finish,  but,  where  considerable  wear  is  expected,  the  usual  mortar  coat  may  be  laid 
as  on  the  upper  floors.  To  prevent  shrinkage  cracks,  the  floor  should  be  divided  into  blocks 
about  8  or  10  ft.  square.  This  may  be  accomplished  by  laying  alternate  blocks,  and  then 
filling  in  the  intermediate  ones  after  the  adjoining  concrete  has  set.  Basement  floors  are 
constructed  in  the  same  manner  as  concrete  sidewalks  (see  Sect.  4). 

It  is  not  safe  to  depend  upon  the  concrete  itself  being  water-tight.  If  the  basement  is 
below  tide-water  or  ground-water  level,  a  layer  of  waterproofing  consisting  of  three  to  six  layers 
of  waterproof  felt  (cemented  together  and  to  the  concrete  by  coal-tar  pitch  or  asphalt)  should 
be  spread  on  the  concrete  and  carried  up  in  continuous  sheets  on  the  walls  to  above  water  level. 
The  whole  surface  should  then  be  covered  with  another  layer  of  concrete  at  least  3  or  4  in. 
thick. 

The  earth  under  the  basement  floor  should  be  well  drained,  and  drains  of  tile  pipe,  or  of 
screened  gravel  and  stone,  may  be  placed  in  trenches  just  below  the  floor.  Sometimes  it  is 
necessary  to  cover  the  entire  area  with  cinders  or  stone;  and  sometimes  the  concrete  must  be 
made  extra  thick,  or  reinforcement  added,  to  resist  the  upward  pressure  of  the  water. 


Sec.  11-11] 


BUILDINGS 


439 


MONOLITHIC  BEAM-AND-GIRDER  CONSTRUCTION 

11.  Ordinary  Type  of  Beam-and-girder  Construction. — The  theory  and  methods  of  design 
of  slabs,  beams,  and  girders  are  given  in  Sect.  7.  If  a  floor  slab  is  reinforced  in  one  direction 
only,  the  load  will  practically  all  be  transmitted  to  the  beams  at  right  angles  to  the  direction 
of  the  reinforcing  rods.  A  small  part,  however,  will  be  transferred  directly  to  the  girders  at 
the  sides  of  the  panels,  but  this  may  well  be  neglected  in  the  calculations  for  cross-beams.  In 
fact,  even  with  reinforcement  in  two  directions,  the  load  should  be  assumed  as  all  transferred 
to  the  cross-beams  unless  the  panel  is  nearly  square. 

If  panels,  nearly  square,  are  reinforced  in  both  directions,  the  loads  carried  to  the  cross- 
beams and  girders  will  not  be  uniformly  distributed  over  the  length  of  such  beams  and  girders, 
but  may  be  assumed  to  vary  in  accordance  with  the  ordinates  of  a  triangle.  This  assumption 
is  surely  on  the  safe  side  in  regard  to  moment,  if  the  area  of  the  triangle  is  made  equal  to  that 
part  of  the  total  load  on  the  panel  which  is  transmitted  to  the  beam  in  question — as  determined 
by  the  formula  of  Art.  29c,  Sect.  7.  Assumptions  of  this  load  being  either  uniformly  distributed, 
or  varying  as  the  ordinates  of  a  parabola,  give  a  lower  resulting  moment  than  the  triangle 
method. 

Let  w  be  the  uniform  load  per  unit  of  area  on  the  slab,  and  W2  and  Wi  the  parts  of  this  unit 
load  that  go  to  the  shorter  and  longer  beams  respectively.  Applying  the  loads  in  the  form  of  a 
triangle  having  its  apex  at  the  middle  of  the  beam,  the  maximum  moment  will  be  for  the  longer 
beam,  and,  if  this  beam  is  considered  simply  supported  and  as  carrying  the  load  from  one  panel 
only, 

M  =  }i2Wihl^ 

and  for  the  shorter  beam 

M  =  li2W2bH 

w 

If  the  slab  is  square,  Wi  is      and  M  =        wl^.    For  beams  made  continuous,  the  bending 

moment  may  be  multiplied  by  the  coefficient  %  or  as  the  case  may  be.  With  beams  or 
girders  common  to  two  panels,  the  bending  moment  should  be  multiplied  by  2. 

Unless  the  panel  is  nearly  square,  floor  slabs  should  not  be  reinforced  in  two  directions, 
as  it  is  evident  that  no  economy  results  from  double  reinforcement  when  the  ratio  of  length  to 
breadth  of  panel  is  greater  than  about  1.2.  If  the  length  of  the  slab  exceeds  1.5  times  its 
breadth,  the  entire  load  should  surely  be  carried  by  the  transverse  reinforcement. 

When  the  floor  surface  is  given  a  granolithic  finish,  this  finish  under  certain  conditions 
may  be  considered  to  act  with  the  slab  proper  in  taking  the  stresses  under  loading.  Usually, 
however,  the  designer  has  no  way  of  finding  out  whether  the  finish  will  be  placed  at  the  same 
time  as  the  concrete,  or  run  a  number  of  hours  later,  and  this  alone  should  call  for  caution  on 
the  part  of  the  designer  in  figuring  the  finish  as  a  part  of  the  slab.  If  the  superintendent  on 
the  job  is  known  as  a  careful  man  and  if  there  is  to  be  very  careful  supervision,  the  floor  may 
be  sometimes  figured  in  this  way,  but  never  without  putting  an  underscored  note  on  the  drawing 
to  the  effect  that  the  finish  shall  be  run  immediately  after  the  pouring  of  the  concrete  slab. 
Also  the  surface  of  the  floor  should  be  blocked  off  only  along  the  center  line  of  columns  and  no 
joint  should  be  made  between  column  lines,  as  such  joints  would  affect  the  needed  strength  of 
the  slab. 

Where  care  in  construction  is  not  assured,  or  where  any  appreciable  wear  on  the  floor  is 
expected,  the  finish  should  properly  not  be  included  in  the  effective  slab  thickness.  It  is  also 
advisable  not  to  figure  this  way  for  a  winter  job  under  any  conditions. 

It  is  possible,  by  taking  great  precautions,  to  bond  a  wearing  surface  to  a  concrete  slab  after 
the  concrete  in  the  slab  has  set.  This  requires  special  treatment  including  thorough  cleaning 
and  soaking  of  the  old  concrete,  providing  a  bond  layer  of  neat  cement  mortar,  and  placing 
the  surface  before  this  neat  cement  has  begun  to  harden.    Poor  joints  occur  quite  frequently, 


440 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-11 


however,  and  it  is  advisable  not  to  figure  the  finish  as  a  part  of  the  slab  in  a  case  of  this  kind, 
even  though  considerable  care  is  assured  at  the  time  of  construction. 

If  it  is  deemed  advisable  in  any  given  design  to  consider  the  finish  as  an  integral  part  of 
the  slab,  the  maximum  fiber  stress  in  compression  may  be  determined  by  the  method  outlined 
in  Fig.  18.  The  distance  b  is  made  equal  to  the  maximum  allowable  stress  on  the  ordinary 
concrete,  and  the  distance  a  which  represents  the  maximum  stress  on  the  cement  finish  is  then 
computed  on  this  ratio.  The  later  stress,  however,  should  not  be  in  excess  of  the  maximum 
allowable  stress  for  cement  finish. 

Fig.  19  shows  an  arrangement  for  slab  steel  such  that  there  is  the  same  steel  area  at  the  top 
of  slab  over  the  cross-beams  as  at  the  bottom  of  the  slab  midway  between  these  beams.  All 
rods  are  bent  and  are  identical  in  shape — namely,  straight  at  one  end,  bent  up  at  the  center 
over  a  beam,  and  bent  over  a  beam  at  the  other  end.    The  required  arrangement  is  effected  by 


&^  i 


Neutral  Plane 


fMax.  allow- 
able fiber  ( 
stress  In 
concrete 


Fig.  18. 


Fig.  19. 


shifting  alternate  rods  7  ft.  ahead.  Some  designers  bend  up  all  the  rods  over  supports,  but  a 
better  method  is  to  continue  some  steel  at  the  bottom  of  slab  and  thus  make  sure  that  no  point 
in  tension  is  unprovided  with  steel.  The  rods  arranged  as  in  Fig.  19  may  be  carried  over  three 
spans  and  still  obtain  the  same  amount  of  steel  over  supports  as  in  the  center  of  span,  but  the 
amount  of  steel  at  the  bottom  of  slab  near  the  supporting  beams  becomes  very  small. 

Fig.  20  shows  another  arrangement  for  the  slab  steel.  Both  straight  and  bent-up  rods 
are  employed,  each  rod  extending  over  three  slab  spans.  The  joints  in  the  bent  rods  occur 
over  supports  and  the  steel  is  lapped  a  sufficient  distance  to  provide  adequate  bond  strength. 


Fig.  20. 


Fig.  21. 


This  lapping  is  so  arranged  that  two-thirds  as  much  steel  occurs  over  the  supports  as  in  the 
center  of  span. 

Fig.  21  shows  an  arrangement  of  steel  which  gives  three-fourths  the  center-of-span  area 
over  supports.  The  arrangement  is  similar  to  that  shown  in  Fig.  20  except  that  the  rods  extend 
over  only  two  spans. 

The  arrangement  shown  in  Fig.  20  requires  the  least  steel  and  that  shown  in  Fig.  19  re- 
quires the  most.    Fig.  19  shows  undoubtedly  the  best  design  for  spans  over  6  or  7  ft. 

For  moments  in  beams  and  girders  due  to  building  acting  as  a  rigid  frame,  see  Sect.  10. 


IiiiiTTSTRATrvE  PROBLEM. — Design  an  interior  floor  bay  to  support  a  live  load  of  250  lb.  per  sq.  ft.  with  the 
columns  spaced  21  ft.  by  21  ft.  on  centers  and  with  two  intermediate  beams.  Working  stresses  recommended  by 
the  Joint  Committee  for  a  2000-lb.  concrete  (see  Appendix  B)  are  to  be  employed  throughout.  (Tables  and 
diagrams  referred  to  are  those  of  Sect.  7.) 

Since  an  interior  floor  bay  has  been  assumed,  the  bending  moment  —  may  be  employed  for  the  three  parts 

of  the  floor  bay,  namely:  the  slab,  the  beam,  and  the  girder.  Fig.  22  shows  the  proposed  arrangement  of  beams 
and  girders. 


Sec.  11-11] 


BUILDINGS 


441 


The  floor  surface  will  be  given  a  granolithic  finish,  consisting  of  a  layer  of  1  :  2  mortar,  1  in.  thick,  spread  upon 
the  surface  of  the  concrete  slab  before  it  has  begun  to  set,  and  troweled  to  a  hard  finish.  For  simplicity,  the  weight 
of  finish  will  be  assumed  as  included  in  the  specified  live  load  of  250  lb.  per  sq.  ft.  Of  course  it  should  be  readily 
understood  that  in  practice,  where  a  definite  live  load  is  required,  the  finish  should  be  considered  separately  as  a 
superimposed  dead  load. 

Slab. — The  main  reinforcement  will  be  placed  in  the  direction  A  A',  Fig.  19,  and  the  span  of  slab  will  be  7  ft. 
Slab  is  to  be  fully  continuous  and  its  total  depth  will  be  taken  to  the  nearest  Yz  in. 

Diagrams  5  and  6,  Sect.  7,  show  that  a  4H-in.  (d  =  ZYi-in.)  slab  with  span  of  7  ft.  will  sustain  a  load  (live  plus 
dead)  of  approximately  325  lb.  per  sq.  ft.    Corresponding  weight  of  slab  is  56  lb.  per  sq.  ft.,  and  the  total  load  per 
square  foot  for  the  slab  to  carry  is  therefore  250  +  56  = 
306  lb. 

For  a  slab  with  d  =  ZYi  in..  Diagram  6,  Part  1, 
gives  As  =  0.325  sq.  in.  Referring  to  Table  6,  it  is 
evident  that  %-in.  round  rods  spaced  4  in.  on  centers 
will  give  sufl5cient  steel  area.  If  desired,  the  span  of 
slab  may  be  taken  as  the  clear  distance  between  faces 
of  supports  (see  Art.  44,  Sect.  7).  Four  round  rods  % 
in.  in  diameter  will  be  placed  transversely  in  each  7-ft. 
panel  to  prevent  shrinkage  and  temperature  cracks,  and 
to  bind  the  entire  structure  together. 

Cross-beams  (Eight-rod  Design). — The  cross-beams 
have  a  span  of  21  ft.  The  beams  and  slab  will  be  poured 
at  the  same  time  and  thoroughly  tied  together  so  that 
a  T-beam  section  may  be  considered.  The  distance  be 
tween  beams  is  7  ft.,  and  the  dead  and  live  loads  of  the 
slab  per  foot  length  of  beam  is  equal  to  7  X  306  =  2140 
lb.  Assume  dead  load  of  the  stem  of  beam  at  240  lb.  per 
lin.  ft.  Then  the  total  loading  per  foot  of  length  equals 
2380  lb.    The  maximum  shear 


T!              TT  r* —  — ■  r-i  1 

'  '             «  1             !  1  '1 
 i-i  i_l  r'-'-i-_ 

s-r^    Tr^^'i — V^" 

A 

j  1          I  1          j  1          1  1 

A-  i 

i'     ii     i'  ji 

j.l        li       l|  |! 

|-  ^'-^'-ffi  7'.o'  iji 

c> 

Si 

ik--- I{ 2/'- <?'•[■■•'   Ij! 

i'l       !'       1'  !' 

1 

1          1 1          1  1 
!          "         i '  ! 

'                II    Girder-  |  1 

—  J-'-h  1-1  a^-  -1-  J  r^'-u-. 

•     1   h-i-i  

1 

 *. 

..^  -u^^- 

!  1              1  1             !  !              !  ! 

V  = 


(2380)  (21) 


and  the  maximum  moment 
(2380)  (21)2  (12) 


M  = 


12 


25,000  lb. 


1,050,000  in.-lb. 


N — u — m^- 


Cross  section  A-A*, 
Fig.  22.^ 


(If  desired,  the  span  of  beam  may  be  taken  as  the  clear  distance  between  faces  of  supports. 
The  required  cross-section  of  web  as  determined  by  shear 


See  Art.  44.,  Sect.  7.) 


25,000 
105 


238  sq.  in. 


The  following  formula  of  Art.  37,  Sect.  7,  gives  the  most  economical  depths  for  various  assumed  web  widths: 


with  r  in  this  design  as  60,  then 


jj  ^ 

It«p  

Cross- section  of  CrossDeam 

Fig.  23. 


d  = 


rM  t 
Ub'  2 


for  b'  =  9  in. 
for  b'  =  10  in. 
for  6'  =  11  in. 


d  =  23.1  in. 
d  =  22.0  in. 
d  =  21.2  in.,  etc. 


In  order  to  provide  for  most  of  the  diagonal  tension  by  means  of 
bent-up  rods,  it  is  proposed  to  use  eight  rods  placed  in  two  rows, 
four  rods  to  a  row.  '  A  value  of  b'  =  10  in.  may  be  satisfactory  as  re- 
gards rod  spacing,  but  b'  X  d  as  given  above  is  not  great  enough  to 
provide  for  shear.  It  will  be  more  economical  to  deepen  the  beam 
of  10-in.  width  to  a  depth  of  23li  in.  than  to  adopt  a  width  of  11 
in.  and  a  depth  of  about  21.2  in.  Fig.  23  shows  the  arrangement 
of  the  steel  which  will  be  tried  in  the  bottom  of  the  beam  at  the 
center  of  the  span.  This  exact  arrangement  will  also  be  tried  at 
the  top  of  beam  over  supports.  It  is  quite  likely  that  there  will  be 
eight  rods  in  the  girder  of  about  1-in.  or  IJi-in.  diameter  and,  since 
the  cross-beam  rods  should  fit  nicely  with  the  girder  rods  over  sup- 
porting columns,  the  two  layers  of  rods  will  be  placed  2  in.  center 
to  center  as  shown. 


The  weight  of  the  stem  is 


(10)  (22.5)  (150) 
144 


=  235  lb.  per  ft.  and  the  weight  assumed  thus  is  satisfactory. 


442 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-11 


1,050,000 


The  width  of  the  flange  of  the  T-beam  is  controlled  in  this  design  (see  Art.  32,  Sect.  7)  by  12  times  the 
thickness  of  slab  plus  the  width  of  stem,  or  64  in.  Then 

4.5 

=  0.19,  Diagram  8  shows  fc  =  300  lb.  per  sq.  in.  and  j  =  0.93.  Then 

As  = 


=  29.7 


M  t 
For  this  value  of  -rj:  and  for  j 


(64) (23.5)2 

0.19,  Diagram  8  shows  fc  =  300  lb.  per  sq.  in.  and  j 
1,050,000 


(16,000)  (0.93)  (23.5) 


=  3.00  sq.  in. 


Four  H-in.  round  rods  and  four  ^^-in.  round  rods  will  be  selected  (Fig.  23),  having  a  total  area  of  3.00  sq.  in.  (see 


Table  5).    Eight  ^yie-in.  round  rods  would  do, 


Elevation  of  Crossbeam 


...ft  a  c 

L  zs"  ■ 

■4- 

zs'  A 

but  the  Yi~  and  ^^-in.  rods  are  more  likely  to  be  found  in  stock. 

The  four  ?4-in.  rods  will  be  placed  in  the  lower  row 
and  it  will  be  sufficiently  accurate  to  consider  the 
center  of  gravity  of  the  steel  area  as  midway  between 
the  two  rows.  It  is  evident  now  that  the  width  of 
beam  for  rod  spacing  was  correctly  assumed.  (Note 
the  rod  spacing  recommended  by  the  Joint  Com- 
mittee in  Art.  23,  Sect.  7.) 

Four  rods  will  be  bent  up  and  lap  over  the  top 
of  the  support.  The  other  four  will  be  continued 
straight  and  lap  over  support  at  the  bottom  of  beam 
(see  Fig.  24).  The  bond  stress  along  the  eight  rods 
at  the  top  of  beam  near  support 


Plan  of  Crossbeam 

(Bent  Oars  nar^^oaaj' 
Fig.  24. 


25,000 


[(4)  (2.356)  +  (4)  (1.964)1(0.85)  (23.5) 


=  73  lb. 
per  sq.  in. 


which  is  satisfactory. 

(The  average  value  of  j  is  taken  in  the  above  equation,  see  Art.  27,  Sect.  7.)  The  proposed  arrangement  of 
rods  is  shown  in  Fig.  24. 

The  rods  at  the  top  of  beam  over  supports  will  have  the  same  effective  depth  (d)  as  the  rods  at  the  bottom 
of  beam  at  the  center  of  span  (Figs.  23  and  24).  Then 

d'  3.5 


23.5 


=  0.149 
3.00 


P  = 


(10)  (23.5) 

The  following  values  may  be  obtained  from  Diagram  12: 
k  =  0.384 
j  =  0.864 

Then,  using  also  Table  9, 
1,050,000 


0.0128  =  p' 


fs 


~  (3.00)  (0.864) (23.5) 
fc  =  (17,200)  (0.0415) 


17,200  lb.  per  sq.  in. 
=  715  lb.  per  sq.  in. 


,  point- -H 

-ax. 


support 


(One  fhird  po/nf- 


Allowable  compression  in  concrete  at  the  support 
may  be  750  lb.  per  sq.  in.,  and  hence  no  haunch  or 
extra  steel  is  necessary  (see  Appendix  B).  The  ten- 
sile stress  in  the  steel  is  greater  than  the  allowable 
but  will  be  considered  as  satisfactory  here  simply 
for  the  purpose  of  presenting  several  comparative 
designs  using  different  numbers  of  rods.  If  a  little 
more  than  the  required  amount  of  steel  had  been 
selected  at  the  center  of  span — say  eight  94-in.  rounds 
— the  stress  in  the  steel  over  supports  would  not 
have  figured  out  greater  than  the  allowable  (see  Art.  39, 

Sect.  7).    The  diagram  given  on  page  298  may  be  employed  to  find  the  points  in  the  beam  where  the  lower  horizontal 


S3"- 


80"-  >j 


.1 


•  30"- 
■■)(.,=  82" 


Fig.  25. 


rods  may  be  bent  up.    Bending  up  the  first  two  rods  is  equivalent  to  bending  up 


(2) (0.307) 
3.00 


=  0.205  or  20}^%  of 


the  steel.  After  bending  up  the  next  two  rods  50  %  of  all  the  steel  is  bent.  The  diagram  above  referred  to  shows 
that  those  bends  may  be  made  at  0.318i  (80  in.)  and  0.210i  (53  in.)  from  the  center  of  support. 

The  rods  at  the  top  near  support  should  be  bent  down  as  explained  in  Art.  39,  Sect.  7 ;  the  first  two  rods  at  a 


distance  not  less  than 


(2)  (0.442)    ,  I 


3.00 


of 


25  in.  from  the  center  of  support  (assuming  zero  moment  at  the  third  point): 


and  the  next  two  at  a  distance  }^  of  ^  =  42 


from  the  same  point  (see  Fig.  25). 


Sec.  11-11] 


BUILDINGS 


443 


The  distance  from  the  support  to  the  point  where  web  reinforcement  is  not  needed  (see  Art.  18,  Sect.  7) 
_  21  _  (40)  (10)  (0.93)  (23.5) 
^'  ~  2  2380 


=  6.86  ft.  =  82  in. 


Also, 


and 


AB  = 


25,000 
(0.85)  (23.5) 


=  830  lb. 


CZ)  =  3  •  (40)  (10)  =  270  lb. 
Fig.  25  shows  the  diagonal-tension  trapezoid. 

The  points  to  bend  rods  at  the  top  of  beam  control  the  design,  as  shown  in  Fig.  25.  The  horizontal  distance 
between  bent  rods  is  about  the  allowable — namely,  about  Hd.  Since  bending  of  longitudinal  reinforcing  bars  at 
an  angle  across  the  web  of  beam  may  be  considered  as  adding  to  diagonal  tension  resistance  for  a  horizontal  dis- 
tance from  the  point  of  bending  equal  to  %d  (see  Art.  21,  Sect.  7),  stirrups  will  be  needed  only  for  the  areas  ABbc 
and  abCD.  Diagonal  tension  represented  by  the  area  abCD  will  be  cared  for  by  the  additional  stirrups  which  will 
be  inserted  to  secure  good  T-beam  action.  The  distance  from  the  center  of  support  to  the  point  where  stirrups  are 
not  necessary  scales  27  in.  The  stirrups  near  the  end  of  beam  will  be  looped  about  the  upper  rods,  and  hence  will 
be  in  an  inverted  position  to  those  in  a  simply  supported  beam. 

We  shall  use  ^i-in.  round  U-shaped  stirrups  bent  at  the  ends  (see  Art.  19,  Sect.  7).  The  minimum  spacing 
of  stirrups  will  occur  at  the  support,  and  this  spacing  is  given  in  Diagram  IV,  Sect.  7,  page  288,  as  4.2  in.  Spac- 
ing at  other  points  along  the  beam  may  be  found  readily  by  means  of  this  diagram.  The  first  stirrup  will  be  placed 
2  in.  from  the  edge  of  girder,  assuming  the  girder  to  have  a  less  width  than  the  column.  In  order  to  secure  good 
T-beam  action,  the  web  and  flange  will  be  tied  together  with  vertical  stirrups  placed  about  18  in.  on  centers  and 
looped  about  the  lower  rods  for  the  center  half  of  beam. 

The  bars  bent  over  the  support  should  run  to  the  third  point  of  the  adjoining  span  to  provide  thoroughly  for 
negative  moment,  assuming  a  very  definite  live  load  (see  Art.  39,  Sect.  7).  The  allowable  stress  in  the  compres- 
sion rods  at  the  support  is  715  X  15  =  10,725  lb.  per  sq.  in.,  and  the  necessary  length  for  bond  of  H-in.  round  rods 
.  (10,725)  (0.75) 
(4)  (80) 

Cross-beams  (Six-rod  Design). — Four  li-in.  round  rods  and  two  ^^-in.  round  rods  will  give  the  required  area 
of  3.00  sq.  in.    The  arrangement  shown  in  Fig.  26  will  be  adopted. 


=  25  in.  (see  Art.  21,  Sect.  7).    This  length  is  shown  in  Fig.  24. 


b  \  a  b 


Fig.  26. 


5                VC  4  C  4  C  1 

^1 

Fig.  27. 


The  three  rods  in  the  upper  row  will  be  bent  up  and  lap  over  supports  as  shown  in  Fig.  27.  The  other  three 
will  lap  over  support  at  the  bottom  of  beam.    The  bond  stress  along  the  six  rods  at  the  top  of  beam  near  support 

25,000 

per  sq. 


~  [(4)  (2.749)  +  (2) (1.964)1(0.85) (23.5) 
which  will  be  considered  satisfactory  for  the  arrangement  of  rods  shown 

The  first  5^-in.  rod  may  be  bent  at  93  in.  from 
center  of  support  and  the  next  two  Ji-in.  rods  may  be 
bent  at  53  in.  from  center  of  support. 

The  two  Ji-in.  rods  may  be  bent  down  at  a  dis- 
(2)(0.6013)    .  I 


84  lb. 

n  Fig.  27  (see  Art. 


16,  Sect.  7). 


3.02 


of 


33  in.  from  the 


<-— -  ss  ■  --J  


and  the  %-\x\.  rod  at  \^  of  ^  =42 


n:1 


\ 


jpoint 


66' 


\ 


tance  not  less  than 

center  of  support, 

from  the  same  point. 

The  points  to  bend  rods  at  the  top  of  beam  con- 
trol the  location  of  the  bends  of  the  two  ^^-in.  rods. 
The  56-in.  rod  will  be  bent  so  as  to  be  about  Y^d  from 
the  other  two  rods  (see  Fig.  28).  The  spacing  of  stir- 
rups, and  the  distance  from  the  center  of  support  to  the 

point  where  stirrups  are  not  necessary  may  be  found  in  the  same  manner  as  for  the  eight-rod  design. 

Cross-beams  {Four-rod  Design). — Four  J^-in.  square  rods  will  give  an  area  of  3.06  sq.  in.  which  is  only  slightly 
more  than  is  required.    These  rods  will  all  be  placed  in  one  row  as  shown  in  Fig.  29. i    Fig.  30  shows  the  complete 


Fig.  28. 


1  The  beam  is  slightly  narrow  according  to  the  rod  spacing  recommended  by  the  Joint  Committee. 


444 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-11 


design.  Stirrups  are  provided  to  take  all  the  diagonal  tension — the  strengthening  action  of  the  bent  rods  not  being 
considered.  It  should  be  noted  that  the  design  is  not  conservative  with  respect  to  the  negative-tension  reinforce- 
ment, since  the  upper  rods  run  only  to  the  fourth  point  and  the  curve  for  negative  moment  has  not  been  con- 
sidered in  bending  down  the  rods  (see  Art.  39,  Sect.  7).  Nevertheless  a  design  of  this  kind  is  generally  considered 
good.  In  fact,  it  is  all  that  is  desired  under  ordinary  conditions  in  roof  design  because  of  the  character  and  amount 
of  the  live  load. 

Of  course,  it  should  be  realized  that  some  latitude  may  generally  be  allowed  in  that  part  of  beam  design 
referred  to  above,  on  account  of  the  improbability  of  obtaining  maximum  conditions,  but  it  is  a  good  idea  to  have 


Fig.  29.  Fig.  30. 

some  conservative  plan  in  mind,  and  to  live  up  to  that  plan  as  nearly  as  circumstances  will  permit.  At  any  rate, 
designs  should  never  become  so  radical  as  to  include  rods  bent  up  close  to  the  support  in  the  computations  for 
negative  reinforcement. 

Fig.  31  shows  a  common  continuous-beam  design  using  separate  straight  rods  over  the  supports.  All  the 
diagonal  tensile  stresses  are  cared  for  by  vertical  stirrups. 

Girder. — The  girder  has  a  span  of  21  ft.  with  concentrated  loads  at  the  third  points.  The  weight  of  the  stem 
>4rill  be  assumed  at  500  lb.  per  lin.  ft.    Reaction  of  concentrated  loads  =  2  X  25,000  =  50,000  lb. 


Fig.  31. 


Maximum  moment  of  concentrated  loads  with  ends  of  beam  simply  supported  would  be 

(50,000)  (7)  (12)  =  4,200,000  in.-lb. 
this  moment  reduces  to 


Taking  M  = 


^^(4,200,000)  =  2,800,000  in.-lb. 
Moment  of  dead  load   =     220,500  in.-lb. 
Total  moment 


3,020,500  in.-lb. 

If  desired,  the  span  of  girder  may  be  taken  as  the  clear  distance  between  faces  of  supports  (see  Art.  44, 
Sect.  7). 

The  total  maximum  shear 

V  =  50,000  +  10.5(500)      =  55,300  lb. 
The  cross-section  of  web  as  determined  by  shear  =   ^  105^  ~  ^■^^  Using  the  formula  for  economical  depths, 

we  have: 

It  is  quite  probable  that  a  breadth  of  12  in.  will  give  proper  rod  spacing,  but  the 
527 

corresponding  depth  of  -^2"  =  i^-  likely  to  be  too  great  when  the  cost  of 
columns  and  walls  is  taken  into  consideration. i    Besides,  the  depth  would  be 

1  In  order  to  include  the  effect  of  columns  and  walls  in  the  formula  d  =  ^J~p 

+     first  determine  the  total  horizontal  area  covered  by  the  stems  of  the  T-beams 

under  consideration  and  the  total  horizontal  sectional  area  of  the  columns  and 
walls  at  the  level  of  the  beams.  If  the  cost  per  cubic  foot  of  the  columns  and  walls 
is  greater  or  less  than  the  cost  per  cubic  foot  of  the  T-beam  stems,  increase  or  de- 
crease their  area  in  proportion  to  the  difference  in  cost.  Then  increase  the  cost 
per  cubic  foot  of  the  T-beam  stems  in  the  ratio  which  the  total  corrected  area  bears  to  the  area  of  the  T-beam 
stems  in  order  to  obtain  the  unit  cost  c  which  is  used  to  determine  the  ratio  r. 


d 

b'  X  d 

(inches) 

(inches) 

(square 
inches) 

12 

33.  1 

397 

14 

30.8 

431 

15 

29.8 

447 

16 

29.0 

464 

Sec.  11-11] 


BUILDINGS 


445 


great  in  proportion  to  the  breadth  of  stem  and  the  beam  would  be  relatively  weak  at  the  junction  of  stem  and  flange. 
Illumination  from  windows  must  also  be  considered.    The  following  cross-section  will  be  taken  as  satisfactory: 


15  in. 


32^2  in. 


The  breadth  of  the  flange  of  the  T-beam  is  controlled  in  this  case  by  12  times  the  thickness  of  slab  plus 
the  width  of  stem,  or  69  in.  Then 

M.  _    3,020,000  _ 

hd^  ~  (69)(32.5)2  -  "^^-^ 

M  t        4  5 

For  this  value  of  ^  and  for  ^  =  =  0.14,  Diagram  8  shows /c  =  415  lb.  per  sq.  in.,  and  j  =  0.935.  Then 


3,020,000 


(16,000)  (0.935)  (32.5) 


6.21  sq.  in. 


Eight  1-in.  rouyd  rods  (total  area  6.28  sq.  in.)  will  be  chosen.  The  bond  stress  along  the  eight  rods  at  the  top  of 
beam  close  to  the  support, 

55,300 

^  =   (8)  (3.14) (0.85) (32.5)  =  P^'' 

which  is  satisfactory. 

Fig.  32  shows  sketch  of  adopted  cross-section.    The  weight  of  the  stem  is 


(15)(31.5)(150) 


144 


and  the  value  assumed  is  on  the  safe  side. 


492  lb.  per  lin.  ft. 


S.4  


abba 


d  d  c 

IS"  >J 


Cross- section  of  Girder 
Fig.  32. 


Fig.  33. 


j.  r 


The  rods  at  the  top  of  girder  over  supporting  columns  will  be  placed  as  shown  in  Fig.  33  in  order  to  fit  in 
nicely  with  the  cross-beam  rods.  It  should  be  noticed  that  the  value  of  d  at  the  support  is  33.5  in.,  or  1  in.  more 
than  at  the  center  of  span.  Then 

6.28 

V  =    l^  -N/QQ  r;^  =  0.0125 

(lo)(33.5) 
V'  =  0.5p  (see  Fig.  34) 


The  following  values  are  obtained  from  Diagram  12  and  Table  9, 

h 


k  =  0.403 


Then 


M 

Asjd 


j  =  0.882 

3,020,000 


=  0.0449 


(6.28)  (0.882)  (33.5) 


n(l  -  k) 
=  16,200  lb.  per  sq.  in. 


fc  =  (16,200)  (0.0449)  =  730  lb.  per  sq.  in. 

These  values  will  be  considered  satisfactory. 

It  is  proposed  to  have  bent  rods  take  as  much  of  the  diagonal  tension  as  possible.  The  total  maximum 
shear  =  55,300  lb.  The  shear  on  the  support  side  of  the  third  point  =  55,300  -  500(7)  =  51,800  lb.  On  the  side  of 
the  third  point  toward  the  center  of  span,  the  shear  =  51,800  -  50,000  =  1800  lb.,  or  «  =  4  lb.  per  sq.  in.  Thus, 
web  reinforcement  is  needed  only  from  the  support  to  the  point  where  the  beam  intersects  the  girder. 

Horizontal  shear  (measures  diagonal  tension)  at  the  support 


and  at  the  third  point,  it  is 


V  _  55,300 
jd       (0.85) (33.5) 

51,800 
(0.93)  (32.5) 


1950  lb.  per  lin.  in. 
1720  lb.  per  Jin.  in. 


446 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-11 


The  total  diagonal  tension  is  represented  by  a  trapezoid,  the  parallel  sides  of  which  are  1950  lb.  and  1720  lb.,  and 
the  length  7  ft.    Hence  total  diagonal  tension  is 

'°°°+'^^°  (7.0)02)  -  154.100  lb. 

Two-thirds  of  this  amount,  or  102,700  lb.,  will  be  taken  by  the  web  reinforcement.  If  six  rods  are  to  be  bent,  their 
tensile  value  is 

(6)  (0.785)  (16,000)  (1.43)  =  108,000  1b. 
which  is  in  excess  of  the  stress  to  be  provided  for. 

Now  shear  is  nearly  uniform  between  the  supports  and  the  third  point,  and,  as  far  as  diagonal  tension  is 
concerned,  it  would  be  sufficiently  accurate  to  give  equal  spacing  to  the  inclined  rods.  Since  the  size  of  columns 
is  not  given,  an  18-in.  diameter  of  column  will  be  considered.  The  spacing  suggested  above,  then,  would  be  taken 
between  a  point  9  in.  from  the  center  of  support  (that  is,  at  the  edge  of  column)  and  a  point  where  the  center  of  the 
beam  intersects  the  girder.  The  plan  proposed  is  to  bend  six  rods',  two  at  a  time,  and  the  points  to  bend  for  diagonal 
tension  should  be  laid  off  on  a  line  approximately  midway  between  the  neutral  axes  for  positive  and  negative 
moment — as  MM,  Fig.  34.  These  points  (1,  2,  and  3)  may  be  determined  by  dividing  the  distance  mentioned 
above  into  three  equal  parts  and  locating  a  point  at  the  center  of  each  part. 

An  investigation  must  now  be  made  to  determine  whether  or  not  the  tensile  stresses  in  the  beam  will  permit 
the  bending  of  the  rods  as  above  suggested.  From  a  study  of  moment  curves  of  continuous  beams  loaded  at  the 
third  points,  for  different  conditions,  it  is  found  sufficiently  on  the  safe  side,  as  regards  bending  up  rods,  to  con- 
sider the  point  of  zero  moment  to  occur  at  a  distance  of  ^•^  of  I  from  the  third  point  measured  toward  the  support 


I 

or      of  g  (56  in.  in 


(see  Art.  53,  Sect.  7).    Also  when  considering  the  bending  down  of  rods,  the  same  distance, 

this  case),  may  be  safely  taken  as  the  distance  out  from  the  support  to  the  point  of  zero  moment.  The  curve  of 
bending  moments  in  each  case  is  to  all  practical  purposes  a  straight  line.    Thus,  the  point  where  the  first  two 

rods  may  be  bent  up,  using  the  above  data,  is  about  - — =  14  in.  from  the  center  of  the  intersection  of  the 

cross-beams.    Allowing  say  4  in.  beyond  the  theoretical  point  for  bending,  this  distance  becomes  18  in. 

As  regards  diagonal  tension,  the  rod  to  intersect  the  center  line  at  point  1  should  be  bent  at  r,  as  shown  by  the 
dotted  line.    Since  rods  cannot  be  bent  at  r,  stirrups  will  be  employed  to  take  the  diagonal  tension  between  the  bent 

rods  and  the  cross-beam.    (Stirrups  will  also 

J'^sr/rru/ts      [* -■  S6'    -  —^S6'  -  >|  be  placed  at  occasional  intervals  throughout 

the  girder  to  bind  together  the  web  and 
flange.)  Round  rods  of  Vz-in.  diameter  may 
be  used  for  stirrups  if  bent  at  the  upper  end. 
The  tensile  value  of  each  stirrup  (U-shape)  is 
(2)  (0.196)  (16,000)  =  6270  lb.  The  shear  to 
be  provided  for  in  1-in.  length  of  beam  is 
1720  lb.  and  it  will  be  necessary  to  space  the 

stirrups  ^^20  ~  ^'^  ^P^^^.  as 

shown  in  Fig.  34. 

It  should  be  noticed  that  in  bending  up 
the  lower  rods  attention  should  be  paid  to  the 
points  where  the  upper  rods  may  be  bent 
down.  In  the  design  at  hand,  using  45-deg. 
angle  bends,  the  rods  may  be  bent  approxi- 
mately as  planned  and  the  design  will  be  ac- 
cepted. The  horizontal  spacing  of  the  bent 
rods  should  not  be  greater  than  the  distance 
between  points  1  and  2,  or  between  points  2  and  3,  unless  stirrups  are  provided  where  such  spacing  occurs. 

The  rods  at  the  top  of  girder  should  extend  each  side  of  the  center  of  support  far  enough  to  obtain  their  full 
strength  in  bond,  which  is  50  in. 

The  maximum  stress  in  the  compression  rods  at  the  support  is  730  X  15  =  11,000  lb.  per  sq.  in.  The 

necessary  length  for  bond  of  1-in.  rods  is  ^^^^^^'^g^^  =  35  in.,  say  36  in.    This  length  is  shown  in  Fig.  34. 
The  top  of  the  slab  over  the  girder  will  be  reinforced  transversely  with  %-in.  rods  spaced  12  in. 


Plan 

(Senr  bars  not  shown) 
Fig.  34. 


to  c,  in 

order  to  provide  for  the  negative  bending  moment  produced  with  the  bending  of  the  slab  next  to  the  girder. 

Designing  Plates. — Plates  I  to  IV  inclusive  give  different  complete  designs  for  the  21  by  21-ft.  floor  bay 
in  question.  If  desired,  all  the  cross-beam  and  girder  reinforcement  may  be  made  into  frames,  except  the  cross- 
beam reinforcement  running  into  columns  in  the  designs  of  Plates  I  and  III.  Even  for  these  beams,  however,  the 
stirrups  may  be  rigidly  spaced  if  wired  at  the  upper  turns  to  longitudinal  rods  of  small  diameter.  After  the  stirrup 
steel  is  suspended  in  the  forms,  the  bent  rods  can  then  be  easily  slipped  into  place  and  wired. 

Fig.  35  and  Plate  II  show  a  girder  design  such  that  both  girder  and  cross-beam  reinforcement  may  be  built 
into  frames.  In  the  arrangement  shown,  the  girder  frames  (with  the  exception  of  the  rods  over  supports)  would  be 
put  in  place  first,  then  the  cross-beam  frames  running  into  columns,  next  the  negative  tension  rods  of  the  girders, 


Sec.  11-12] 


BUILDINGS 


447 


and  finally  the  two  intermediate  cross-beam  frames.  The  arrangement  as  regards  strength  is  not  as  ideal  as  in 
the  girder  design  of  Plates  I,  III,  and  IV  since  the  bent-up  rods  do  not  extend  over  supports,  but  in  the  design  shown 
there  is  a  surplus  of  diagonal-tension  reinforcement  which  offsets  this  v.eakness.  To  be  sure  the  bent  rods  are 
anchored  by  transverse  rods  placed  between  layers  of  steel,  but  the  danger  lies  in  the  liability  of  these  bars  to  slip 
horizontally  when  a  force  inclined  to  the  vertical  is  exerted  upon  them.  The  additional  amount  of  diagonal- 
tension  reinforcement,  however,  over  and  above  that  figured  will  make  the  design  a  safe  one.  The  liability  to 
slip  applies  more  especially  to  the  lower  transverse  rods,  as  the  upper  rods  are  long  and  well  anchored  in  the  slab. 

If  the  croBs-beam  steel  in  Plate  III  could  have  been  placed  over  the  top  of  the  girder  steel  at  columns,  then 
all  reinforcement  shown  on  this  plate  could  have  been  made  up  into  frames  before  being  placed  in  the  forms.  The 
reason  why  the  cross-beam  rods  were  not  placed  above  the  girder  rods  in  the  design  in  question  was  because  the 
cross-beam  rods  would  then  interfere  with  the  main  reinforcement  of  the  slab.  To  prevent  this,  the  girder  rods 
over  supports  would  need  to  be  lowered  and  this  could  not  be  accomplished  in  the  design  in  question  because  of 
the  compressive  stress  in  the  concrete  being  already  a  maximum  at  this  point.  It  could  be  accomplished,  how- 
ever, by  either  forming  a  flat  haunch,  by  inserting  extra  compressive  steel,  or  by  deepening  the  girder. 

Placing  of  the  reinforcement  in  the  forms  in  frames  insures  accurate  location  of  all  steel.  If  a  loose-rod  method 
is  used,  great  care  is  required  in  construction  to  make  sure  that  the  steel  is  not  disturbed  during  the  pouring  of  the 
concrete.    Usually  small  diameter  rods  are  needed  to  make  the  frames,  in  addition  to  the  main  reinforcement. 

The  placing  of  inverted  stirrups  near  the  supports  has  not  been  considered  in  the  above  discussion.  These 
are  placed  after  all  other  reinforcement  is  in  its  proper  pjosition  and  are  slipped  down  over  the  negative-tension 
steel  and  wired  to  it.  The  continuous  stirrup  shown  in  some  of  the  designs  is  convenient  for  this  purpose.  In 
schemes  3  and  4  the  continuous  stirrup  is  also  used  in  place  of  some  of  the  upright  U-stirrups. 

Spacing  rods  should  be  placed  in  all  beams  and  girders  between  the  upper  and  lower  rows  of  steel.  These 
are  plain  rods  of  the  desired  size  and  should  be  placed  transversely  not  more  than  5  ft.  on  centers.    Special  frame 


^  .  S6'  --- 

K   SS'- 

|<          40'  ■ 

 56'  -  --  v 

f^rods  Z'-0"k 

/7y 

Stirrups 

"cfoc 

r  1 1  loX , 

/  /  // 

t 

"  ei±a_ 

T 

4 

>k-  

<-  •  40'  .-. >!<..- 

*.—  so'   > 

<-  -  -   7'-0 

■  58'-  

...  44'.- 
<-..-  U' 

<—  IS'  Column  y 

'   Z-y^rods  s'/ont 

 -  7'-0'    >■ 

r 

Fig.  35. 


supports  may  be  provided,  if  desired,  or  U-shaped  stirrups  may  be  employed  if  the  length  of  the  hook  is  made 
sufficient  to  permit  the  stirrups  to  rest  on  the  slab  form.  If  special  supports  are  used,  they  should  be  spaced  about 
5  ft.  on  centers.    In  the  steel  schedules  given,  special  frame  supports  and  spacing  rods  are  omitted  for  simplicity. 

The  width  of  stirrups  is  given  in  the  bending  schedules  as  the  clear  width  inside  of  the  outer  strands,  and  the 
vertical  height  is  given  inside  the  turns.  A  little  thought  will  make  clear  that  these  are  the  dimensions  needed 
in  bending. 

12.  Hollow-tile  Construction. — Hollow-tile  construction  is  used  to  a  considerable  extent 
for  light  buildings  such  as  modern  store  buildings  and  office  structures. 

Fig.  36  shows  a  typical  one-way  hollow-tile  slab  and  Fig.  37  a  two-way  tile  construction. 
No  cross-beams  are  employed  in  the  one-way  type  except  the  small  ribs  of  the  floor  slab  formed 
between  the  rows  of  hollow  tile.  In  the  two-way  type,  cross-beams  are  placed  at  the  columns. 
The  tiles  are  placed  directly  upon  the  forms  with  the  reinforcing  rods  in  the  spaces  between 
them,  and  the  concrete  is  filled  in  between  the  tiles  and  poured  over  the  top  to  form  the  floor. 
The  ribs  form  a  series  of  comparatively  light  T-beams  side  by  side  with  flanges  usually  2  or  more 
inches  in  thickness.  The  main  beams  or  girders  are  also  of  T-shape.  The  flanges  of  these  beams 
or  girders  are  usually  of  the  same  thickness  as  the  floor  slab,  but  lighter  tiles  are  sometimes  used 
near  the  stem,  in  which  case  the  flange  becomes  thinner  than  when  the  tiles  are  entirely  omitted 
at  this  part  of  the  floor.  The  function  of  the  tiles  is  simply  to  create  a  void  in  the  concrete 
and  thus  to  decrease  the  dead  weight  of  slab,  and  they  do  not  enter  into  the  calculations  for 
strength  of  floor. 

Either  hard-burned  or  semi-porous  tile  may  be  used  in  reinforced-concrete  floor  construe- 


448 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-12 


Plate  I 


J-l|  I  I  ILL 


z/'-o" 


I  111 

'si  5 


^1 


I  I  IK 
I  I  I 


si  Slab 
I  'gran 


/  *rods  ii\  \c  roc 
S'-O' long  I 
of  Slab  over 
entire  g/r'aer 


— 1-|  

5/^  is',  36'  3  /" 
f'Grano/ithic  ■■  , 


Cross  secTion  X-x 
(Enlarged) 


Gt  is'.j$'  a- 1"* 


■  Upper  row  of  rods 
  Lower  roiv 


Note  •  Inverred  sfirrLips  are  markec/  o 
Concrete  12  4  mix 


OETAIUS  OP 
AN  INTERIOR  FLOOR  BAY 


/Irrangemem      Steel  in  Crossbeam 


Arrangement  of  Steel  in  Gircfer 


Plate  1(A) 


BEAM  AND  GIRDER  RODS 


Bends 


6-6" 


Lengffh 


30  Ol 


For 
beam 

girder 


BZ 


82 


vxantBd 
■for 
each 
beam 


tin 


Length 


Number 
wonted 

■for 
each 
beam 


S\'    3'.  6'  \S 

■    ■    /7'-6"'                '  ' 

j'0Slat>3tee/  7bTa//en^  n'/O' 


STEEL  BENDING  SCHEDULE 
roR 

AN  INTERIOR  FLOOR  BAY 
SCHEME  I 


Sec.  11-12] 


BUILDINGS 


449 


Plate  II 


/  Proa's /a"\c  n>c 
S'-o'lon^  \aTTvp 
of  slab  oyer 
entire  girder 

II 

Reinforcemenr 


,  Zro(. 

s 

T-0- 

finish  . 

 zie  ^ 

1'* stirrup  i                  ,'  /'" 

UlL 

I'll 

i 

4; 

J'-O" 

69  about-  /-7 

-J'-O' 

Cross  section  X-X 
J/,  {Enlarged) 

j  ^  Upper  row  of  rods  ~ 


Note  ■    Inverted  stirrups  are  marked  a 
Concrete  12  4  mix 


DETAILS  OF 

AN    INTERIOR   FLOOR  BAY 


Arrangement  of  Steel  'a  Crossbeam 


/irrangement  of  Steel  in  Girder 


Plate  11(A) 


BEAM  AND  GIRDER  RODS 


Straight 


36- 4' 


52 


3/ 


/$'-3" 


Total 

numcer 
wanted 


U-  STIRRUPS 


Leng'th 


S'-9'' 


7'- 6" 


Beam 

or 
Girder 


82 


Number 
■for 
eaci-i 


TotO» 

No- 
vo n-fed 


CONTINUOUS  STIRRUPS 


a 

b 

Spacers 

Size 

Length 

Beam 

No  for 
each 

Total 
No 

N? 

Deem 

wantec 

7 

4-4@5 

29'- 6" 

Bl 

2 

2 

■  4 

24 

a4'-  7" 

B2 

1 

2 

2 

^4 

// 

3@/Z 

28'- 4" 

6/ 

1 

2 

2 

V — yn~  

7^-o"  \s\s'a" 

> 

/ 

7-^" 

STEEL  BENDING  SCHEDULE 


AN  INTERIOR  FLOOR  BAY 
SCHEME  2 


29 


450 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-12 


Plate  III 


_U±L 


IP! 


V 


■f rods /e\"\c  roc 
S'-O"  long  \  \af  K 
of  s!ab  over  ei 
girder  | 

ReinfcrcemenT 
spaced  4"c  to  c 


^  /"granolithic  fmisn 


~T\  \-\ 

Gh  IS",  36'  8-i'" 
"Oranolifhic  -  ^k^, 


Lj-jJi-i.  LU  J. 


I "  Grano/ifhic 

finish  >  |- 
^  ii" Stirrups  a 


Kl 


6  g>  abcuT  I'-e" 


\  B2 


10".  ay"  4- 


Cross  section  X  X 
(  £nlorgec/J 


/  granolithic 
finish-.     1 1' If.  ' 

■■.  I  '^stirrups 


Gl-  15", ^S'  S-i" 


z 


Upper  row  of  rods 
  Lower  ran 


Arrangement  of  Steel  m  Crossbeam 


Arrangement  of  Steel  in  Girder' 


Note'    Inverted  stirrups  are  marked  a 
Concrete  15  4  mix 


DETAILS  OF 

AN  INTERIOR   FLOOR  BAY 


Plate  III  (A) 


BEAM    AND  GIRDER  RODS 


MI 


Lengi-h 


Bi 


29'- 


30' 


28'- 2-^" 


61 


61 


Number 
wanTed 
for 
each 
Deam 


numcer 
wonted 


Spacers 


U-  STIRRUPS 


Bends 

Length 

For 

beam 
girder 

Number 
wonted 
for  each 
beam 

Total 

number 
wan-ted 

No 

7" 

s'e" 

Bl 

2 

15 

■45 

B2 

1 

IS 

i/'' 

i"0 

7'- 6" 

6/ 

/ 

5 

S 

CONTINUOUS  STIRRUPS 


a 

b 

Spacers 

S>ze 

Length 

For 
beomor 
qirder 

Number 
for  each 
beam 

Totol 
numDer 
wanted 

24 

7 

4-4@S 

8 

29-6" 

Bl 

2 

Z 

6 

4@S 

e4'-  7" 

B2 

1 

2 

// 

53'-2" 

Gl 

1 

2 

2 

27'-7" 

? 

^ 

7'J 

17'- 

6" 

^"^5iai>  5 fee/  Total  len^fii  /7'/0' 


Continuous  Stirrup 


STEEL   BENDING  SCHEDULE 
FOR 

AN  INTERIOR  FLOOR  BAY 
SCHEME  3 


Sec.  11-12] 


BUILDINGS 


451 


Plate  IV 


II  I  I  ll-L 


I  I  ' 


V 


I  I  I  I 
I  I  I  I 


S/a£> 


/  Proofs  /^'{c  ^pc 
S'-0"long\  \aT  ; 
of  slab  oyer 
entire  ^irtier 

Retnforcemen  t 


■ncluding  \ 
gronolithic 


"1"! 

Gi  is', 36'  e 
I'Orano/ifhic  :.  \ 
finisn 


Note  Both  upright 
and  inverted  stirrups 
at  points  marked  "b' 


Cross-secTion  X-X 
(  Enlarged] 


Upper  row  of  rods 
  Lomr  rotv.. 


/Arrangement  of  Steel  in  Crossbeam 


/Irrangewent  of  Steel  in  Girder 


Note  ■   Inverted  stirrups  are  markect  a 
Concrete  I' 2  -4  mix 


DETAILS  OF 

AN   INTERIOR   FLOOR  BAY 


Plate  IV(A) 


BEAM    AND   GIRDER  RODS 


Straight 


Lengti- 


30'- 0-2 


28-Z-2 


BZ 


Number 
wan+ed 
■for  eoch 


Toral 
No 

wonted 


Spacers 


U-STIRRUPS 


Bends 

Size 

Length 

For 
beorn 

or 
gi  rder 

Number 
for 
each 
beam 

Total 
No 

wonted 

No 

S'-9" 

3i 

2 

15 

45 

B2 

1 

IS 

■ 

2 

7'-e" 

c-/ 

1 

S 

S 

CONTINUOUS  STIRRUPS 


a 

b 

Spacers 

Size 

Length 

Beam  or 
Girder 

No  for 
each 
beam 

TotQl 
NO 

wanted 

24 

7 

4-S@5- 

/> 

so'-o 

4S'->" 

Bl 

2 

Z 

6 

B2 

1 

2 

^4 

i"0 

SS'2" 

6/ 

1 

2 

2 

3@9 

27'-  7" 

2 

*^   \ 

7'-  0  " 

y 

5 

_  2'- 8" 

s\  s'-e"  U 

"  2'-8''S 

/7'-6" 

3"'^  5/at>  Stee/  Tata/  length  /vW 


Continuous  Stirrup 


STEEL    BENDING  SCHEDULE 

FOR 

AN  INTERIOR  FLOOR  BAY 
SCHEME  4 


452 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-12 


tion.  Hard-burned  tile,  due  to  its  density,  has  a  higher  crushing  strength  and  will,  therefore, 
undergo  a  greater  stress  without  any  sign  of  failure,  but  it  does  not  seem  to  be  as  good  a  fire- 
resisting  material  as  the  semi-porous. 

The  following  table  gives  average  weights  of  the  common  sizes  of  hollow  tile : 

Weights  of  Hollow  Tile 

4  by  12  by  12   16  lb.        8  by  12  by  12   30  lb. 

5  by  12  by  12   20  lb.         9  by  12  by  12   33  lb. 

6  by  12  by  12   22  1b.       10  by  12  by  12   35  1b. 

7  by  12  by  12   27  lb.       12  by  12  by  12   40  lb. 


H- J  I  I  L  JL  JL-jML  JULJUL'j^ 
]C]  1   I  LJLJrjuJiTj 


-inrTr-ir-TrTr- 
L  JLjl  jljLji-JL 
nr-irT^  


JLJLjLJL_J  j   I  LJU 

JLJL. 


•ir-ir 


•Tru-TrTr-in" — I 


L"]L:i[:in!:]:]rj!:][:]r]nc]L]L]q  i  □ 

r-"nt-->nrTnnnr-,rnrTr-^rnr-|.  n      1  r-i 


r-ir-tr-iT-.f^r- 


JL_ll_ 

...   ,    .  -\r-ir 

_iLjL  jLJlU 


JLJ1-J1.JUJLJLJ1.J  I  Ljd 

Tr-,rnnr-|rn(— in  1  |  nrl 
JL Ji_1i_jlJLjljL J      ,  LJLJ 


H-ir-1i->r-;rnr--.rT 


iJl 


-inr->rT"i-inr 


(-JI-JLJuJl-ULJI- JLjl_Jl.Jl_Jl_JLJLJL  J  L 

LTJr:irj:D[]rx][::[:]::irjrx]::  [ 


Plan, 


77/e--' 
Half  Section  A-A' 

Fig.  36. 


Hollow  'Tile 

Section  A- a' 

Fig.  37. 


The  commercial  sizes  of  tiles  are  usually  12  by  12  in.  in  plan  and  vary  in  depth  from  4  to 
16  in.  The  depth  of  a  tile  concrete  floor  should  be  designed  so  as  to  allow  for  these  commercial 
sizes.  The  standard  sizes  manufactured  by  the  National  Fire  Proofing  Co.  are  all  12  by  12  in. 
in  plan  with  the  following  depths :  4  in.,  5  in.,  6  in.,  7  in.,  8  in.,  9  in.,  10  in.,  12  in.,  15  in.  Special 
sizes  of  tile  may  be  obtained  if  the  order  is  of  sufficient  size  to  warrant  the  manufacturing  of  the 
same. 

Tiles  are  likely  to  vary  in.  from  the  dimensions  specified  so  that  the  plans  should  show 
the  full  thickness  of  the  floor  and  the  minimum  amount  of  concrete  topping.  If  the  tiles  are 
small,  due  to  shrinking  in  burning,  the  thickness  of  floor  should  be  made  up  in  concrete. 

Unless  the  tile  is  thoroughly  sprinkled  before  the  floor  is  poured,  slight  depressions  will 
occur  over  the  ribs.  This  is  because  the  hollow  tile  absorbs  the  moisture  in  the  concrete  of  the 
top  coat,  causing  it  to  set  more  quickly  than  the  rib  with  its  greater  body  of  concrete  and  greater 
shrinkage.    Sprinkling  of  the  tile  should  be  insisted  upon,  especially  in  hot  weather. 

Hollow-tile  floors  are  generally  plastered  on  the  underside  as  it  is  only  in  the  roughest  kind 
of  work  that  this  is  not  done.  The  surface  of  the  tiles  should  be  deeply  scored  so  that  the 
plaster  will  bind  firmly. 

Ordinary  hollow  tile  is  open  at  both  ends  and  cannot  be  used  when  the  floor  is  reinforced 
in  both  directions.    For  such  floors  two-way  tile  should  be  procured. 


Sec.  11-12] 


BUILDINGS 


453 


Hollow-tile  jfloors  are  used  mostly  in  long-span  construction,  and  where  the  loads  are  light 
and  distributed.  The  reason  for  this  is  the  small  dead  load,  the  flat  ceiling,  and  the  simplicity 
of  the  form  work.  The  cost  of  the  sohd  type  of  beam  and  girder  construction  for  the  conditions 
of  long  span  and  light  loads  is  generaly  much  greater  than  for  hollow  tile. 

Illustrative  Problem. — Design  an  interior  panel  of  a  one-way  hollow-tile  floor  to  carry  a  live  load  of  100 
lb.  per  sq.  ft.  with  the  rows  of  girders  spaced  21  ft.  on  centers.  The  recommendations  of  the  Joint  Committe 
will  be  followed  for  a  2000-lb.  concrete  (see  Appendix  B).  The  ratio  of  the  unit  cost  of  steel  in  place  to  unit  cost 
of  concrete  in  place  (r)  will  be  taken  at  70,  with  20  cts.  as  the  cost  of  concrete  per  cubic  foot. 

The  finished  flooring  will  consist  of  maple  boards  nailed  to  2  by  3-in.  sleepers.    The  sleepers  will  be 

placed  on  the  concrete  slab  and  cinder  concrete  in  proportions  1:3:6  filled  in  between  them.  The  following  weights 
will  be  taken  in  pounds  per  square  foot  of  floor  area:  wooden  floor,  5;  sleepers  or  nailing  strips,  2;  concrete  filling, 
15;  plaster,  5. 

Ribs  4  in.  wide  will  be  assumed  making  a  16-in.  width  of  flange  for  the  small  T-beams.  The  concrete  topping 
will  be  made  2  in.  If  a  9-in.  tile  is  assumed,  the  total  load  per  linear  foot  of  beam  will  be  274  lb.,  made  up  of  the 
following  items: 

Live  load  =  100  X  ^y\2  =  133  lb. 
Wood  floor  =  5  X  H  =     7  lb. 
Sleepers  =  2X%=  Z\h. 
Concrete  filling  =  15  X  ^  =  20  lb. 
Concrete  topping  =  25  X      =  33  lb. 

Tile  =  33  lb. 

Stem  =  X  (150)  =  38  lb. 

Plaster  =  5  X      =    7  lb. 

Total  =  274  lb. 


The  bending  moment. 


wl'^       (274)  (21)  (21)  (12) 
M  =  Y2   =   12  ^  121,000  m.-lb. 


The  economical  depth  of  floor  now  needs  to  be  determined.  Using  the  same  notation  as  in  Art.  37  of  Sect.  7 
and,  in  addition,  using  the  term  c<  to  represent  the  variation  in  cost  of  tile  in  place  per  1-in.  change  in  depth,  we 
have 

crM 

C  =  cb'd'  +  ■  ■  —  +  d'ct 

+ 2) 

as  the  total  cost  of  the  small  T-beams  per  unit  length.  The  following  expression  has  been  deduced  from  the  pre- 
ceding equation  by  the  aid  of  the  calculus,  and  will  give  the  value  of  d  for  minimum  cost  when  the  value  of  b' 
is  fixed: 


Mfsib'Cc  + 


M  t 
+  0 


144c0   '  2 

The  term  Cc  in  this  formula  means  the  cost  of  concrete  per  cubic  foot.  A  value  of  IH  cts.  will  be  given  to  cr 
Then 


d  =  a/(20)(70)(121,000)  +  2_  =  7.4  in. 
\    (16.000U260)     ^  2 


(16,000)  (260) 

The  effective  depth  d  must  be  taken  so  as  to  provide  for  a  commercial  depth  of  tile.  A  7\^-\n.  effective  depth 
will  be  tried  with  a  IJ^-in.  fireproof  covering  below  the  center  of  steel.  This  assumption  would  permit  of  a  7-in. 
tile. 

Proceeding  with  the  design,  however,  we  find  that 

M  121,000 


and 


6d2      (16)  (7.5) 
t  2 


I  =  135 


-  7.5  - 


Diagram  8,  Sect.  7,  shows  the  stress  in  the  concrete  to  be  above  650  lb.  per  sq.  in.,  which  cannot  be  allowed.  By 
trial  it  is  found  that  a  Q'^-in.  effective  depth  is  needed  to  bring  the  concrete  stress  to  an  allowable  value.  For  this 
depth, 

M  _  121,000  _ 
6d2  ~  (16) (9.5)2  - 


454 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-12 


From  Diagram  8,  j  =  0.91.  Then 

121,000 


(16,000)(0.91)(9.5) 


Two  round  rods  will  be  employed  in  each  rib — one  will  lie  straight  and  the  other  will  be  bent  up  at  both  ends 

and  extend  along  the  top  of  beam  to  the  quarter  point  of  the  adjoining  span.    This  arrangement  will  give  the  same 
steel  over  supports  as  in  the  center  of  span. 
The  total  shear  close  to  support 

y.^i^  =  2880  1b. 


The  bond  along  the  two  rods  at  the  top  over  supports 

2880 


76  lb.  per  sq.  in. 


(2)  (2.36)  (0.85)  (9.5^ 
The  distance  from  the  support  to  where  stirrups  are  unnecessary 
21       (40)  (4)  (0.91)  (9.5) 


274 


=  5.4  ft.  =  65  in. 


All  the  diagonal  tension  not  taken  by  the  concrete  will  be  provided  for  by  vertical  stirrups;  in  other  words,  the 
strengthening  action  of  the  bent  rod  will  not  be  considered.  Round  stirrups  H-in.  diameter  will  be  employed, 
bent  at  the  ends.    Stirrup  spacing  near  the  support: 

3    (0.049)  (2)  (16,000)  (0.85)  (9.5) 
"  =  2   2880  = 

The  spacing  adopted  is  shown  in  Plate  V. 

The  moment,  shear,  and  bond  considerations  given  above  do  not  take  into  account  the  strengthening  action 
of  the  flange  of  the  T-shaped  girders,  and  allowance  may  be  made  for  this  when  thought  necessary.  It  is  quite 
evident  that  the  concrete  is  not  overstressed  in  compression  over  supports,  but  the  stress  at  the  edge  of  girder 
flange  should  be  investigated.  For  the  width  of  girder  flange  shown  in  Plate  V,  the  bending  moment  may  be 
taken  at  ^/j  (121,000)  =  104,000  in. -lb.  This  value  is  obtained  by  considering  the  point  of  zero  moment  at  the 
third  point. 

Diagram  12  and  Table  9  give  the  values: 

k 

k  =  0.440     j  =  0.848  _       =  0.0524 

Then 

M  104,000  ,.^nniu 

Ajd=  (0.88)  (0.848)  (9.5)  =  ^^'^^^ 

fc  =  (14,700)  (0.0524)  =  770  lb.  per  sq.  in. 

The  load  on  the  floor  is  (274)  (i^ie)  =  205  lb.  per  sq.  ft.,  and  the  girder  therefore  caTries  a  load  of  (205)  (21)  = 
4300  lb.  per  lin.  ft.,  to  which  should  be  added  the  weight  of  the  girder  itself.  This  weight  will  be  assumed  at  360 
lb.  making  a  total  load,  which  may  be  considered  uniform,  of  4660  lb.  per  lin.  ft.    The  bending  moment 

(4660)  (21)  (21)  (12) 
M  =  j2  =  2,0o5,000  in.-lb. 

Assume  the  total  depth  of  girder  to  be  limited  to  36  in.,  effective  depth  to  32}^  in.    Then  ^  =         =  0.34. 

t  M 
Diagram  8  shows  that,  for  j  =  0.34  and  fc  =  650,  ^  =  107,  or 

2,055,000 

=  18.2  m. 


(32.5)2(107) 

M 

An  arbitrary  value  of  24  in.  will  be  adopted  by  b,  which  makes  ^  =  81.    Diagram  8  shows  the  neutral  axis  to 

lie  in  the  flange.    Diagram  2  shows  p  =  0.0057,  or 

As  =  (0.0057) (24) (32.5)  =  4.4  sq.  in. 

Eight  %-in.  round  rods  will  be  selected,  with  a  total  area  of  4.81  sq.  in.  The  width  of  stem  will  be  made  14  in.  to 
proviile  properly  for  shear.    The  remaining  computations  for  stresses  in  the  steel  and  concrete  at  the  support,  and 


Sec.  11-12] 


BUILDINGS 


456 


Plate  V 


1 

7'-0" 

*/m  ips 

7'o  ^ 
2rocrs  a 

/ 

H 

■  /s'Co/- 

r" 

Jti9'  1 

Stirrup  spacing 
?'           Se>  about  /'-I/" 

M 

Z'Conavte  5/ab 

F/n/shed  F/oor 

^1  J 


Crossbeam  ^'t//' Z-^'^ 

 S'j-J'S/eepers 

-/  j^'.'je  g//7gigy  concrete  f///- 1  S  6  mix 

Note:  Inserted  stirrups  are marAea  !r' 
Concrete  IZ4  mix 


TT 


Section  A/t 
T/7roug/7  Girder 


Section  BB 


DESIGN  OF 
AN  INTERIOR  FLOOR  BAY 

FOR  A 

ONE-WAY  HOLLOW  TILE  FLOOR 


Plate  V(A) 


SEAM   AND  GIRDER  RODS 


Bends 


8'-s" 

> 

>  - 

\/ 

S'-J"  ^ 

S/'-6" 

Straight 


Size 


Length 


30'-//'' 


Beam 

or 
Girder 


No 
wanted 

for 
each 
beam 


Total 

No. 
wanTed 


\l 


■  Spacers 


Continuous  Stirrup 


U- STIRRUPS 


Bends 


Length 


7-8' 


Beam 

or 
Girder 


No 
wanted 

for 
each 
beam 


CONTINUOUS  STIRRUPS 


a 

b 

Size 

Length 

Beam 

or 
Girder 

No  for 
each 
beam 

5/' 

iO 

e&s"- 

-3<S>4-  -& 

8 

69- O" 

O 

Z 

9 

4 

6-e-6-7 

iO'-3f 

B 

STEEL  BENDING  SCHEDULE 

FOR 

AN  INTERIOR  FLOOR  BAY 
ONE  WAY  HOLLOW  TILE  FLOOR 


456 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-12 


for  shear  and  bond,  are  similar  in  every  way  to  those  given  under  cross-beam  design  in  two-intermediate  beam 
construction.    In  Plate  V  an  18-in.  column  is  assumed  for  convenience. 

As  in  solid  concrete  floors,  the  pwoper  depth  for  girders  in  hollow-tile  construction  depends  upon  the  use  to 
which  the  building  is  to  be  put,  and  the  cost  of  all  columns  and  walls  in  the  building  per  unit  increase  in  height. 
The  cost  of  formwork  should  also  receive  attention.  Of  course,  as  regards  the  materials  in  the  girder  itself,  cost 
decreases  with  depth.  The  problem  resolves  itself  into  finding  the  limiting  depth  of  the  girder  in  view  of  the  many 
conditions  which  must  be  considered.  Very  often  a  perfectly  flat  ceiling  is  desired,  and  very  wide  girders  must 
then  result. 

The  following  table  has  been  prepared  to  simplify  the  computations  in  the  design  of  the  small  T-beams  of  a 
hollow-tile  floor.  The  table  shows  at  a  glance,  for  any  given  thickness  of  concrete  topping,  the  minimum  depth  of 
tile  needed  for  any  given  bending  moment,  and  the  corresponding  steel  area  required.  Greater  depths  of  tile  may 
sometimes  prove  more  economical. 

It  is  quite  evident  from  a  study  of  the  table  that  different  thicknesses  of  concrete  topping  should  be  con- 
sidered in  order  to  arrive  at  the  most  economical  design.  When  the  rib  width  does  not  change  in  the  economical 
considerations,  the  economy  of  the  various  designs  may  be  based  on  the  cost  per  foot  length  of  floor  having  a 
width,  the  distance  center  to  center  of  ribs ;  but  when  the  steel  area  is  such  that  the  width  of  rib  varies,  the  economy 
of  the  designs  should  be  based  on  the  cost  per  square  foot  of  floor. 


Table  for  Hollow-tile  Floors 


Depth  of  tile 
(inches) 

—  

Based  on  fc  =  650;  fs  =  16,000;  n  =  15 
in.  allowed  from  center  of  steel  to  bottom  of  slab) 

Bending  moments  and  steel  areas  for  various  depths  of  tile  and  concrete 
(Moments  in  thousands  of  inch-pounds;  steel  areas  in  square  inches) 

4-in.  rib 

For  any  other  width  of  rib  multiply  all  values  in  table  by  distance  center  to  center  of  ribs 

and  divide  by  16 

Thickness  of  concrete  topping  (inches) 

1.5 

2.0 

2.5 

3.0 

3.5 

4.0 

4.5 

5.0 

4 

27/ 

/ 

/0.49 

• 

35/ 
/ 

/0.55 

43/ 

/ 

/0.62 

52/ 
/ 

/0.68 

41/ 

/ 

/0.58 

52/ 
/0.68 

69/ 
/ 

/0.74 

72/ 
/0.80 

* 

84/ 

/ 

/0.86 

6 

56/ 
/ 

/0.65 

71/ 

/ 

/0.78 

84/ 
/ 

/0.86 

* 

96/ 

/ 

/0.92 

• 

110/ 

/ 

/0.98 

* 

124/ 

/ 

/1. 04 

7 

71/ 

/ 

/0.70 

90/ 

/ 

/0.84 

107/ 

/ 

/0.96 

124/ 
/ 

/1. 04 

139/ 

/ 

/1. 10 

155/ 
/1. 17 

• 

172/ 
/ 

/1. 23 

8 

86/ 
/0 . 73 

110/ 

/ 

/0.90 

131/ 

/ 

/1. 03 

152/ 

/ 

/1. 14 

171/ 
/ 

/1. 23 

• 

189/ 
/ 

/1. 29 

• 

208/ 
/ 

/1. 35 

227/ 
/ 

/1. 41 

9 

104/ 
/0.76 

130/ 
/ 

/0.94 

156/ 
/ 

/1. 09 

181/ 

/ 

/1. 21 

204/ 
/ 

/1. 32 

226/ 

/ 

/1. 41 

248/ 
/ 

/1. 48 

* 

268/ 
/1. 53 

10 

117/ 

/ 

/0.78 

150/ 

/ 

/0.98 

181/ 

/ 

/1. 14 

210/ 
/1. 28 

233/ 
/1. 40 

243/ 
/1. 51 

290/ 
/ 

/1. 59 

314/ 

/ 

/1. 67 

12 

147/ 
/0.81 

190/ 
/ 

/1. 03 

231/ 
/1. 22 

269/ 
/ 

/1. 38 

309/ 
/ 

/1. 52 

340/ 
/1. 65 

374/ 
/1. 77 

407/ 
/ 

/1. 87 

•  Neutral  axis  in  flange. 


Sec.  11-13] 


BUILDINGS 


457 


FLAT-SLAB  CONSTRUCTION 

By  Walter  S.  Edge^ 

13.  General  Description. — The  term  flat-slab  construction  as  here  employed  may  be  con- 
sidered to  include  that  type  of  building  construction  employing  a  reinforced-concrete  slab  in 
which  the  load  upon  the  floor  is  carried  directly  to  the  columns  without  the  agency  of  other 
elements,  such  as  beams  or  girders. 

As  commonly  constructed,  a  reinforced-concrete  floor  slab  of  uniform  thickness  (for  all 
or  the  greater  part  of  its  area)  is  supported  symmetrically  upon  columns  provided  with  wide 
conical-shaped  capitals  at  their  junction  with  the  under  side  of  slab  (see  Fig.  38.)  The  slab 
may  be  uniform  in  thickness  from  the  edge  of  one  capital  to  another;  or  a  portion  of  it,  sym- 
metrical with  respect  to  the  column,  may  be  increased  in  thickness,  forming  a  drop  panel  (see 
Fig.  39).  Another  form  occasionally  used,  carries  the  thickened  slab  from  column  to  column, 
thus  forming  in  reality  shallow  beams  between  columns,  and  giving  the  effect  of  a  paneled 
ceiling. 

The  methods  of  reinforcing  the  slab  and  columns  differ  radically  in  different  systems,  and 
are  described  in  Art.  17.    In  general  it  may  be  said  that  the  slab  reinforcement  consists  of  a 


Fig.  38. — Velie  Motor  Vehicle  Co.'s  factory  building,  Moline,  111. 


large  number  of  comparatively  small-diameter  rods,  a  considerable  percentage  of  which  radiate 
from  the  center  of  the  various  columns  and  are  commonly  located  in  the  bottom  of  the  slab  at 
the  center  of  the  span,  and  in  the  top  of  the  slab  over  the  column  head.  While  in  some  respects 
flat-slab  construction  is  structurally  the  simplest  form  of  concrete-steel  design,  it  is  of  compara- 
tively recent  development,  and  has  a  present-day  use  out  of  all  proportion  to  the  time  that  has 
elapsed  since  its  first  introduction.  Since  the  erection  in  1903  of  the  first  flat-slab  building, 
their  relative  number  has  steadily  increased  until  at  present,  probably  80%  of  new  reinforced- 
concrete  construction  (in  which  the  live  load  is  100  lb.  per  sq.  ft.  or  more)  is  of  this  type. 

14.  Advantages  Over  the  Beam-and-girder  Type.— The  reasons  for  its  popularity  as 
might  be  supposed  are  economic  ones,  and  may  be  summarized  as  follows : 

1.  The  ceiling,  being  flat  or  practically  so,  offers  no  obstruction  to  the  passage  of  light;  and, 
as  the  windows  may  extend  to  the  underside  of  floor,  good  daylight  illumination  may  be  obtained 
when  desired  for  the  maximum  width  of  building  (see  Figs.  38  and  39). 

2.  The  failure,  or  partial  failure,  of  concrete  structures  under  fire  has  been  first  to  develop 
at  the  corners  of  the  columns,  beams,  and  girders  where  spalling  of  the  concrete  is  apt  to  take 
place.    A  flat-slab  floor  supported  upon  round  concrete  columns  offers  practically  no  sharp 

I  Consulting  Engineer,  New  York  City. 


458 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-15 


angles  for  spalling  to  begin,  and  experience  shows  that  such  construction  will  suffer  little  damage 
where  a  beam-and-girder  building  would  be  seriously  injured. 

3.  The  automatic  sprinkler  system  is  after  all  the  final  safeguard  where  inflamable  materials 
are  stored  in  the  building,  and  a  much  more  efficient  installation  can  be  made  with  the  fiat 
ceiling,  than  with  an  unfinished  ceiling  of  the  beam-and-girder  type  (see  Fig.  39). 

4.  A  considerable  saving  in  story  height  and  in  total  height  of  a  multi-storied  building 
(or  an  increase  in  clear  story  height  with  the  same  height  of  building)  may  be  secured  by  the 
use  of  flat-slab  construction  as  compared  with  the  common  form  of  beam-and-girder  design 
(see  Fig.  40). 

5.  The  danger  of  sudden  collapse  from  excessive  overload — particularly  in  the  case  of  the 
so-called  four-way  type  of  floor,  due  to  the  interlacing  of  a  great  number  of  small  steel  rods  run- 
ning in  four  directions — is  much  less  than  in  beam-and-girder  type  of  construction. 


Fig.  39. — Stewart  Warner  Speedometer  Corporation  building,  Chicago,  111. 


6.  The  slab  formwork  is  much  simplified  and  no  added  complication  is  introduced  by  the 
round  columns  or  ornamental  column  head,  since  it  is  now  common  practice  to  use  metal 
forms  which  are  fairly  well  standardized  and  may  be  rented  from  a  number  of  firms  making  a 
specialty  of  this  work. 

7.  For  average  conditions,  the  flat-slab  type  of  construction  is  more  economical  than  the 
beam-and-girder  type  for  live  loads  of  100  lb.  per  sq.  ft.  and  over,  and  the  economy  increases 
with  the  load. 

15.  Classes  of  Buildings  to  Which  Adapted. — The  many  advantages  which  the  flat-slab 
system  of  floor  construction  possesses  has  developed  an  excess  of  enthusiasm  for  its  use  and  has 
caused  its  adoption  in  some  cases  where  an  adherence  to  the  beam-and-girder  type  would  un- 
doubtedly have  been  the  part  of  wisdom.  The  stern  realities,  however,  of  the  economic  side 
of  the  case,  due  to  the  present  high  cost  of  structural-steel  shapes,  has  brought  about  the 
adoption  of  flat-slab  floors  in  many  types  of  buildings  which  were  heretofore  almost  universally 


Sec,  11-16] 


BUILDINGS 


459 


constructed  with  structural-steel  skeleton  frames.  Among  these  may  be  mentioned  apartment 
houses,  stores,  hotels,  and  loft  buildings  for  light  manufacturing. 

Structures  to  which  this  system  is  best  adapted  may  be  summarized  as  follows : 

1.  Warehouses.  5.  Wharves. 

2.  Factories.  6.  Coal-storage  bins,  etc. 

3.  Cold-storage  plants.  7.  Railroad  terminals. 

4.  Garages  and  auto  service  stations. 

The  conditions  which  make  for  -economy  in  the  use  of  flat-slab  floors  are  as  follows : 

1.  An  approximately  uniform  and  equal  spacing  of  supporting  columns. 

2.  The  absence  of  frequent  large  openings  in  the  floor. 

3.  A  superimposed  live  load  of  100  lb.  per  sq.  ft.  or  more. 


FLAT  SLAB  CONSTRUCTION  BEAM  AND  QIRDER  CONSTRUCTION 

Fig.  40. 


While  other  considerations  may  make  the  use  of  flat-slab  construction  advisable,  it  will 
frequently  be  found  that  other  types — such  as  steel-tile  construction  or  combination  terra-cotta 
block  and  concrete — will  prove  to  be  more  economical  for  lighter  loads  or  irregular  spans. 

In  the  great  majority  of  buildings  in  which  this  system  of  floor  construction  is  employed, 
utilitarian  considerations  alone  prevail;  nevertheless,  it  can,  on  occasion,  be  combined  with  a 
simple  scheme  of  decoration  to  give  a  very  pleasing  effect. 

16.  Remarks  Regarding  Design. — The  methods  used  in  the  design  of  flat-slab  floors  are 
almost  entirely  based  on  the  results  of  extensometer  measurements  of  the  deformation  of  con- 
crete and  steel  in  actual  buildings  under  test  loads  (see  Art.  19).  The  theoretical  analyses  of 
stress  which  have  been  made  have  proved  to  be  ultr.aconservative  as  compared  to  test  results, 
due  undoubtedly  to  the  fact  that  it  is  extremely  difficult  to  take  all  factors  into  consideration 
in  any  formula.    No  theoretical  method  of  analysis  has  been  developed  which  really  meets 


460 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-16 


the  conditions  of  actual  design,  and  it  seems  highly  improbable  that  any  method  will  be  devised 
that  will  give  more  than  a  close  approximation,  which  the  present  methods  of  empirical  design 
undoubtedly  give.  The  reason  for  this  lies  in  the  materials  which  go  to  make  up  the  con- 
struction. Steel  is  a  thoroughly  tested  material  and  may  be  secured  with  well-determined 
physical  properties.  The  quality  of  concrete,  however,  is  far  more  uncertain  and  its  physical 
properties  can  only  be  controlled  within  certain  limits  and  cannot  be  accurately  forecast. 
Even  if  samples  are  taken  and  tested,  it  cannot  be  safely  predicted  that  the  quality  of  the  mate- 
rial in  the  structure  will  agree  with  that  in  the  sample  to  the  degree  of  accuracy  that  a  theoretical 
analysis  would  require.  Further  than  this,  there  are  shrinkage  and  temperature  stresses  set 
up  in  any  structure  having  considerable  area,  and  these  stresses  are  not  subject  to  accurate  de- 
termination beforehand  since  the  methods  of  construction  cannot  be  always  known  in  advance. 

Flat-slab  floors,  as  ordinarily  designed,  are  figured  to  carry  uniform  loads  or,  at  most, 
only  moderate  concentrations,  such  as  light  partitions,  etc.  When  concentrated  loads  must 
be  carried  in  addition  to  the  uniform  live  load,  it  is  common  to  introduce  beams  for  this  purpose. 
These  may  be  either  of  customary  sections  or  they  may  be  of  the  wide  and  shallow  type  involv- 
ing only  a  small  loss  in  clear  story  height  of  the  building.  The  same  practice  is  followed  with 
reference  to  openings  of  stairs,  etc. 

The  calculation  of  beams  of  this  class  involve  many  considerations.  Under  some  condi- 
tions, safe  results  will  be  secured  if  the  beam  is  computed  for  the  concentrated  load  alone,  but 
usually  a  portion  of  the  live  and  dead  load  of  the  slab  should  be  included.  Where  the  con- 
tinuity of  the  slab  is  destroyed  by  an  opening,  the  marginal  beams  should  be  figured  to  carry 
their  share  of  the  floor  in  addition  to  the  concentrated  loads  and,  of  course,  their  own  weight. 

When  necessary  to  secure  drainage,  flat-slab  floors  or  roofs  may  be  pitched  and  this  is 
common  practice  in  warehouse  construction.  When  it  is  necessary  to  introduce  steps  or  sudden 
changes  of  slope,  however,  special  treatment  will  be  required. 

Probably  the  great  majority  of  floors  of  this  type  are  laid  with  a  cement  flnish.  If  this  is 
laid  at  the  same  time  or  very  shortly  after  the  pouring  of  the  structural  slab  and  before  the 
concrete  has  taken  its  flnal  set,  it  may  be  safely  considered  as  a  part  of  same  and  the  reinforcing 
steel  so  calculated.  In  the  absence  of  positive  information  to  this  effect,  it  is  better  to  include 
the  weight  of  the  finish  but  not  its  thickness  in  the  computations  for  reinforcement,  for  in  the 
majority  of  cases  the  finish  is  laid  at  some  later  time  and  does  not  bond  with  the  floor  slab. 

Exterior  columns,  particularly  in  the  upper  stories  of  buildings,  require  special  reinforce- 
ment to  resist  bending.  Interior  columns  are  also  subject  to  bending  stresses  but  usually  they 
are  more  heavily  reinforced  than  the  exterior  columns  and,  further,  the  slab  on  the  unloaded 
side  of  the  column  acts  to  a  certain  extent  to  relieve  the  bending  in  the  column.  While  this 
point  should  be  given  due  consideration  it  is  seldom  that  the  interior  columns  need  extra  steel 
if  the  recommendations  of  the  Chicago  Code  or  the  American  Concrete  Institute  (A.  C.  I.),  as 
regards  size,  are  followed.  The  interior  columns  under  the  roof  are  really  very  unlikely  to 
be  subjected  to  unbalanced  live  load  and  in  the  lower  stories  where  it  may  occur,  the  direct 
load  and  column  diameter  are  both  greater,  tending  to  reduce  the  bending  effect. 

A  majority  of  the  designs  of  flat-slab  structures  have  been  made  by  specialists  who  have 
made  a  special  study  of  this  particular  form  of  construction.  It  is  well  that  such  is  the  case, 
for  the  subject  is  a  specialty  and,  while  simple  enough  in  many  cases,  the  production  of  a  safe 
and  economical  design  is  a  task  that  demands  a  skill  not  quickly  acquired.  It  is  manifestly 
impossible  in  a  book  of  this  character  to  embody  and  arrange  sufficient  information  so  that 
any  one  could  proceed  with  safety  with  its  aid  to  lay  out  any  and  every  problem,  and  such  is 
not  its  purpose. 

Failures  of  flat-slab  structures  have  occurred  and  other  structures  which  have  so  far  es- 
eaped  will  certainly  give  trouble  if  they  ever  receive  their  full  designed  load.  Causes  for  such 
shameful  occurrence  are  usually  easily  to  be  found.  The  first  and  probably  most  common  cause 
is  a  fierce  commercial  competition  which,  in  the  absence  of  strict  building  code  requirements, 
has  led  unscrupulous  designers  to  place  a  sublime  confidence  in  thin  sections  which  no  tests  can 


Sec.  11-17] 


BUILDINGS 


461 


justify.  Another  cause  has  been  poor  construction  which,  of  course,  is  fatal  to  any  design  but 
probably  in  no  class  of  construction  is  first-class  concrete  work  more  essential  to  success.  A 
third  contributing  cause  has  been  gross  ignorance. 

It  is  the  part  of  wisdom  and  true  economy,  therefore,  to  entrust  work  of  this  class  only 
to  those  who  have  had  experience  under  a  competent  designer  or,  better  still,  to  have  the  design 
made  by  or  reviewed  by  a  consulting  engineer  who  has  successful  constructions  of  this  class  to 
his  credit. 

17.  Systems. — A  number  of  systems  of  designing  and  reinforcing  flat-slab  floors  have  been 
developed  which,  so  far  as  the  external  appearance  of  the  finished  building  is  concerned,  are 
very  similar  but  differ  radically  in  structural  features  and  in  method  of  design.  They  may  be 
divided  into  four  general  classes  with  regard  to  the  method  of  reinforcement  which,  stated  in 
the  order  of  the  total  number  of  buildings  constructed  of  each  class,  are:  (1)  The  four-way 
system;  (2)  the  two-way  system;  (3)  the  circumferential  system;  and  (4)  the  three-way  system. 

In  the  four-way  system  the  slab  may  be  designed  either  of  a  uniform  thickness,  or  drop 
panels  may  be  used  at  the  column  capitals.  The  reinforcement  is  placed  in  four  direct  bands 
running  in  two  directions  and  two  diagonal  bands  which  pass  diagonally  across  the  panel  from 
column  to  column.  In  this  system  the  center  line  of  each  band  passes  over  the  center  of  the 
supporting  columns.  A  portion  of  the  rods  are  usually  bent  up  over  the  column  capital. 
Several  systems  of  this  type  do  not  follow  the  rule  in  this  respect,  however.  Additional  trans- 
verse steel  is  placed  in  the  top  of  the  slab  over  the  direct  bands  in  many  cases. 

In  the  two-way  system  the  reinforcement  is  all  placed  in  two  directions.  The  direct  bands 
of  reinforcement  are  carried  from  column  to  column  and  the  rectangular  area  remaining  is  rein- 
forced in  both  directions  parallel  to  the  direct  bands  by  similar  bars  which  pass  across  them. 
It  is  common  practice  in  this  system  to  carry  the  bars  of  the  direct  bands  in  the  top  of  the  slab 
at  the  column  head  and  in  the  bottom  of  the  slab  at  the  center  of  span.  Also  the  slab  bars  are 
commonly  bent  up  where  they  pass  over  the  direct  bands. 

The  circumferential  system  makes  use  of  both  radial  and  circumferential  reinforcement 
around  the  column  head.  The  region  between  column  heads  which  is  commonly  occupied 
by  the  direct  bands  is  also  reinforced  with  concentric  rings  which  overlap  with  those  around 
the  column  head.    Finally,  the  slab  in  the  center  of  the  panel  is  reinforced  in  a  similar  manner. 

The  three-way  system  requires  a  special  arrangement  of  columns  and,  while  it  possesses 
certain  theoretical  advantages  over  the  four-way  and  two-way  systems,  its  use  so  far  has  been 
comparatively  limited.  In  this  system  the  interior  columns  are  placed  in  such  a  manner  that 
the  lines  connecting  their  center  lines  form  equilateral  triangles.  By  this  arrangement  all  the 
bands  of  reinforcement  have  equal  spans  and  all  pass  over  the  column  heads. 

The  majority  of  the  systems  herein  described  are  operating  under  license  from  the  Flat 
Slab  Patents  Co.  of  Chicago  and  are  protected  by  special  detail  patents. 

The  more  important  systems  will  now  be  described  in  detail. 

17a.  Barton  Spider  Web  System. — The  Barton  Spider  Web  system  is  similar 
to  other  flat-slab  systems  as  to  the  arrangement  of  columns,  column  heads,  and  drop  panels, 
'  but  differs  radically  in  the  type  of  reinforcement  used.  As  regards  the  slab,  it  is  a  four- way 
system  and  over  the  column  head  it  is  a  two-way  system.  It  will  be  seen  by  referring  to  Fig.  41 
that  the  slab  reinforcement  is  made  up  of  straight  rods  of  small  diameter  which  run  from  column 
to  column  and  are  not  continuous.  The  negative  reinforcement  over  the  column  head  con- 
sists of  two  systems  of  bent  rods  at  right  angles  to  each  other  which  are  placed  in  the  top  of 
slab  and  have  their  looped  ends  bent  down. 

Two  methods  of  fabricating  this  steel  are  in  use.  In  the  first,  that  shown  in  Fig.  41,  the 
column-head  steel  is  in  the  form  of  a  fabricated  mattress  of  bars  in  one  direction  which  comes 
to  the  job  bent  and  ready  to  place.  In  this  case  the  mat  serves  to  space  and  support  the  floor- 
slab  reinforcement.  In  the  other  type  the  column  head  steel  consists  of  loose  bars  supported  from 
the  forms  by  blocks  of  concrete  cast  in  the  field.    A  zig-zag  stirrup  hangs  from  these  bars  and 


462 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  ll-17a 


supports  the  ends  of  the  direct  belts  of  steel  in  the  bottom  of  the  slab.  The  negative  moment 
in  the  slab  across  the  line  between  columns  is  taken  care  of  by  a  belt  of  steel  in  the  top  of  the 
slab  at  right  angles  to  and  over  the  direct  belt. 

The  designers  of  this  system  recognize  the  necessity  of  additional  vertical  reinforcement 
in  the  exterior  columns  to  resist  bending,  particularly  in  the  upper  stories. 

In  order  to  govern  the  design,  it  is  assumed  that  the  loads  will  seek  to  enter  the  columns  by 
the  shortest  possible  route  and  will,  therefore,  cause  a  radiation  of  stress  out  from  the  column  in 
all  directions.  Also,  it  is  assumed  that  these  stresses  will  pass  through  a  point  of  inflection 
on  account  of  the  slab  being  fixed.  This  point  of  contrafiexure  cannot  be  definitely  located, 
inasmuch  as  variations  in  the  loading,  such  as  naturally  occurs  on  all  floors,  will  cause  the  point 
to  shift  either  toward  or  away  from  the  columns. 

To  meet  the  above  conditions  the  Barton  Spider  Web  system  is  a  four-way  system  in 
which  all  the  major  slab  reinforcement  radiates  from  the  column  head  and  also  is  composed 
of  separate  units  of  negative  (column  head)  and  positive  (slab  center)  steel,  which  lap  past 


Fig.  41. 


each  other  so  as  to  provide  steel  at  top  and  bottom  of  the  slab  in  the  region  of  the  shiftin 
point  of  inflection. 

So  far  as  the  methods  of  arriving  at  bending  moments  in  the  different  belts  are  concerned 
the  engineers  of  the  Barton  Spider  Web  system  believe  the  American  Society  method  to  b 
the  most  mathematically  correct,  but  that  their  coefficients  are  needlessly  conservative.  The 
believe  the  Chicago  Code  to  be  the  most  satisfactory  for  practical  use  and,  as  every  test  made  o 
these  floors  in  that  city  gave  a  deflection  of  less  than  H200  of  the  span  for  a  test  load  o 
twice  the  live  load  plus  a  superimposed  dead  load  and  showed  perfect  elasticity,  it  is  felt  tha 
the  Chicago  coefficients  are  amply  safe.  The  Cleveland  Code  with  respect  to  columns  i 
favored  above  others  by  the  designers  of  this  system. 

Fig.  39  is  a  typical  interior  of  a  building  constructed  according  to  this  system. 

Fig.  42  is  copied  from  the  working  plans  of  a  building  designed  under  this  system  and 
illustrates  its  practical  application.  Much  labor  is  saved  on  drawings  by  the  method  of  lettering 
bands  here  adopted.  The  method  of  framing  openings  is  by  the  use  of  wide,  shallow  beams, 
which  method  is  quite  commonly  used  by  other  designers. 

For  cuts  and  descriptive  matter,  the  writer  is  indebted  to  the  Barton  Spider  Web  system. 


Sec.  11-176] 


BUILDINGS 


463 


176.  Cantilever  Flat-slab  Construction. — Flat-slab  floors  are  designed  by  the 
Concrete  Steel  Products  Co.,  Consulting  Engineers,  Chicago,  under  the  trade  name  of  ''Canti- 


1-> 


III  r , 


shm 


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Second  floor  slab  s-hsel 


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top  bars 

I        I  n  n  n   l^o^'^-  The  last  leHer 
Vat  A  W\T\\  of  the  mark  ofa/ayer 
I        I  I  U  U  K  o/^  column  headshel 
This  indir.qf^5  map"  gives  ihe  locafion  oT 
of  Sonne    B  indicates  boffom  layer -'T 
indicarl'es  fop  layer  All  layers  or  column 
.head  slwel  or  mats  are  called  ibr  like 
Cffher  belts  of  bars,  i.e.  al  riqhf  anafes 
with  bars.  ^ 


JpB^'rs"^ spBars     Typicql  slab  steel  layout 


Section  "X-X* 


Fig.  42. 


Fig.  43. 


lever  Flat-slab  Construction."  In  their  designing,  use  is  made  of  either  a  true  flat  slab  or  a 
slab  stiffened  by  the  use  of  drop  panels  around  the  column  capitals  as  is  done  with  other  systems. 


464 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  ll-17fc 


Earlier  designs  prepared  by  this  company  made  use  of  radial  rods,  rings  around  the  column 
heads,  and  column  rods  bent  down  into  the  slab ;  but  as  extensometer  tests  proved  these  to  be 
ineflScient,  their  use  has  been  discontinued  in  later  work. 

The  system  of  reinforcement  commonly  employed  is  the  four- way  system  which  was 
developed  and  perfected  by  the  engineers  of  this  company.  On  account  of  the  greater  stiffness 
and  economy  of  materials  secured,  the  drop-panel  type  of  floor  is  always  favored,  although 
many  floors  have  been  designed  and  built  of  the  true  flat  type. 


Section  A-B 

Fig.  44. 


Great  stress  is  laid  on  the  accurate  placing  and  anchoring  of  the  reinforcement  in  place. 
The  negative  reinforcement  passing  over  the  column  head  is  supported  by  head  rods  which  in 
turn  are  carried  on  concrete  blocks  and  in  the  center  of  span  the  accurate  spacing  of  bars  is 
maintained  by  bar  spacers,  tying  devices,  or  wiring.    A  view  of  a  typical  floor  is  shown  iii  Fig.  43. 

Hundreds  of  buildings  have  been  constructed  according  to  this  system  and  a  number  of 
these  located  in  Chicago  have  been  tested  with  very  satisfactory  results  (see  Art.  19). 

For  information  and  cut  the  writer  is  indebted  to  the  Concrete  Steel  Products  Co.  of 
Chicago. 


Sec.  ll-17cl 


BUILDINGS 


465 


17c.  Simplex  System. — The  Simplex  system  of  flat-slab  construction  developed 
by  the  Concrete  Steel  Co.  of  New  York  is  a  four-way  system  with  certain  added  refinements 
in  the  way  of  devices  for  anchoring  the  rods  in  place  (see  Figs.  44  and  45).  It  is  designed  on 
conservative  Hues — particularly  with  respect  to  the  stresses  on  the  concrete  which  are  not 
allowed  to  exceed  the  New  York  City  Building  Code  requirements.  In  the  great  majority 
of  cases  a  drop  head  is  used  around  the  column  capital.  The  steel  reinforcement  is  commonly 
calculated  on  the  basis  of  the  Pittsburgh  or  Chicago  Ruling,  although  it  may  be  designed  to  meet 
the  requirements  of  any  building  code.  In  the  design  of  the  interior  and  exterior  columns 
the  Chicago  Ruling  is  used. 


0^  (D,      ^  Headra/..  0 


METHOD  OF  PLACING 
FLAT  SLAB  STEEL 

OPERATION 

No.  I.  P/ace  head  rod  supports  using  eigh-h  Hy- Chairs 

per  inferior  column. 
No.  2.  Place  head  rods  on  supporfs. 
No.a  Half  way  befween  columns.place  Slab  Spacer 

for  short  cross  band  bars. 
No  A  Place  shorf  cross  band  bars  being  carefiil 
fo'hickey'fhem  so  fhai-  fhey  lie  fled  across 
head  rods. 

Na5.  Half  way  beftveen  columns  place  Slab  Spacer 

for  long  crossband  bars 
No.6.  Place  long  cross  band  bars;  being  careful  fo 
'hickey'fhem  fo  lie  flaf  across  shorf  cross 
band  bars  over  columns. 
No.  7.  Tie  long  and  shorf  cross  band  bars  wifh  No.  I 

Bar-Tys  af  iheir  infer secf ion  over  columns. 
No. 8.  Place  diagonal  band  bars,  being  carefi/l  fo 
"hickey'fhem  fo  lie  flaf  across  long  crossband 
bars  over  columns.. 
No.9.  Place  second  diagonal  band  bars  bein^  car^ 
ful  fa  'hickey"fhem  so  fhai  fop  offhese  ban 
is  I'  below  fop  ofcancrefe  slab. 
No.  10.  Tie  and  support  diagonal  band  bars  rrifh 
Slab  Spacer  af  fheir  infersecfion  af  cenfsrof 
panel 

Note  -  Ty-Chairs,  ten  in  number  may  be  used  in 
operation  No.  10  instead  or  Slab  Spacer 


KEY. 

■I      denotes  Hy- Chair, 
^-v--  denotes  Slab  Spacer, 

«       denotes  No.t.  Bar-Ty, 

o      demfea  Ty- Chair, 


FLAT  SLAB  CONSTRUCTION 

COncrelte:  steel  co. 


Fig  45. 


The  concrete  sizes  to  use  with  the  system  for  the  Pittsburgh  and  Chicago  Rulings  have 
been  computed  and  are  given  in  the  tables  of  Art.  21.  The  dimensions  there  given  apply  only 
to  square  interior  panels.    Exterior  panels  may  require  special  treatment. 

The  method  of  placing  the  steel  reinforcement  is  explained  in  detail  in  Fig.  45.  In  practice 
it  is  frequently  found  that  the  weight  of  the  rods  themselves  will  give  them  sufficient  sag  so 
that  Uttle  or  no  bending  is  required. 

This  system  has  been  used  very  extensively  and  with  great  success  and,  since  the  policy 
of  its  sponsors  has  always  been  a  conservative  one,  it  has  never  failed  to  give  satisfaction. 

VJd.  The  Mushroom  System. — The  Mushroom  system  was  developed  by  C.  A. 
P.  Turner  and  was  in  very  extensive  use  until  quite  recently.    Further  use  of  the  system, 
unless  licensed  by  the  Flat  Slab  Patents  Co.,  was  prevented  by  order  of  Court  on  account  of 
alleged  infringement  of  the  Norcross  patent  (see  Art.  18). 
30 


466 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  ll-17e 


The  system,  as  originally  developed,  was  a  four-way  system  with  certain  added  features. 
In  some  cases  the  column  bars  were  bent  down  into  the  slab  around  the  column  head  to  form 
a  radial  reinforcement.  In  other  cases  special  elbow  rods  were  inserted  in  the  column  head 
for  the  same  purpose.  A  series  of  ring  rods,  spaced  by  radials  forming  a  spider,  were  also  used 
as  a  reinforcement  at  the  column  head  and  as  a  support  to  the  slab  steel.  In  some  cases  a  flat 
spiral  was  used  in  the  same  position.  The  use  of  this  system  has  been  pushed  with  much 
business  enterprise,  but  the  severe  service  to  which  this  class  of  buildings  is  almost  sure  to  be 
subjected  has  shown  beyond  question,  that  the  concrete  sections  used  in  many  of  the  earher 


N  i6 xSXoncrefe block 
to  support  arvie  bar  j'/^/rj/ii 


Formulae  ■•-('^or  bending  moTients  in  foot  pounds) 
Negafive  bending  moment  at  A  (to  be  resisted  by  one  cross  belt  and i 
fhsitive  bending  moment  at  B  (to  be  resisted  by  one  cross  belt. 

Negative  bending  moment  at  B  (to  tie  resisted  By  one  center  belt)- ■■  -^/^ 

Positive  bending  moment  at  C[to  be  resisted  Joy  one  diagonal  Mt)  w 

KT  '  total  had  per  sq  ft  (bath  dead  and  live) 

L- Side  ofsq.  panel{in  feet).  L-mean  of  sides  in  rectangular  panels  (in  feet) 
When  the  long  side  exceeds  the  short  side  by  more  than  10%.  the  steel  in  the 
belts  shall  be  proportioned  according  to  the  cutie  of  the  rario  of  the  side  of 
thp  panel  to  the  side  of  the  assumed  square  panel 

Fig.  46. 


Li 

Note-.'  h- 

{ Belt  bars  notsupport- 
\  ed  directly  ontbrmi-^ 
\  bars  are  to  be  win}^ 
to  the  first  bar,  aboH 


i'xC'CorKmte 


All  belt  bars  to  be 
depressed  atthecenler 


aepi 

of  the  panel  so  as  to 

.    ,       .        -  provide  4' concrete 

-i  or  below  which  is  so  Section  thru  in  the  clear,  below 


concrete 

.  _  ^   iki     ■  ■ 

I  supported.  column  head  ^^f- 

i  Provide  a  sufficient  nunber  of  concrete  blocks  to  insure 
!  against  excessive  deflection  of  the  forming  ban 

J  '^fprminij 


6W  Concrete  block 
f      ^rCenter  belt  JsXkS!^ 


Width  of  all  bona 


Section  taken  on  center  line 
of  bay  showing  center 
belta 


Order  of  placing  steel 
Belts  are  designated  as  shown  on  plan 

1.  Lay  circular  form  bars 

2.  Lay  all  cross  belts  running  in  one  direction 

3.  Lay  all  cross  belts  running  in  opposite  direction 
A.  Lay  all  diagonal  belts  running  in  one  direction 
5.  Lay  all  diagonal  belts  running  in  'opposite  diPBcffon 
^-        '^^^  form  bars  for  center  belts 
7.  Lay  all  center  belts  running  in  one  direction 


A     Q  Lay  all  center  belts  running  in  opposite  direction 
®        The  cross  belts  and  diagonal  belts  are  in  the  top  or 
the  slab  over  the  colunnn  head,  and  in  the  bottom  of  the 
slab  between  the  columns.     The  center  belts  are  in 
the  top  of  the  slab  over  the  cross  belts  an(J  In  the  bof^ 
torn  of  the  slab  over  the  diagonal  belts 
5+andard  four-way  flat  slab  construction 


designs  were  entirely  too  light,  since  sagging  and  cracking  of  floors  have  resulted.  The  right 
requirements  of  the  various  building  codes  are  intended  to  and  do  remedy  this  condition,  so 
that  now  all  systems  must  compete  on  a  substantially  uniform  basis. 

Vie.  Watson  System. — A  modified  type  of  the  four-way  system  is  that  developed 
by  Wilbur  J.  Watson  &  Co.  of  Cleveland,  Ohio.  This  system  differs  from  the  standard  four- 
way  system  in  the  introduction  of  center  belts  or  bands  of  reinforcement  which  do  not  pass 
over  the  column  heads,  in  addition  to  the  usual  direct  and  diagonal  bands. 

The  details  of  this  system  together  with  the  methods  of  computation  and  methods  of 
placing  are  clearly  shown  in  Fig.  46. 


Sec.  11-17/] 


BUILDINGS 


467 


17/.  Akme  System. — The  Akme  system  of  girderless-floor  construction  was 
developed  by  the  Condron  Co.,  Structural  Engineers  of  Chicago.  It  is  a  two-way  system  of 
very  simple  construction  and  has  had  a  wide  and  successful  use. 

When  building  codes  are  in  use  which  have  special  rulings  regarding  flat-slab  floors,  the 
system  is  designed  to  meet  their  requirements  but,  in  order  to  govern  design  where  such  rulings 
do  not  apply,  the  Condron  Co.  have  prepared  a  set  of  instructions  which  are  given  below. 
These  are  to  be  used  in  connection  with  design  standards  (see  Figs.  47  and  48). 


Typical  square  panet 


Main  Dand  i 


P-or>35i 


'Mid  band 


"Spain  of  mid 
Slab 


^yercpTunihj, 


I  tomp. wiTfh for\\ 
\mginbcin  iafcenk[\ 


Typical  recfangular  g:inel 


C=or>./ 


'A 

Moments  sauare  panels      Moments  rectangular  panels 

Moment  mam  bandar  cof.  =^  =•  M      Compute  moments  forsquare  panel  with  L  ''La 
Moment mainbandat  center=^=Mc  T^tl^Scj^et^c  =  Moments  long  span. 
Moment  mid  band  at  center  -^j^--m    i^M  &-^>Mc  =  f^oments^  sport  span. 
For  determining  moments  at  olher       --/i  ((^^)u^Gs    =  iz  ■(^^') = Moment  of  long  span 
sections  for  mam  bands  assume    rn,=jl(^\ufG,Gf=^^(j^)^Moment  of  short  span 
line  of  contra-flexure  0.2S  from    J  ^^'^^^'^n         '^^^^t^'^  ,  ^ 
capital  and  a  stmightlitle  variation  ^^^"^^^  allowable  punching  shear  =100  Ib.persq.in. 
betmen  edge  cfcap  and  this  line.    ^T^^^'^  '^'ff^?  ^1%  n.,a,v-  ,  < . 

•C^rs.ncLed.ithmain  bands.  'jTml^^^/^t^^^^^^^^^ 


-4- 


1^ 


K 

I 


roof 


:^,al5omln  =  6'' 


Approximate  length  of  bar  L+0.075^-3" 
3"= approximately  amount  taken  up  by  bend 
'd"=  nominal  size  of  bar  Stagger =0.075 
'C'=  tvidth  of  plate.  Dimensions  gi/en  are  apprvximode  and 
may  be  changed  slightly  to  sum  conditions 


 U—  H 

uf=(LL+D0per5q.ft 
W=(LL+DL)(L'-C')i^ 
if  head  is  not  square  use 
C=5ide  of  equivalent  square. 
5=  L-C=  Clear  span. 
G  =  Clear'  span  behveen  main  bands 
L/r^''^=  Average  span. 
Sa<L,-C) 
Recommended  unit  stresses 
750  lb  per  sq  in  for.  concrete  with 
ultimate  strength  ofdftOO 
18, 000  lb.  per  sq.  in  tor  steel  with  elas- 
tic limit  of  ar least  50,000  lb.pers(j.  in 

■"JiolQ^  \0p5 


— > 


Fig.  47. — Akme  system.    Drop  panel  type.    Design  standards, 


■0015  0.145-M..^. 

<- Line  of  col.  capital-  

Condron  Co. 


RULES  FOR  THE  DESIGN  OF  GIRDERLESS  FLOORS 

(To  Accompany  Akme  Design  Standards) 

The  term  girderless  floors  as  herein  used  refers  to  flat  slabs  of  uniform  or  varying  thickness  supported  without 
beams  or  girders  on  columns  having  flaring  heads. 

Flat-slab  Type. — In  this  type  the  slab  thickness  is  uniform  between  column  heads. 

Drop-panel  Type. — In  this  type  the  lower  face  of  the  slab  is  dropped  so  as  to  increase  the  thickness  of  the  slab 
above  the  column  head.  The  lateral  dimensions  of  this  portion  of  the  slab,  which  is  usually  made  square,  should 
be  not  less  than  0.35L. 

Paneled-ceiling  Type. — This  type  may  conform  in  general  to  either  of  the  above  types  with  the  exception  that 
the  slab  is  reduced  in  thickness  in  the  central  portion  of  the  panel. 


468 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-17/ 


Columns. — The  diameter  or  side  of  any  interior  concrete  column  shall  be  not  less  than  one-thirteenth  of  the 
panel  length  or  one-twelfth  of  the  clear  story  height,  except  that  for  columns  supporting  roofs  only  this  dimension 
shall  be  not  less  than  one-fifteenth  of  the  panel  length.  In  any  case  the  diameter  or  side  of  the  column  shall  be 
not  less  than  12  in. 

Bending  in  Columns. — Exterior  or  wall  columns  supporting  floors  or  roofs  shall  be  designed  to  resist,  in  addi- 
tion to  direct  load,  40  %  of  the  negative  bending  moment  for  exterior  floor  panels  or  80  %  for  exterior  roof  panels. 

Column  Head. — The  diameter  of  the  column  head,  measured  where  it  intersects  the  underside  of  the  slab, 
should  be  approximately  0.235L,  but  may  vary  to  suit  conditions.  It  shall  have  a  vertical  face  below  the  slab  of 
IH  in.,  below  which  the  surface  of  the  head  shall  have  a  slope  of  45  deg.  to  the  vertical  face  of  the  column  shaft. 
If  other  shapes  of  column  head  are  used,  the  surface  of  the  same  shall  nowhere  fall  inside  of  the  surface  of  the 
above-defined  conical  head.    Heads  may  be  round,  octagonal,  or  square. 


Typ/cal  square  panel 


1_ 


lypical  necf angular  parie\ 


'7X: 


-f- 


Main  band  T  WW  i  \  y^dMn^^^^ 

Comp-  widfl^lxincif-4t 
maxoffL] 


,  G  

Span  of  mid 


slab 


Si 

C3: 


Comp  widfh  over  col. 


t)and+4fbutnof 

r 


TL 


.omp.  wia 
"'n  ml/7 1 

it; 


\mmo 


-K 


Hi:— 


Main^band  \ 
Wiolfh  ofmainbar^0.4Ls 


Midband 


O.EL> 


[< --  Ls^Shorf  dimension  5^ 


Moments  rectangular  panels 


Momenfs  square  panels 

Momenl  main  band  a  f  col.=j^=M 
Moment  main  band  afcenfer=j^,-- 
Moment  mid  band  af- center  =  -^^^ 
fbr  determining  moments  af  other 

sections  for  main  bands  assume      ^  wq^/^f  =Momentof5ho-tspan 

ine  of  contra- fexure  0.25  from     a/  ^^Z*^^' v     J  '^^^^t^L^  ,  — >r— 
capita/ anda  straight  line. anatlon  ^frn.TnTrnf^^^^^^^ 

""rn'^^^'V'^    7nTmtAr  sL^^^^^^^^^^  Recommend.dunitstr.5ses 
C bars  included  with  mam  bands.    ""'"T""  T    =%,a/somin  ^6^   750ib.per5a.ln  for  concr^e  mth 

Thickness  of  plate  =.4f  with  a  minimum  of  4"    ultimate  strength  of^fiOOIbpersqin. 

18,000 lb.  per  so.  in.  for  steel  with  elas- 

Approximate  length  of  bar  L^0.075-f3"  tic  limit  of  at  least  50,000 Ib.persq.in. 


ur=(LL-/-DL)per3a.ft 

W=(LLWL)(L^-C9^2 

if  head  is  not  square  use 

C=  Side  of  equivalent  square. 

5  =  L-C  =  C/earspan. 

G=Clear  spanbetween  main  bands 

L/'f''^^ Average  span. 


3"= approximately  amount  taken  up  by  bend 
Y=  nominal  size  of  bar  Stagger =0.075 
"0"=^  widtb'of  plate.  Dimensions  giyen  are  approx/maf&  and 
may  be  changed  slightly  to  surf  conditions. 


\.o.eL 


f^^-  '^  Une  of  col  capital  •  ■ ->l 


-S 


Fig.  48. — Akme  system.    Flat  slab  design  standards,  Condron  Co. 


If  round  or  octagonal  heads  are  used,  the  diameter  of  head  to  be  used  in  the  slab  calculations  shall  be  the  side 
of  an  equivalent  square.  Where  a  square  plate  is  used  as  part  of  the  column  head  and  its  lateral  dimension  is 
within  the  45  deg.  slope  of  the  conical  head,  the  size  of  said  square  plate  shall  be  used  as  the  diameter  of  column 
head  in  making  slab  calculations,  provided  the  thickness  of  said  plate  is  equal  to  or  greater  than  one-half  the  thick- 
ness of  the  slab  and  not  less  than  4  in. 

Slab  Thickness. — The  minimum  thickness  of  the  slab  (except  in  paneled-ceiling  type)  shall  be  not  less  than 

^  for  floors  and  ^  for  roofs,  nor  less  than  given  by  the  following  formula: 

t  =  O.OIQLVu'  +  in. 
where  t  =  total  slab  thickness  in  inches;  L  =  panel  length  in  feet;  and  w 
per  square  foot. 


total  live  and  dead  load  in  pounds 


Sec.  11-17/] 


BUILDINGS 


469 


In  the  paneled-ceiling  type  the  thickness  of  the  enclosed  panel  shall  be  not  less  than  one  thirty-seoond  of  its 
clear  span. 

Drop  Panel. — The  depth  of  drop  panel  where  used  shall  be  determined  by  using  its  width  at  the  section 
considered  as  the  full  width  to  resist  compression  resulting  from  negative  moment. 

Panel  Strips — For  purposes  of  computation  each  panel  of  the  slab  is  to  be  divided  into  two  sets  of  strips  called 
A  (main  slab  strips)  and  B  (mid-slab  strips).    Strips  A  extend  from  column  to  column  and  have  a  width  equal  to 

— ,  and  strips  B  occupy  the  space  between  strips  A,  and  likewise  have  a  width  of 

Reinforcement  in  strips  A  shall  be  placed  symmetrically  about  column  centers  for  a  width  of  approximately 
0.4L  at  mid-span  and  approximately  0.5L  over  columns.  The  width  for  compression  shall  be  taken  as  the  width  of 
the  belts  of  reinforcement,  plus  4  times  the  thickness  of  the  slab,  but  shall  not  exceed  YzL.  The  width  of  main 
belts  of  reinforcement  over  the  columns  shall  not  exceed  twice  the  width  of  the  column  head. 

B ending-moment  Coefficients,  Interior  Panels. — For  the  flat-slab  type  the  negative  bending  moment  taken  at 

WS 

a  cross-section  of  each  strip  A  at  the  edge  of  a  column  head  shall  be  The  positive  bending  moment  taken 


at  a  cross-section  of  each  strip  A  midway  between  column  supports  shall  be  "jg"    The  positive  and  negative 


WS 
18 

bending  moments  taken  at  a  cross-section  of  each  strip  B  at  the  middle  of  the  panel  on  the  center  line  of  columns, 

w 

respectively,  shall  be  • 

WS  WS 

For  the  drop-panel  type  the  corresponding  moments  at  the  above-mentioned  section  shall  be  ~2o' 
and  j^- 

For  paneled-ceiling  type  the  moment  coefficients  shall  be  the  same  as  for  the  flat-slab  type. 

For  determining  moments  at  other  sections  of  main  strips  A,  the  line  of  contraflexure  shall  be  assumed  to  be 

at  a  distance  equal  to     from  the  center  of  column,  with  a  straight-line  variation  moment  between  the  edge  of  the 

head  and  the  said  line  of  contraflexure. 

In  the  above  W  =  one-half  total  live  and  dead  load  on  the  panel,  exclusive  of  the  area  over  the  column  head ; 
S  =  the  clear  span  in  feet  between  column  heads;  w  =  total  live  and  dead  load  per  square  foot;  and  G  =  the 
clear  distance  in  feet  between  main  belts  of  bars  at  the  section  midway  between  columns. 

B ending-moment  Coeffi,cients,  Exterior  Panels. — For  exterior  panels  without  cantilever  overhang,  where  wall 
columns  with  flaring  heads  or  brackets  are  used,  and  for  other  spans  not  continuous  over  both  supports,  the  positive 
bending  moment  coefficients  shall  be  increased  20%. 

When  bearing  walls  or  piers  and  girders  are  substituted  for  the  above  wall  columns  with  flaring  heads  or 
brackets,  compute  the  moments  for  the  exterior  panels  of  such  construction  by  assuming  the  distance  from  the  face 
of  column  head  to  inside  face  of  wall  or  girder  as  S;  and  the  distance  between  the  first  interior  main  belt  and  the 
inside  face  of  wall  or  girder  as  G. 

Oblong  Panels. — For  oblong  panels  the  moments  shall  first  be  determined  for  an  assumed  square  panel  with 
sides  equal  to  the  mean  of  the  length  and  breadth  of  the  oblong  panel.  The  moments  thus  found  for  strips  A 
shall  be  multiplied  by  the  ratio  of  the  square  of  the  span  in  question  and  the  square  of  the  span  of  the  assumed 
square  panel,  and  the  moments  thus  found  used  in  determining  the  steel  required  in  strips  A. 

The  moments  for  strips  B  shall  be  computed  as  follows:  The  load  carried  by  the  long  and  short  span  strips  B 
shall  be  in  the  proportion  of  the  ratio  of  the  square  of  the  short  span  to  sum  of  squares  of  long  and  short  spans  and 
the  ratio  of  the  square  of  the  long  span  to  sum  of  squares  of  long  and  short  spans  respectively.    The  moments  shall 

then  be  found  as  for  square  panel  using  the  proportion  of  w  carried  by  the  span  in  question  instead  of 

When  the  length  of  panel  does  not  exceed  the  breadth  by  more  than  5  % ,  all  computations  may  be  made  on 
the  basis  of  a  square  with  sides  equal  to  the  mean  of  the  length  and  breadth.  The  rules  given  herein  shall  not  be 
used  for  rectangular  panels  in  which  the  length  exceeds  four-thirds  of  the  breadth,  but  special  consideration  shall 
be  given  to  such  cases. 

Stresses  in  Steel  and  Concrete. — The  stresses  shall  be  calculated  on  the  basis  of  the  straight-line  formula, 
neglecting  the  tension  value  of  the  concrete.  The  depth  of  the  slab  for  calculation  of  stresses  shall  be  taken  as  the 
distance  from  the  compressive  face  to  the  center  of  gravity  of  the  belt  of  reinforcement  in  a  given  strip.  The 
tensile  stress  in  steel  reinforcement  should  not  exceed  16,000  lb.  per  sq.  in.  for  structural-steel  grade  nor  18,000 
lb.  per  sq.  in.  for  cold-twisted  or  high-carbon  deformed  bars.  The  maximum  allowable  compression  in  the  concrete 
shall  not  exceed  750  lb.  per  sq.  in.  The  allowable  punching  shear  on  the  perimeter  of  the  column  head  shall  not 
exceed  100  lb.  per  sq.  in.  Where  governing  ordinances  or  laws  require  lower  allowable  unit  stresses,  such  unit 
stresses  shall  be  substituted  for  the  above. 

Walls  and  Openings. — Where  necessary,  slabs  shall  be  thickened  or  girders  or  beams  shall  be  used  under  walls 
and  around  openings  to  carry  concentrated  loads. 

Placing  of  Reinforcement. — Reinforcement  shall  be  rigidly  held  in  its  designed  position  while  pouring  con- 
crete. The  bars  in  the  upper  portion  of  the  slab  should  be  rigidly  supported  by  frames  or  transverse  bars  resting 
on  concrete  blocks  of  proper  height.    Bars  in  the  lower  portion  of  the  slab  should  be  raised  from  the  forms  and 


470 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  ll-17j^ 


held  ih  proper  position,  preferably  by  a  continuous  combined  spacing  and  raising  device.  The  lateral  spacing  of 
bars  shall  not  exceed  lyi  times  the  thickness  of  the  slab,  nor  more  than  12  in. 

Bars  shall  be  bent  to  conform  to  the  bending  diagrams  shown  in  Figs.  47  and  48  and  shall  be  so  placed  in  the 
slab  that  they  will  not  be  nearer  than  %  in.  from  the  face  of  the  concrete. 

A  great  number  of  buildings  have  been  constructed  under  this  system  and  many  of  them 
have  been  tested  with  very  satisfactory  results.  Fig.  49  shows  one  of  these  floors  during  the 
steel-placing  process  in  which  the  simplicity  of  the  arrangement  is  apparent.  For  data  and 
cuts  the  writer  is  indebted  to  the  Condron  Co.  of  Chicago. 


Fig.  49, 


llg.  Corr -plate  Floors. — A  type  of  flat-slab  floor  known  commercially  as  the 
Corr-plate  floor,  developed  by  the  Corrugated  Bar  Co.  of  Buffalo,  N.  Y.,  is  having  a  very  wide 
and  successful  use. 

The  general  features  of  the  slab  and  columns  as  used  with  this  system  are  similar  to  those 
used  with  other  types,  and  it  may  be  designed  either  with  or  without  drop  heads.  When 
drop  heads  are  used,  they  are  frequently  made  somewhat  shallower  than  is  the  practice  of 
other  designers.  In  other  respects  there  is  little  to  distinguish  the  system  from  others  so  far 
as  the  exterior  appearance  goes. 

It  has  been  the  practice  of  the  engineers  of  this  system  to  give  due  consideration  to  the 
reinforcement  of  the  exterior  columns  to  resist  their  share  of  the  bending,  the  necessity  of  which 
has  been  demonstrated  by  numerous  load  tests  of  actual  buildings. 

The  method  of  reinforcement  used  is  that  known  as  the  two-way  system  and  was  developed 
primarily  from  a  series  of  very  interesting  tests  performed  upon  a  small  model.  For  information 
regarding  this  the  reader  is  referred  to  Art.  19. 

The  practice  of  the  designers  of  this  system  has  been  somewhat  modified  as  the  result 
of  tests  which  have  been  made  on  actual  Corr-plate  floors  but  only  as  regards  minor  details, 
the  original  findings  having  been  demonstrated  to  be  substantially  correct. 

With  regard  to  the  design  of  exterior  columns  and  lintel  beams,  the  engineers  of  the  Cor- 
rugated Bar  Co.  feel  that  a  universal  practice  should  be  laid  down  which  should  be  followed  by 
all,  such  as  the  recommendations  of  the  American  Concrete  Institute  or  the  Special  Committee 
of  the  A.  S.  C.  E.    This  system  may  be  designed  to  meet  the  requirements  of  any  code. 

Among  its  advantages  are  the  use  of  bars  of  moderate  length  and  extending  over  one  span 
only  (Fig.  49 A).  It  is  also  common  practice  to  use  bars  of  a  larger  diameter  than  is  customary 
with  other  systems,  thus  giving  a  saving  in  unit  price  for  slab  reinforcement.    The  slab  reinforce- 


Sec.  11-17A] 


BUILDINGS 


471 


ment  extends  in  two  directions  at  right  angles  to  each  other.  A  portion  of  the  rods  in  the  center 
of  the  slab  are  bent  up  over  the  center  line  of  columns  so  that  extra  rods  are  not  needed  at  this 
point  in  the  top  of  slab. 

llh.  S-M-I  System. — This  system,  more  commonly  known  as  the  Smulski 
system,  was  invented  and  patented  by  Edward  Smulski  and  is  the  best-known  if  not  the  only 
type  of  circumferential  system.  Its  introduction  is  of  very  recent  date  but  it  has  been  quite 
extensively  used,  particularly  in  certain  portions  of  the  Eastern  States. 

The  feature  which  differentiates  this  system  from  others  that  have  been  described  is  the 
arrangement  of  the  reinforcement  for,  as  regards  the  slab,  the  proportions  are  much  the  same 
in  all  systems.  Use  is  made  of  circumferential  and  radial  reinforcement  in  both  top  and  bottom 
of  the  slab  with  only  a  small  amount  of  steel  passing  from  column  to  column.  For  the  following 
description  and  theoretical  discussion  the  writer  is  indebted  to  the  inventor  of  the  system : 


Fig.  49A. 


Description  of  the  System 

The  reinforcement  of  a  typical  interior  panel,  fully  illustrated  in  Figs.  50  and  51,  consists  of  three  types  of 

units. 

1.  Unit  C  at  the  column  head  composed  of  cings  and  radial  bars  in  the  shape  of  hair  pins,  the  upper  prong  of 
which  resists  tension  while  the  lower  prong  resists  compression  (see  Fig.  52). 

2.  Unit  A  between  columns  consisting  of  two  trussed  bars  and  rings. 

3.  Unit  B  in  central  portion  consisting  of  four  diagonal  trussed  bars  and  rings. 
Units  T  are  sometimes  used  as  shown  in  "Top  Reinforcement,"  Fig.  50. 

The  radial  bars  are  provided  with  a  semicircular  hook  of  sufficient  dimensions  to  transfer  the  stresses  into 
the  concrete  by  bond  and  bearing.  The  center  ring  which  they  sometimes  engage  keeps  them  in  place  and  forms 
an    additional  factor  of  safety. 

The  trussed  bars  of  Units  A  and  B  are  bent  up  near  the  points  of  inflection  and  carried  near  the  top  and 
parallel  to  the  surface  of  the  slab  to  the  column  head,  where  they  engage  the  center  ring.  The  bent  portion  resists 
shear  and  binds  the  column-head  section  to  the  rest  of  the  slab.  The  straight  portion  of  the  trussed  bars  in  the 
center  of  the  slab  and  at  the  column  head  resists  tension  due  to  the  positive  and  negative  bending  moments 
reBpectively. 


472 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec  ll'-VJk 


I  /  5ec+ion  thru  column  hed 
Top  reinforcement 


Fig.  50. 


>1      Plan  , 
If  required  unit  T  can    placed  over  unmA 


Section  thru  column  hea 


Typical  panel 


showing  top  and  bottom  re^Trforcem^nf 
.   Fig.  51, 


Sec.  11-17/?] 


BUILDINGS 


473 


The  trussed  bar  extends  into  the  column  head  a  sufficient  distance  beyond  the  point  of  maximum  stress 
{i.e.,  the  edge  of  the  column  head)  to  develop,  in  combination  with  the  hook,  their  full  tensile  strength.  The  ring 
which  they  engage  serves  to  distribute  the  bearing  stresses  laterally  on  to  a  large  area  of  concrete. 

Position  of  Units. — Units  A  and  B  are  placed  near  the  bottom  while  unit  C  is  near  the  top  of  the  slab. 

Compression  Reinforcement. — By  introduction  of  compression  reinforcement  in  the  shape  of  lower  prongs  of 
the  radials,  the  slab  is  stiffened  at  the  support,  and  the  compression  stresses  in  concrete  reduced.  If  desired, 
therefore,  it  is  possible  to  omit  the  drop  panel  at  the  column  head  and  use  an  altogether  flat  ceiling.  This  is  often 
desirable  either  for  the  sake  of  appearance  or  to  simplify  shafting  or  piping. 

Secondary  Reinforcement. — Sometimes  to  prevent  cracks  on  the  top  of  the  slab  between  columns,  additional 
secondary  reinforcement  consisting  of  short  gtraight  bars,  and  called  Units  T,  is  used.  These  bars  are  usually 
placed  after  the  concrete  of  the  slab  is  poured. 


Fig.  52. 


Theoretical  Discussion 

The  scientific  basis  of  the  S-M-I  system  is  evident  from  the  following  discussion  of  the  action  of  a  flat  slab 
under  load. 

Shape  of  the  Slab  after  Deflection. — After  deflection  a  flat  slab  assumes  a  composite  shape,  namely,  the  shape 
of  an  umbrella  at  the  column  head,  and  the  shape  of  a  saucer  in  the  central  portion. 

Lines  of  Equal  Deflection. — The  shape  of  a  deflected  slab  can  be  seen  better  from  Fig.  53,  which  shows  in 
sections  the  deflection  curve  along  the  side  and  the  diagonal  of  the  panel,  and  in  plan  the  lines  of  equal  deflection. 
The  lines  of  equal  deflection,  which  are  based  on  tests,  were  obtained  by  connecting  the  points  which  deflected 
an  equal  distance  below  their  original  position. 

Direction  of  Stresses  and  Reinforcement. — By  referring  to  the  plan  and  the  sections,  it  is  evident  that  deforma- 
tion of  fibers  are  equal  and  therefore  the  fiber  stresses  act  perpendicularly  to  the  lines  of  equal  deflection  as  indicated 
by  arrows  in  Fig.  53.  The  best  method  of  resisting  these  stresses,  or  preventing  the  deformation,  is  either  by 
placing  the  bars  perpendicularly  to  the  lines  of  equal  deflection,  or  by  enclosing  them  by  means  of  a  ring,  the  hooping 
action  of  which  is  explained  later.  Fig.  54  shows  the  deflection  lines  in  light  dash  lines  and  the  reinforcement 
according  to  the  S-M-I  system  in  heavy  lines.  The  radials  and  trussed  bars  are  perpendicular  to  the  lines  of  equal 
deflection.  The  rings  either  intersect  the  deflection  lines  at  angles  close  to  90  deg.,  or  they  enclose  the  same  and  pre- 
vent the  enclosed  concrete  from  spreading.  The  combination  therefore  fulfills  all  the  requirements  of  efficient 
and  economical  reinforcement. 


474 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-1 7/i 


Continuous  Construction  Separated  into  Simple  Parts. — In  continuous  beams  and  slabs  the  bending  moment 
at  the  points  of  inflection  is  zero.    Therefore,  it  is  possible  to  separate  the  structure  at  these  points  without  chang- 


4  s/.-  'Cb^un^n  Mad 


Line  of  I 
irrfivcfion  h— —  ^ 


.V-Li-bL.ti 

I  I  1  I  J  i^r-\  ■Infermedlaf^  lines 


Arrows  in  sections  and  p/an 
indicafff  direction  of  fensile  stress 


Fig.  53. 

ing  the  stresses  in  the  remainder  of  the  structure.  This  may  be  accomplished  by  insertion  of  a  hinge  or  other 
connection  capable  of  transferring  shear.    The  same  is  possible  in  flat-slab  construction. 

Separating  Flat  Slab  into  Simple  Parts. — As  ex- 
plained above,  a  flat  slab  may  be  separated  into 
simple  parts,  namely:  Circular  cantilevers  at  the 
column  head;  slabs  between  columns;  and  slabs  sup- 
ported at  four  points  subjected  to  stresses  in  all  direc- 
tions. 

In  designing  the  reinforcement  it  is  permissible 
to  treat  the  separate  parts  independently  and  to 
provide  in  each  of  them  a  sufficient  amount  of  steel 
to  resist  the  particular  bending  moments  to  which 
they  may  be  subjected. 

The  unit  shear  at  the  points  of  inflection"  is 
always  low,  not  exceeding  40  lb.  per  sq.  in.,  so  that 
concrete  is  capable  of  taking  care  of  the  shearing 
stresses.  Since  it  is  not  advisable  to  rely  on  con- 
crete alone,  the  parts  of  the  slab  subjected  to  posi- 
tive bending  moment  and  reinforced  by  Units  A  and 
B  are  tied  securely  to  the  circular  cantilever  at  the 
column  head  by  the  bent  portions  of  the  trussed  bars 
and  by  overlapping  of  Units  A  and  C. 

The  position  of  the  points  of  inflection  is  vari- 
able for  different  positions  of  the  live  load.  To 
provide  for  this  and  also  to  prevent  secondary  cracks, 
due  to  temperature  and  shrinkage,  the  reinforcement 
in  the  various  units  overlaps,  thereby  tying  the  slab 
together  and  enabling  it  to  act  as  a  whole  if  such  ac- 
tion is  required  by  any  contingencies. 

Column-head  Section. — At  the  column  head  the 
portion  of  the  slab  within  the  points  of  inflection  acts 
like  a  circular  cantilever  loaded  uniformly  over  its  area,  and  also  along  its  circumference  by  the  loads  transferred 
to  it  from  the  rest  of  the  slab.    This  portion  is  subject  to  negative  bending  moments:  i.e.,  the  particles  in  the 
upper  part  of  the  slab  elongate  while  the  particles  in  the  lower  part  compress. 


For  explanai-ion  of  action  of  rings  see  text 
Heavy  lines  shov/  reinforcement 
Light  dashed  lines  show  curves  of  equal  deflection, 
fr^inlbrcement  at  column  head  is  near  loo  of  slab. 

Fig.  54. 


Sec.  11-1 7/i] 


BUILDINGS 


475 


Section  "A-A" 
Fig.  55. 


The  negative  bending  moment  at  the  column  head  is  larger  than  the  positive  bending  moment  in  the  center 
of  the  slab.    The  amount  of  steel  required  there  is  consequently  larger  than  in  any  other  part  of  the  slab. 

The  most  unfavorable  condition  of  loading  for  the  column-head  section  is  when  all  the  spans  surrounding  the 
column  are  loaded.  In  such  case  the  shape  of  the  cantilever  will  be  as  shown  in  Fig.  55.  Since  after  deflection  any 
circle  increases  its  radius  as  well  as  its  circumference,  the  par- 
ticles must  elongate  in  radial  as  well  as  in  circumferential  di- 
rection and  are  therefore  subjected  to  radial  and  circumferen- 
tial stresses.  The  most  effective  tensile  reinforcement  is  by 
means  of  rings  and  radial  bars. 

Compressive  stresses  act  also  in  radial  and  circumferen- 
tial direction.  The  compression  acting  radially  composes 
the  bulk  of  compressive  stresses  and  may  be  resisted  by  the 
compressive  prongs  of  radial  bars  in  combination  with  con- 
crete. The  efficiency  of  steel  in  resisting  compression  is  well 
established  by  tests  of  Prof.  Withey  in  America  and  Prof. 
Bach  in  Germany.  These  tests  are  described  in  Taylor  and 
Thompson's  "Concrete,  Plain  and  Reinforced,  3d  Edition. 

Slabs  Between  Columns. — The  principal  stresses  in  this 
part  act  mainly  in  one  direction  which  at  first  is  parallel  to  the 
edge  of  the  panel  and  then  gradually  becomes  inclined,  as  is 
evident  from  Figs.  53  and  54.  In  addition  secondary  stresses 
due  to  cross-bending  and  also  due  to  shrinkage  and  tem- 
perature changes  act  across  the  principal  stresses. 

The  advantages  of  using  rings  in  this  part  to  resist  the 
various  stresses  are  as  follows:  (1)  They  intersect  the  lines  of 
equal  deflection  more  nearly  at  right  angles  than  straight  bars 
(see  Fig.  54) ;  (2)  they  bind  the  Units  A  and  B,  thereby  pre- 
venting secondary  cracks;  (3)  the  rings  in  the  two  units  sup- 
plement each  other;  and  (4)  the  arrangement  is  economical 
as  the  rings  cover  the  whole  surface  without  waste  of  material. 

Central  Part  of  Slab. — The  central  portion  acts  like  a 
slab  supported  at  four  corners  and  loaded  with  uniform  load. 

The  bending  moment  is  positive  so  that  the  top  is  in  compression  and  the  bottom  in  tension.  As  evident  from 
Fig.  53,  the  stresses  act  in  all  directions;  the  reinforcement  consisting  of  rings,  therefore,  is  fully  effective. 

Action  of  Rings. — The  following  discussion  demonstrates  that  rings  resist  effectively  stresses  acting  within  the 
ring  in  any  direction. 

In  considering  the  action  of  rings  it  must  be  remembered  that  they  are  filled  with  solid  concrete  which  governs 

their   shape.    The  deformation  and 

,fbinf3  £'^-^^^2__^^j^!!;^e^'nf/ecf/on        ^   ^  stresses  in  the  rings  are  caused  by  the 

'  "   "     *■       ^~  '         pressure  of  the  concrete  on  their  cir- 

cumference so  that  the  rings  assume 
the  shape  of  the  solid  concrete  which 
they  enclose. 

Fig.  56  shows  parts  of  the  slab 
at  the  column  and  also  in  the  center 
of  the  slab,  subjected  to  stresses  in  all 
directions.  AA  is  a  section  in  any 
direction. 

Under  load  the  slab  compresses 
near  one  surface  and  expands  near 
the  other  surface  so  that  0-3  shortens 
by  3-3',  while  0-4  expands  by  4-4'. 
The  same  is  true  of  a  section  in  any 
direction;  therefore  the  circle  4-4  tends 
to  assume  the  shape  of  4'-4'.  Before 
assuming  the  new  position  the  con- 
crete must  stretch  the  ring  by  which 
it  is  enclosed;  i.e.,  increase  its  radius 
and  therefore  its  circumference.  The 
concrete  exerts  a  pressure  along  the 
circumference  of  the  ring  similar  to 
Since  the  modulus  of  elasticity  of  the  steel  is  different  from  that  of  the 

It  stretches,  how- 


Section  "A-A" 
R/ngs  in  unit  C 


^       ,      ^      ^  Section  '>\-A" 

4- 4  =  elongation  of  distance  0-4 
Z- 2'-  elongation  cf  distance  0-Z 


lis  4-4^pli^5  elongation  of 


distance  2-4) 


Rings  in  unit  B 


Fig.  56. 


the  pressure  of  water  in  a  reservoir. 

enclosed  concrete,  the  steel  ring  by  its  tensile  resistance  prevents  partially  the  movement, 
ever,  to  some  extent,  causing  tensile  stresses  in  the  steel. 

Considering  the  second  ring,  it  is  evident  that  the  movement  of  point  2  consists  not  only  of  the  elongation 


476 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-172 


of  the  distance  0-4  but  also  of  the  elongation  of  the  distance  2-4.  The  outside  ring  therefore  shares  the  stresses 
with  the  ring  inside.  Any  deformation  of  the  concrete  irrespective  of  its  direction  is  talcen  up  at  once  by  all  the 
rings  placed  outside  of  the  place  of  deformation.  All  rings  are  therefore  effective  in  resisting  stresses  (see  also  Art. 
19). 

Forces  Acting  in  All  Directions. — Where  the  forces  act  in  all  directions  as  in  the  center  of  the  slab  and  at  the 
column  head,  the  ring  stretches  uniformly  along  its  circumference.  After  deformation  the  shape  of  the  ring  remains 
substantially  circular  and  the  stresses  are  uniform  along  its  circumference. 

Forces  Acting  Principally  in  One  Direction. — If  the  forces  act  principally  in  one  direction,  as  in  unit  A,  the 
condition  is  similar  to  that  of  a  solid  disc  of  concrete  with  a  tight-fitting  steel  ring  around  it,  subject  to  a  force  in 
one  direction.  Under  the  pressure  of  the  enclosed  concrete  the  shape  of  the  ring  changes  gradually  into  an  oblong 
curve  with  the  concrete  following  and  still  pressing  tightly  on  the  ring.  In  this  case  the  stresses  in  the  ring  are  a 
maximum  at  the  sections  cut  by  a  diameter  perpendicular  to  the  direction  of  the  stress,  and  decrease  to  zero  at 
points  90  deg.  from  the  point  of  maximum  stress. 

From  the  above  it  is  evident  that  the  stresses  due  to  the  principal  bending  moment  are  small  in  the  parts  of 
rings  of  Unit  A  which  are  near  the  column  head,  so  that  they  can  resist  stresses  in  the  diagonal  direction  in  places 
where  they  run  almost  parallel  to  the  diagonal  trussed  bars. 


Fig.  57. 


The  advantages  claimed  for  this  system  by  its  sponsors  are:  (1)  An  economy  of  steel 
over  other  systems;  (2)  freedom  from  obstruction  over  the  column  head,  an  advantage  when 
structural-steel  column  cores  are  used;  and  (3)  ease  of  pouring  column  head  and  slab  due  to 
the  large  diameter  and  comparatively  small  number  of  rods  used. 

The  bending  of  the  circular  slab  rods  may  be  done  in  a  shop  and  the  large  rings  shipped  in 
two  parts  with  a  liberal  lap  provided,  or  it  may  be  bent  on  the  job  with  a  form  of  tire  bender. 

This  system  has  been  used  in  the  construction  of  about  70  buildings  to  date,  all  of  which 
have  given  satisfactory  service. 

m.  Three-way  System. — The  three-way  system  was  invented  and  patented 
(Patent  No.  1,064,850)  by  David  W.  Morrow,  Civil  and  Architectural  Engineer  of  Cleveland, 
Ohio,  and  has  been  successfully  used  in  buildings  for  the  Cleveland  Railway  Co.  of  Cleveland. 

The  principal  novelty  of  this  design  lies  in  the  arrangement  of  interior  columns  which  are 
located  at  the  apices  of  equilateral  triangles.  Under  this  arrangement  the  bands  of  steel 
reinforcement  are  all  of  equal  span.  Fig.  57  is  a  plan  of  a  building  laid  out  on  this  system, 
and  Fig.  58  shows  the  detail  at  the  column  head  for  the  same  design. 


Sec  ll-17i] 


BUILDINGS 


477 


avoided 
60  deg., 
carriers 

possible 


The  advantages  claimed  for  this  system  are  as  follows:  Right-angle  turns  are 
and  in  passing  from  one  aisle  to  another  it  is  only  necessary  to  turn  through  an  angle  of 
thus  making  it  easy  for  the  running  of  vehicles  or  the  free  movement  of  overhead 
handling  long  material. 

The  reinforcing  steel  over  the  column  head  is  placed  in  three  layers,  thus  giving  it  a 
slight  advantage  over  the  four-way  system  in  effective 
depth  at  this  point. 

The  interior  column  spacing  being  equal,  the  spans 
and  consequently  the  amount  of  steel  and  length  of  rods 
in  the  bands  will  be  equal. 

It  is  claimed  that  the  three-way  system  is  par- 
ticularly adapted  to  garages  on  account  of  the  ease 
with  which  a  car  may  be  turned  into  one  of  the  aisles 
between  columns,  the  plan  being,  of  course,  to  park  the 
cars  in  the  diagonal  aisles. 

The  following  data  with  regard  to  one  of  the  build- 
ings designed,  according  to  this  system,  has  been  fur- 
nished by  Mr.  Morrow  and  may  be  useful  to  those  who 
may  wish  to  compare  this  type  with  others. 

The  floor,  in  what  is  known  as  the  storeroom,  is  184 
ft.  long  and  120  ft.  wide,  the  columns  being  spaced  23 
ft.  c.  to  c,  giving  20  ft.  wide  longitudinal  and  diagonal 
aisles.    It  was  designed  for  a  live  load  of  350  lb. 

The  floor  slab  is  WH  in.  thick  reinforced  with  twenty-one 
H-in.  round  rods  per  band,  spaced  6  in.  c.  to  c,  all  rods  lapping 
over  the  column  head  and  extending  5  ft.  6  in.  beyond  the  center  of 
columns,  the  rods  being  approximately  34  ft.  long. 

The  floor  slab  is  supported  on  20-in.  spirally  reinforced 
columns  with  a  flaring  cap  5  ft.  in  diameter,  and  a  hexagonal  drop 
panel  4^^  in.  thick  and  8  ft.  across.    The  outside  edge  of  the  slab 

rests  on  a  17-in.  brick  wall  with  pilasters  at  column  points  and  is  bounded  with  a  depressed  slab  in.  thick  and 
4  ft.  wide. 


Buildings  designed  by  Mr.  Morrow  have  been  designed  in  accordance  with  the  Cleveland 
Building  Code  and,  of  course,  none  of  the  building  codes  really  cover  this  system. 

The  Cleveland  law  requires  that  flat-slab  construction  shall  be  figured  with  a  bending 

moment  in   any  quadrant  over  the  column 


head  of  not  less  than 


27 


in  foot-pounds,  in 


Fig.  59. 


which  W  equals  total  weight  per  square  foot, 
dead  and  live  load,  and  L  equals  length  in  feet 
of  a  side  of  an  equivalent  square  in  rectangular 
panels,  and  the  side  of  a  square  in  square 
panels.  The  length  L  shall  be  taken  center 
to  center  of  columns.  For  the  three-way 
system,  L  is  taken  as  the  side  of  a  square  which 


has  the  same  area  as  a  parallelogram  panel  (see  Figs.  59a  and  596). 

The  bending  moment  of  the  Cleveland  Code  in  the  quadrant  over  the  head  is  -^^y  .  There 

fore  the  bending  moment  in  the  sextant  =       X  substituting  the  value  of  L  in  terms 

WP 

of  I,  we  have  for  the  bending  moment  in  the  sextant,  M  =        at  the  column  cap.    The  bending 


moment  at  the  center  of  span  is  taken  to  be  one-half  of  the  above,  or  ikf  =  • 


478 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-1 7i 


42 


entire 


Mr.  Morrow  has  also  figured  this  system  on  what  might  be  called  a  cantilever  and  sus- 
pended-span method.  In  this  he  assumes  the  line  of  inflection  to  be  out  three-tenths  of  the  span 
from  the  center  of  column  and  that  the  minimum  size  of  the  column  cap  is  two-tenths  of  the 
span. 

The  bending  moment  on  a  sextant  at  the  edge  of  the  head  by  this  method  is  M  = 
which  is  more  conservative  than  the  Cleveland  Code. 

By  the  Pittsburgh  Ruling  we  would  have  M  =         for  the  center  of  span  for 

periphery  which  would  be  equal  to  -g^-  for  a  single  band  at  the  center  of  span.    The  method 

of  computing  the  steel  required  over  the  column  head  by  the  Pittsburgh  Ruling  depends  upon 
the  size  of  column  cap,  but  since  the  steel  in  the  center  of  span  is  usually  the  determining 
element,  it  is  evident  that  this  ruling  checks  the  Cleveland  Code  quite  closely  in  this  case. 

In  all  the  buildings  so  far  constructed  under  this  system,  a  depressed  head  has  been  used 
to  assist  in  taking  care  of  the  bending  stress  and  shear  in  the  concrete  at  the  edge  of  the  column 

cap.    It  has  been  the  practice  to  lap  all  rods 

^  ,^3./  over  the  columns,  extending  them  three-tenths 

of  the  span  beyond  the  center. 

A  computation  made  by  Mr.  Morrow 
would  tend  to  show  that  the  bending  moment 
in  the  three-way  system  is  less  than  that  in  a 
four-way  system  and  that  the  diagonal  bands 
are  less  efficient  than  the  direct  bands  in  the 
four-way,  while  the  equal  spans -and  equal  loads 
of  the  three-way  system  are  probably  more  effi- 
cient.   The  demonstration  of  this  is  as  follows. 


 /  • 

....> 

/ 

I!— 

/ 

(o) 


Comparing  two  panels  of  equal  area  [see  Fig.  60(a)  and  (6)]  the  one  (a)  a  square  panel  supported  by  the 
ordinary  arrangement  of  columns,  and  the  other  (6)  a  parallelogram  panel  such  as  is  found  in  the  three-way  system. 
Let  (a)  represent  a  panel  having  four-way  reinforcing.  Then  the  loads  in  the  panel  are  carried  to  the  columns 
by  four  half  bands  on  the  sides  and  two  full  bands  on  the  diagonals,  making  four  full  bands  per  panel. 

Let  (6)  represent  a  parallelogram  panel  having  three-way  reinforcing.  In  this  case  the  loads  are  carried  by 
four  half  bands  around  the  edge,  and  one  full  diagonal  band,  making  three  full  bands  per  panel.  The  average  span 
of  the  bands  in  the  square  panel  is 


The  span  of  the  bands  in  the  parallelogr  am  are  all  of  the  same  length  being  1.075Z/. 

Assuming  that  the  bending  moment  varies  as  the  span,  we  can  make  a  comparison  of  the  bending  moments 
in  the  two  panels  by  comparing  their  average  span: 
1.207L  =  average  span  in  square  panel. 
1.075L  =  average  span  in  parallelogram  panel. 

0.132L 
1.075L 


=  0.12.3  =  12.3% 


Therefore,  if  the  above  assumptions  are  correct,  the  bending  moment  in  a  square  panel  is  12.3%  more  than 
the  bending  moment  in  a  hexagonal  panel  carrying  the  same  load. 

The  question  naturally  arises  as  to  whether  or  not  one-half  of  the  load  of  the  panel  goes 
to  the  diagonals. 

If  we  lay  out  a  square  panel  so  that  the  sides  of  the  diagonal  bands  intersect  on  the  sides 
of  the  square  bands,  all  bands  being  equal  to  0.414L  in  width,  and  figure  the  area  in  the  panel 
falling  in  common  over  side  and  diagonal  bands,  we  will  find  them  to  be  as  follows : 

Area  in  panel  falling  in  common  over  side  and  diagonal  bands,  48.5%. 

Area  in  panel  falling  over  side  bands,  17.2%. 

Area  in  panel  falling  only  over  diagonal  bands,  34.3%. 

This  would  apparently  tend  to  show  that  a  large  portion  of  the  load  falls  on  the  diagonals 


Sec.  11-18] 


BUILDINGS 


479 


and  that  they,  due  to  their  long  span,  are  not  able  to  carry  it  and  that  it  is  transferred  to  the 
side  bands  producing  an  inverse  moment  over  their  center.  As  is  well  known,  cracks  usually 
appear  at  these  points  in  loading  tests  of  flat-slab  floors  which  are  not  reinforced  to  resist  this 
moment. 

18.  Patents. — O.  W.  Norcross,  on  Nov.  22,  1901,  applied  for  a  patent  on  a  "new  and  useful 
flooring  for  buildings."  On  April  29,  1902,  he  was  granted  Patent  No.  698,542  covering  the 
following  claims: 

1.  The  combination  of  separate  posts  or  supports,  and  a  flooring  consisting  of  a  metallic  network  formed 
by  strips  of  wire  netting  enclosed  therein,  so  as  to  radiate  from  the  posts  or  supports  on  which  the  floor  rests. 

2.  A  flooring  resting  on  separate  supports  and  consisting  of  concrete  with  metallic  network  so  arranged  therein 
that  the  amount  of  metal  will  be  greatest  at  the  points  where  the  greatest  tensile  and  shearing  strains  are  to  be 
supported. 

3.  A  flooring  resting  on  separate  posts,  and  consisting  of  metallic  network  formed  by  strips  of  wire  netting 
laid  from  post  to  post,  to  cross  each  other  in  cob-house  fashion,  and  concrete  enclosing  the  metallic  network. 

4.  A  flooring  resting  on  separate  posts,  and  consisting  of  metallic  network  formed  by  strips  of  wire  netting 
laid  from  post  to  post,  and  in  the  diagonals  of  the  figures  outlined  by  the  posts,  and  concrete  enclosing  the  metallic 
network. 

5.  A  flooring  resting  on  separate  supports,  consisting  of  concrete  having  a  metallic  network  enclosed  in  the 
bottom  layer  thereof,  with  the  body  portion  of  said  concrete  of  lighter  material  than  the  bottom  layer  thereof. 

On  the  same  date,  April  29,  1902,  Patent  No.  698,543  was  also  granted  to  Mr.  Norcross, 
covering  flooring  for  buildings,  the  claims  of  which  are  similar  to  No.  698,542  except  that 
instead  of  columns,  walls  or  other  longitudinal  supports  are  specified. 

Norcross  Patent  No.  698,542  was  sustained  by  the  United  States  Circuit  Court  of  Appeals 
for  the  Eighth  Judicial  District  on  Dec.  10,  1914,  in  the  case  of  John  L.  Drum  vs.  C.  A.  P.  Turner. 
Upon  petition  of  defendant,  that  Court  decided  not  to  reopen  the  case  or  to  permit  the  intro- 

I  duction  of  additiohal  evidence  offered  by  the  defendant.    On  June  1,  1915,  the  Supreme  Court 

I  of  the  United  States  refused  to  set  aside  the  decision  of  the  lower  court  or  grant  the  defendant 
any  relief  whatever.  On  June  9,  1915,  the  United  States  District  Court  for  the  District  of 
Minnesota,  entered  a  decree  against  the  defendant,  C.  A.  P.  Turner,  for  infringement  of  the 
Norcross  patent  and  an  injunction  against  further  infringement. 

On  Aug.  3,  1915,  the  United  States  District  Court  for  the  District  of  Minnesota,  held 
that  Mr.  Turner's  ''Spiral  Mushroom  System"  was  an  infringement  of  the  said  Norcross 
patent,  and  imposed  a  fine  for  the  violation  of  the  injunction.  On  Jan.  21,  1916,  the  Circuit- 
Court  of  Appeals  for  the  Eighth  Circuit  unanimously  refused  to  reconsider  the  decision  of  the 

it  District  Court  on  the  question  of  infringement,  and  denied  Mr.  Turner's  petition  for  a  writ 

I  of  certiorari. 

On  Oct.  4,  1916,  the  United  States  District  Court  for  the  District  of  Minnesota  in  the  case 
of  C.  A.  P.  Turner,  plaintiff,  and  Deere  Webber  Building  Co.  and  Deere  Webber  Co.,  defendants, 
decided  "that  the  defendants'  structure  does  not  infringe  any  of  claims  1,  2,  4,  6  or  8"  of  C.  A.  P. 
Turner  Patent  No.  985,119,  and  "that  said  claims  and  each  of  them  are  void  for  lack  of  inven- 
I  tion  in  view  of  the  prior  art,  as  held  in  the  case  of  Turner  vs.  Moore  supra." 

In  the  United  States  District  Court  in  the  District  of  New  Jersey  in  the  case  of  C.  A.  P. 
Turner,  plaintiff,  vs.  Lauter  Piano  Co.  and  American  Concrete  Steel  Co.,  defendants,  the  Court 
held  that  the  claims  of  Patents,  Nos.  985,119  and  1,003,384,  granted  to  the  plaintiff  and  which 
were  relied  upon  by  him  in  this  suit  are  invalid. 

As  the  matter  now  stands,  therefore,  Mr.  Turner  is  under  injunction  both  as  to  his  original 
construction  and  his  so-called  "Spiral  Mushroom  System." 

The  leading  flat-slab  promoters  in  the  United  States  are  now  licensed  under  the  Norcross 
patent.    This  is  true  of  two-way,  three-way  and  four-way  flat-slab  advocates  alike. 

Besides  the  Norcross  patent  which  has  been  declared  basic,  there  are  several  other  patents 
which  have  been  granted  covering  special  methods  of  construction  and  reinforcement.  Some 
I  of  these  have  been  tested  in  the  courts.  It  is  evident,  therefore,  that  the  field  for  the  designer 
of  flat  slabs  is  not  a  free  one  and,  unless  he  can  invent  a  method  of  reinforcement  that  is  entirely 


I 


480 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-19 


new  and  an  advance  in  the  art,  he  must  be  licensed  under  one  of  the  ''Systems"  so-called.  The 
possibilities  are  so  well  covered  that  it  is  difficult  to  see  how  a  really  new  system  can  be  devised. 
Rather  should  we  seek  to  advance  by  improving  our  materials  or  methods  of  construction, 
or  both. 

19.  Loading  Tests. — Since  the  first  introduction  of  the  flat-slab  type  of  construction 
there  have  been  erected  in  the  United  States  many  hundreds  of  buildings  of  this  kind.  The 
majority  have  been  subjected  to  test  loads  over  one  or  more  floor  panels  of  at  least  1^  times  j 
the  designed  live  load,  and  have  passed  the  test  without  cracking  or  serious  deflection., 
There  have  been  a  few  cases  of  flat-slab  floors  which  have  given  trouble  just  as  there  have  been' 
cases  of  poor  design  with  other  systems,  but  it  is  undoubtedly  true  that  the  flat-slab  type  will ! 
stand  more  abuse  in  this  respect  than  any  other  form  of  reinforced-concrete  construction. 
The  continuous  bands  of  small  steel  rods  running  in  two  or  more  directions  and  all  passing  over 
the  column  heads  form  a  network  of  remarkable  strength.  When  a  structure  of  this  type  is 
loaded  to  destruction  it  shows  a  very  slow  yielding,  and  it  is  safe  to  say  that  a  properly  designed 
flat  slab  with  continuous  bands  of  steel  passing  over  the  column  heads  cannot  show  a  sudden 
collapse  either  under  test  or  in  actual  service. 

Besides  the  loading  tests  before  referred  to,  which  have  been  made  to  satisfy  architects 
and  building  superintendents,  in  which  at  most  the  deflection  of  the  floor  slab  only  was  measured, 
there  have  been  numerous  extensometer  tests  (so-called)  made  of  complete  buildings  under  a 
variety  of  conditions  of  loading. 

In  these  tests  a  portion  of  the  floor  slab  in  a  completed  building  has  been  subjected  to 
load  very  much  as  a  beam  is  tested  in  a  testing  laboratory,  and  the  actual  deformations  of 
exposed  portions  of  the  reinforcing  steel  at  various  points  in  the  slab  have  been  measured. 
Also,  measurements  have  been  made  of  the  deformations  of  the  concrete  of  the  slab.  Measure- 
ments of  the  deformations  of  the  steel  and  concrete  in  both  the  exterior  and  interior  columns 
have  also  been  made  in  many  of  the  recent  tests. 

Much  of  this  information  has  been  held  as  confidential  by  various  designers,  but  the  results 
of  many  such  tests  have  been  published  and  are  thus  available  for  the  use  of  all.  Tests  of 
this  kind  giving  as  they  do  actual  distortion  in  the  individual  steel  rods  and  in  the  concrete 
itself,  give  a  very  accurate  indication  of  the  stresses  in  the  structures  at  the  time  of  making  the 
test  due  to  the  applied  load.  Of  course,  there  are  initial  stresses  due  to  dead  load  and  tempera- 
ture which  can  be  computed  with  more  or  less  accuracy  and  stresses  due  to  the  shrinkage  of 
concrete,  which  are  more  uncertain,  which  must  be  allowed  for  in  addition  to  the  live-load  stress. 

The  performing  of  tests  of  this  kind  entailed  a  great  amount  of  physical  labor  in  their 
actual  execution.  A  high  order  of  ability  was  shown  in  planning  and  organizing  the  operation, 
and  an  equally  high  degree  of  skill  was  required  to  secure  satisfactory  results  in  the  use  of 
laboratory  instruments  under  such  trying  conditions.  The  cost  of  these  tests  was  great,  but 
the  value  of  the  results  obtained  and  the  advance  given  to  the  art  of  design  has  justified  the 
cost  in  money  and  in  personal  sacrifice. 

A  list  of  the  more  important  tests  relating  to  flat-slab  floors  is  given  below : 

Experiments  on  Models. — An  interesting  series  of  experiments  upon  laboratory  models 
was  performed  by  the  research  department  of  the  Corrugated  Bar  Co.  to  obtain  a  scientific 
basis  for  the  design  of  flat-slab  floors.    A  rubber  plate  0.5  in.  thick  was  stretched  over  a  box 
which  had  cylindrical  plugs  projecting  from  the  bottom  to  just  touch  the  rubber  sheet,  so  spaced 
that  they  would,  acting  as  miniature  columns,  divide  the  slab  up  into  nine  equal  panels.    Half  | 
rounds  were  used  at  the  sides  to  act  as  wall  columns.    Load  was  applied  by  exhausting  air  I 
from  the  box  so  that  the  rubber  sheet  deflected  just  as  a  flat  slab  is  supposed  to  do  and  this  load  I 
was  maintained  very  exactly  by  means  of  a  water  jet  aspirator  and  U-tube  manometer.    Deflec-  ' 
tion  readings  were  taken  at  points  0.1  of  the  span  apart. 

Test  of  Flat-slab  Floor  of  the  Deere  &  Webber  Co.'s  Building,  Minneapolis,  Published  December, 
1910. — The  type  of  floor  is  four-way  and  is  typical  of  the  standard  practice  of  the  Concrete 
Steel  Products  Co.  at  that  time.    Deformation  measurements  were  made  on  concrete  and  steel 


Sec.  11-19] 


BUILDINGS 


481 


in  the  slab  only.  Tests  are  described  by  Arthur  R.  Lord  in  papers  entitled  "A  Test  of  a  Flat- 
slab  Floor  in  a  Reinforced  Concrete  Building"  and  "A  Discussion  of  the  Basis  of  Design  of 
Reinforced-Concrete  Flat  Slabs,"  presented  before  the  Annual  Convention  of  the  National 
Association  of  Cement  Users  (Am.  Cone.  Inst.).  These  articles  appeared  in  Engineering 
News,  Dec.  22  and  29,  1910  and  Jan.  12,  1911. 

Test  of  Franks  Building,  Chicago. — Floors  were  constructed  according  to  the  Cantilever 
Flat-slab  system  by  the  Leonard  Co.  of  Chicago.  The  panel  size  was  19  ft.  4  in.  by  20  ft.  3  in. 
Four  interior  panels  located  on  the  tenth  (top)  floor  were  tested.  The  slab  thickness  was  9)^ 
in.,  and  133^  in.  at  the  drop  panels. 

Test  of  Powers  Building,  Minneapolis. — Described  in  a  paper  by  F.  J.  Trelease  read  before 
the  American  Concrete  Institute  in  March,  1912  (vol.  viii,  Proceedings). 

Test  of  Larkin  Warehouse. — Test  of  a  four-way  slab  described  in  a  paper  presented  by 
Arthur  R.  Lord  before  the  American  Concr&te  Institute  in  December,  1912.  Test  was  also 
published  in  the  Engineering  Record,  January,  1913  and  in  the  Cement  Era,  January,  1913. 

Test  of  Soo  Line  Terminal,  Chicago, '^Te&i  of  single-story  structure  which  carries  railroad 
tracks  on  the  upper  deck.  For  complete  description  of  this  building  see  Engineering  Record, 
Aug.  16,  1913,  Engineering  News,  Aug.  21,  1913,  and  Railway  Age  Gazette,  Aug.  22,  1913.  For 
description  of  test  see  article  in  Bulletin  84  of  the  Engineering  Experiment  Station  of  the 
University  of  Illinois. 

Test  of  Schulze  Baking  Co.'s  Building,  Chicago. — Floor  slab  is  of  the  four-way  type  with 
short  transverse  bars  in  top  of  slab  on  the  center  line  of  columns.  Test  is  described  in  Bulletin 
84  of  the  Engineering  Experiment  Station  of  the  University  of  Illinois. 

Tests  of  S-M-I  Flat  Slabs. — Test  made  under  the  supervision  of  Sanford  E.  Thompson 
of  a  slab  20  ft.  square  supported  upon  columns  spaced  12  ft.  on  centers  so  that  the  slab  projected 
4  ft.  on  all  sides  in  order  that  a  condition  of  continuity  over  the  columns  would  exist. 

Test  of  Shredded  Wheat  Factory  Niagara  Falls,  N.  Y. — Type  of  floor  is  two-way,  designed 
by  the  Corrugated  Bar  Co.  and  known  commercially  as  Corr-plate  Floor.  Test  is  described 
in  Bulletin  84  of  the  Engineering  Experiment  Station  of  the  University  of  Illinois.  It  is  also 
reported  in  the  Journal  of  the  American  Concrete  Institute,  vol.  ii,  No.  6,  1914,  in  an  article  by 
W.  A.  Slater. 

Tests  of  Circumferential  Cantilevers. — Tests  were  made  upon  octagonal  slabs  each  carried 
upon  an  8-in.  square  column  having  an  octagonal  flare  head  2  ft.  in  diameter.  For  description 
of  tests  see  Engineering  Record,  vol.  73,  page  249. 

Worcester  Slab  Test. — The  structure  upon  which  this  test  was  performed  was  constructed 
especially  for  that  purpose  at  Worcester,  Mass.  The  objects  were  to  determine  the  effect 
of  different  steel  arrangements  and  the  effect  of  variation  in  size  of  the  column  capital.  A  com- 
plete description  of  this  test  will  be  found  in  Bulletin  84  of  the  Engineering  Experiment  Station 
of  the  University  of  Illinois. 

Test  of  Schwinn  Building,  Chicago. — The  floors  are  of  the  four-way  type  and  were  designed 
before  the  present  Chicago  ruling  was  adopted.  Description  of  this  test  is  given  in  an  article 
by  Arthur  R.  Lord  in  vol.  xiii  of  the  Proceedings  of  the  American  Concrete  Institute,  1917. 

Test  of  Curtis-Ledger  Factory,  Chicago. — Floor  tested  was  designed  according  to  the  Barton 
Spider  Web  system.  Summary  of  this  test  is  given  in  Bulletin  84  of  the  Engineering  Experiment 
Station  of  the  University  of  Illinois. 

Test  of  Sears-Roebuck  Building,  Seattle. — Floor  was  designed  according  to  the  Akme  Two- 
way  system.  Test  was  performed  under  the  supervision  of  the  Building  Department  of  the 
City  of  Seattle  and  is  reported  in  the  Proceedings  of  the  Pacific  North  west  Society  of  Civil 
Engineers,  vol.  xv  for  January  and  February,  1916,  in  a  paper  presented  by  D.  E.  Hooker. 

Test  of  Bell  Street  Warehouse,  Seattle. — The  type  of  floor  used  in  this  structure  is  a  four-way 
system  designed  according  to  the  Mushroom  system  by  C.  A.  P.  Turner.  The  first  test  made 
on  this  building  is  described  in  an  article  by  D.  E.  Hooker  in  Engineering  Record,  vol.  73,  page 
647. 

31 


482 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-19 


Since  the  slab  tested  was  cast  in  freezing  weather  and  the  temperature  near  the  freezing 
point  for  several  days,  it  was  claimed  by  the  designers  that  the  concrete  was  not  thoroughly 
cured  at  the  time  of  making  the  test  and  that,  therefore,  conclusions  drawn  from  the  test  were 
unwarranted.  In  order  to  satisfy  all  concerned  a  second  test  was  made  upon  four  panels 
of  the  same  floor  slab  previously  tested.  Description  of  the  second  test  is  given  in  Engineering 
News— Record,  April  19,  1917. 

Test  of  Building  of  Pierce  Arroiv  Motor  Car  Co.,  Buffalo,  N.  Y. — Floor  is  a  four-way  system 
designed  according  to  the  Chicago  Code. 

■  Test  of  S-M-I  Flat  Slab  at  Purdue  University,  April  19,  1917. — Test  was  performed  upon 
a  structure  erected  for  the  purpose  and  did  not  form  a  part  of  a  building  built  for  commercial 
use.    Test  was  reported  by  Prof.  F.  K.  Hatt  of  Purdue  University  to  Edward  Smulski. 

Discussion  of  Tests. — To  those  who  are  familiar  with  the  accurate  results  which  are  to  be 
obtained  in  laboratory  testing,  the  results  secured  in  field  tests  of  buildings  are  apt  to  be  a 
disappointment. 

Many  factors  enter  into  these  tests  which  cannot  be  entirely  controlled  and  inconsistencies 
develop  in  the  measured  results  which  cannot  always  be  explained.  In  the  first  place  the 
structure  is  composed  of  two  materials  of  radically  differing  properties.  The  steel  possesses 
definite  qualities,  properties,  and  areas  which  can  be  accurately  measured.  Its  accurate 
location  in  the  structure  also  can  be  secured  by  the  exercise  of  proper  care.  The  concrete,  on 
the  other  hand,  as  at  present  manufactured,  does  not  possess  qualities  which  can  be  accurately 
forecast  either  in  similar  structures  or  in  different  parts  of  the  same  structure  and,  as  is  well 
known,  those  which  it  does  possess  are  subject  to  change  with  time,  but  even  this  change  cannot 
be  known  in  advance.    Accurate  test  results  are,  therefore,  not  to  be  expected. 

The  tested  slab  in  the  majority  of  cases  form  but  a  small  portion  of  the  floor  and  the 
distribution  of  stress  to  the  surrounding  portions  has  a  modifying  effect  upon  the  results.  Also, 
the  relative  size  and  stiffness  of  the  columns  above  and  below  the  floor  will  cause  differing 
results  in  the  tests  of  floors  otherwise  similar.  Shrinkage  and  temperature  changes  produce 
effects  which  are  difficult  to  measure  and  eliminate,  and  additional  complications  are  introduced 
by  settlement  of  the  columns,  either  due  to  yielding  of  the  foundation  or  to  shortening  in  the 
columns  themselves  under  direct  load. 

A  brief  summary  of  the  more  important  results  of  tests  is  given  below: 

1.  Tests  of  wide  beams  and  later  of  flat-slab  buildings  proved  that  a  beam  may  be  made 
much  wider  than  the  support,  with  only  a  moderate  loss  of  efficiency. 

2.  Tests  of  models  and  of  actual  buildings  have  demonstrated  the  advisability  of  transverse 
reinforcement  placed  on  the  edge  of  the  panel  in  the  top  of  slab,  particularly  where  no  drop 
panel  is  used. 

3.  For  the  true  flat  slab,  i.e.,  where  no  drop  heads  are  used,  the  critical  section  so  far  as 
the  steel  is  concerned,  is  at  the  edge  of  the  column  capital. 

4.  With  sections  and  reinforcement  as  specified  under  the  Chicago  ruling,  surprisingly 
low  stresses  have  been  measured  in  the  steel.  This  is  particularly  true  of  slabs  having  drop 
panels. 

5.  Eccentric  action  of  the  load  produces  a  marked  bending  action  in  interior  and  particu- 
larly in  exterior  columns  which  should  be  reinforced  accordingly.  Columns  for  single-story 
structures,  where  unbalanced  live  load  is  carried  on  the  roof,  should  receive  attention  in  this 
regard. 

6.  Footings  for  single-story  structures  of  this  class  should  be  designed  with  a  liberal  factor 
of  safety  as  the  danger  of  settlement  is  apparently  greater  in  this  class  of  structure. 

7.  Structures  with  relatively  thick  slabs  show  low  steel  stress  as  compared  to  thinner 
slabs  designed  in  the  same  manner. 

8.  Stresses  due  to  dead  load  can  be  measured  if  proper  precautions  are  taken  during 
construction. 


Sec.  11-19] 


BUILDINGS 


483 


9.  Different  arrangements  of  load  have  different  effects  upon  the  same  panel  and  single- 
panel  loading  does  not  necessarily  develop  the  greatest  stresses. 

10.  In  flat-slab  design,  deflection  rather  than  stress  in  the  steel  controls  because  large 
deflection  results  in  serious  cracking  of  the  slab.  Floors  designed  under  the  Chicago  ruling 
do  not  exceed  one-eight-hundredth  of  the  span  and  most  of  them  show  but  slightly  more  than 
one-half  of  this  amount. 

11.  Relative  deformations  in  the  concrete  are  of  value  as  a  comparison,  but  as  an  accurate 
indication  of  stress  they  have  little  weight  due  to  lack  of  uniformity  in  the  elastic  properties 
of  concrete. 

12.  Buildings  designed  according  to  the  flat-slab  rulings  of  any  of  our  better  cities, 
under  any  of  the  systems,  and  constructed  with  a  reasonable  amount  of  intelligent  supervision, 
give  entire  satisfaction  in  service.  Of  these  rulings,  that  of  Chicago  is  the  best  and  most 
conservative. 

.  13.  Many  more  tests  on  four-way  reinforced  slabs  are  available  than  of  other  systems  and 
for  this  reason  comparisons,  which  are  largely  a  matter  of  judgment,  cannot  be  made 
with  certainty.  Analyses  of  published  data  made  by  a  number  of  engineers  would  indicate  that 
given  the  same  span,  load,  and  concrete  sections,  the  circumferential  system  will  show  the 
lowest  stress  per  pound  of  steel,  the  four-way  system  next,  and  the  two-way  system  last.  This 
is  not  necessarily  their  order  with  regard  to  total  economy,  however.  Bending  and  placing 
costs  and  the  unit  price  of  steel  are  contributing  factors  which  modify  the  final  result. 

14.  The  ruling  adopted  by  the  American  Concrete  Institute  meets  certain  objections  to 
the  Chicago  ruling  and  harmonizes  better  in  some  respects  with  the  results  of  later  tests.  It 
is  recommended  for  use  as  the  best  that  is  now  available. 

15.  The  ruling  adopted  by  the  Special  Committee  of  the  American  Society  of  Civil  Engi- 
neers, while  theoretically  sound  in  some  respects,  is  incorrect  in  others,  and  adopts  coefficients 
which  are  unnecessarily  severe  and  not  justified  by  the  facts.  This  ruling,  if  generally 
adopted,  would,  in  the  author's  opinion,  impose  a  needless  burden  on  the  industry. 

The  following  very  able  analysis  of  this  subject  based  on  four-way  tests  is  taken  from  a 
paper  by  Arthur  R.  Lord,  Structural  and  Testing  Engineer  of  Chicago,  read  before  the  South- 
western Cement  Association  at  Kansas  City,  Feb.  22,  1917. 

The  total  positive  and  negative  moment  is  taken  in  the  A.  C.  I.  report  as  0.09  whih  —  qc)'^  and  the  division 
of  this  moment  between  the  various  sections  is  given  in  Table  I.  The  Joint  Committee  report  increases  the  total 
moment  to  O.lOTwhih  —  %c)^-  and  allows  a  much  less  flexible  design  than  the  A.  C.  I.  report.  Reduced  to  the 
same  basis  the  Chicago  Ruling  total  moment  is  0.092i(;Zi(l2  —  ^6c)2. 


Table  P 


Code 

Type 
of  flat 
slab 

Total 
—  and 

+ 
mom., 
coef.2 

Total 
—  mom., 

% 

Total 
+  mom., 

% 

Distribution  limits 

Col.  head 
section,  % 

Middle 
section,  % 

Outer 
section,  % 

Inner 
section,  % 

Sum, 

% 

1 

2 

3 

4        1  5 

6 

7 

8 

9 

10 

Chicago 
Ruling. .  . 

4-way 
2-way 

0.087 
0.093 

66.7 
62.5 

33.3 
37.5 

53.2 
50.0 

13.4 
12.5 

20.0 
25.0 

13.4 
12.5 

100 
100 

A.  C.  I. 

report 

Drop 
No  drop 

0.090 
0.090 

70 . 0  to  60 . 0 
70 . 0  to  50 . 0 

30.0  to  40.0 
30.0  to  50.0 

60 . 0  to  50 . 0 
60.0  to  40.0 

10.0  to  20.0 
10.0  to  30.0 

18.0  to  28.0 
18.0  to  38.0 

12.0  to  22.0 
12.0  to  32.0 

100 
100 

J.  C. 

report 

Drop 
No  drop 

0.107 
0.107 

62.5 
62.5 

37.5 
37.5 

50.0 
50.0  to  40.6 

12.5 
12.5  to  21.9 

28 . 1  to  22 . 5 
28 . 1  to  20 . 6 

9.4  to  15.0 
9.4  to  16.9 

100 

100 

Total  Moment  Requirement. — It  will  be  seen  from  Table  I  that  the  A.  C.  I.  report  and  the  Chicago  Ruling 
adopt  the  same  total  moment  coefficient.    In  passing  it  may  be  mentioned  that  this  coefficient  is  the  highest  called 

1  Table  taken  from  discussion  by  T.  L.  Condbon  at  the  A.  C.  I.  convention  at  Chicago,  Feb.  8,  1917, 

2  Coefficient  in  formula.  Total  mom.  =  Kwl\{h  —  qc)^. 


484 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-19 


for  in  any  building  code  in  the  United  States  so  far  as  I  know  and  the  highest  heretofore  used  in  practical  designing. 
It  represents  the  most  conservative  past  practice.    The  J.  C.  report  increases  this  moment  18.5%.   Let  us  investigate 
what  extensometer  tests  of  buildings  erected  under  Chicago  regulations  show  as  to  the  actual  stresses  developed  in  ij 
flat  slabs.    Table  II  gives  a  summary  of  four  Chicago  tests,  all  of  four-way  flat  slabs  of  the  drop  type — that  is,  with 


Table  II 


Test 

S 

presses  over 

column  headi 

Steel  stresses 

In  steel 

In  concrete 

At  panel  center^ 

Top  rods 

.  Tests 

Chicago* 

Test  5 

Chicago* 

Tests 

Chicago* 

Tests 

Chicago* 

1 

2 

3 

4 

5 

6 

7 

8 

9 

9,200 

23,700 

1,110 

1,400 

10,100 

31,000 

Larkin  

8,500 

23,000 

800 

1,120 

16,000 

37,000 

Schulze  

7,100 

22,500 

530 

1,230 

6,200 

34,000 

4,900 

71,500 

Schwinn^  

9,300 

38,000 

300 

1,160 

18,900 

39,000 

9,900 

70,000 

a  greater  thickness  adjacent  to  the  support  than  in  the  slab  proper.  All  these  floors  were  loaded  to  or  in  excess  of 
twice  the  total  dead  and  live  design  load  as  indicated  in  Table  III.  It  certainly  seems  to  me  that  these  tests 
indicate  eminently  safe  and  conservative  design.  The  average  steel  stress  at  the  support  measured  about  9000  lb. 
per  sq.  in.  against  a  computed  stress  of  about  27,000  lb.  per  sq.  in.,  and  the  concrete  stress  about  700  lb.  per  sq.  in. 
against  a  computed  value  of  about  1250  lb.  per  sq.  in.  At  the  panel  center  the  average  steel  stress  was  about  13,000 
lb.  per  sq.  in.  against  a  computed  value  of  37,000  lb.  per  sq.  in.  The  concrete  stress  at  the  center  is  always  very 
low — less  than  half  that  at  the  supports.  The  average  stress  in  the  top  rods  was  less  than  8000  lb.  per  sq.  in. 
against  a  computed  value  of  over  70,000  lb.  per  sq.  in.  Taking  into  account  the  possible  and  reasonable  effect 
of  various  loadings  and  of  long-continued  loading,  it  would  appear  that  a  factor  of  safety  of  four  was  largely 
exceeded. 

Table  III 


Test 


Panel  size 


Length  Breadth 


Slab  thickness 


Slab  Drop 


Test  load: 
live 

dead  total 


Area  loaded 


Twice 
design 
load  in 
place 


Floor 
tested 


Franks . 


20'-3" 


Larkin  


24'-2' 


20' -0" 


9.0" 


13.00' 


624 
115 


739 


9.0" 


15.75' 


618 

120  738 


Schulze 


20'-0" 


17' 


Schwinn . 


26'-0" 


25'-0" 


9.0' 


15.00" 


10.0' 


.00" 


722 

122  844 


450 
125 


575 


24  hr. 


10th  (top) 


24  hr. 


2d 


m 


24  hr. 


379  days 


6th  (top) 


1  Average  of  readings  in  fully  loaded  area. 

2  Average  of  readings  on  direct  and  diagonal  bands, 
s  Observed  steel  stresses  as  reported  in  tests. 

*  Stresses  calculated  by  Chicago  RuHng  for  a  design  load  equal  to  applied  test  load. 

^  Concrete  stresses  reduced  to  80%  of  those  reported  for  the  teste  and  computed  on  the  basis  of  the  initial 
modulus  of  elasticity. 

8  Stresses  given  are  for  readings  taken  with  full  test  load  in  place  over  1  year. 


Sec.  11-19] 


BUILDINGS 


485 


Table  III  gives  information  about  the  Chicago  tests  referred  to  in  this  paper.  Table  IV  gives  further  data 
including  a  calculation  of  the  various  resisting  moments  from  the  measured  steel  stresses.  In  considering  these 
tests  the  stress  in  slab  steel  of  direct  bands  at  the  edge  of  the  loaded  area  has  been  increased  so  that  the  stress  in 
rods  outside  the  loaded  area  has  been  added  to  the  stress  in  the  rods  under  the  load  and  the  total  stress  figured  on 
this  basis.  Also,  in  column  12  of  Table  IV,  all  the  head  rods  are  considered  as  stressed  as  highly  as  the  slab  rods, 
though  they  lie  much  nearer  the  neutral  axis  of  the  slab.  Even  on  this  extremely  conservative  basis  the  average  total 
moment  is  only  0.025WL,  equal  to  0.035wh(h  —  qc)-,  as  against  the  value  of  Q.09xvh{h  —  qc)^  used  in  the  Chicago 
and  A.  C.  I.  Codes.  It  is  possible  that  other  loadings  may  increase  even  the  sum  of  the  moments  somewhat  and 
that  very  long  continued  loading  may  have  its  effect.  One  test  involved  a  full  year  under  load  and  the  increase 
in  the  total  moment  was  about  7%,  with  no  increase  during  the  last  3  or  4  months.  But  taking  all  influences  into 
account  I  do  not  see  how  any  one  can  fairly  ask  for  a  more  conservative  moment  coefficient  than  that  adopted  by  the 
A.  C.  I.  and  Chicago  Codes.  In  one  test  at  Seattle  of  a  flat-slab  building  built  on  a  very  deficient  basis  as  compared 
with  either  of  these  codes,  and  in  which  as  a  result  exceedingly  high  stresses  were  developed,  reaching  as  high  as 
50,0001b.  per  sq.  in.  in  the  steel,  and  in  which  modifying  actions  were  reduced  to  a  minimum,  the  total  resisting 
moment  on  the  basis  of  the  A.  C.  I.  Code  was  0.066  whih  —  qc)-  against  the  code  specification  of  O.OQwhih  —  qc)"^. 


Table  IV 


Test 

Section 
considered 

Right  area  of  all 
slab  rods  and  ef- 
fective laps 

Effective  section, 
all  slab  rods  and 
effective  laps 

d,  for  steel  areas 
in  columns  3 
1           and  4 

Right  area  of 
slab  rods,  laps 
and  head  rods 

Effective  section, 
slab  rods,  laps 
and  head  rods 

d,  for  steel  areas 
given  in  6  and  7 

Resisting  moment  of  observed  steel  stresses 

All  slab  rods  and 
effective  laps 

Slab  rods,  laps  and 
head  rods 

Right 
area 

Effective 
section 

Right 
area 

Effective 
section 

1 

2 

3  in. 

4 

sq.  in. 

5 

sq. in. 

6 

sq.  in. 

7 

sq.  in. 

8  in. 

9 

10 

11 

12 

Franks. .  . 

Over  column 

Center  of  panel 
Top  rods 

10.40 

6.88 

13.31 
8.33 

10.88 
7.62 

11.98 

14.88 

10.68 

0.0129PFL 
0.00681FL 

0.0197irL 

0.0165TFI/ 
0.0081IFL 

0 . 0246  WL 

0. 0149 PFL 
0.0068PFL 

0. 0217  WL 

0. 0185 PFL 
0.0081  TFL 

0. 0266 PFL 

Larkin. .  . 

Over  column 

head  

Center  of  panel 
Top  rods 

11.33 
7.75 

13.70 
9.37 

13.87 
7.84 

12.53 

14.89 

13.75 

0. 0123  PFL 
0.0090PFL 

0.0213TFL 

0.0149PFL 
0.0109]FL 

0.0258PFL 

0.0135PFL 
0.0090PFL 

0.0225TFL 

0.0161PFL 
0.0109T^^L 

0.0270PFL 

Schulze.  . 

Over  column 
Center  of  panel 

9.20 
5.95 
1.10 

10.84 
7.18 
1.10 

12.10 
7.75 
7.88 

9.20 

10.84 

12.10 

0.0105PFL 
0.0038PFL 
0.0006TFL 
0.0149TFL 

0.0123TFL 
0.0046PFL 
0.00061FL 
0.0175TFL 

0.0105TFL 
0.0038TFL 
0.0006PFL 
0.0149PrL 

0.0123TFL 
0.0046TFL 
0.0006TFL 
0.0175PFL 

Schwinn . 

Over  column 

head  

Center  of  panel 
Top  rods  

13.74 
9.57 
1.77 

16.42 
11.58 
1.77 

10.40 
8.85 
8.75 

13.74 

16.42 

10.40 

0.0102PFL 
0. 0122  PFL 
0.00121FL 
0.0236PyL 

0.0122PFL 
0.0148TFL 
Q.0Q\2WL 
0.0282TFL 

0. 0102 IFZ, 
0.0122WL 
0. 0012 PFL 
0.0236TFL 

0.0122PFL 
0.0148IFL 
0.0012PFL 
0.0282PFZ/ 

In  view  of  the  extensometer  test  record  and  the  fact  that  hundreds  of  other  buildings  designed  on  the  Chicago 
basis  have  indicated  by  deflections  under  test  load  that  they  have  equally  low  stresses  and  moments,  I  believe  the 
position  of  the  Joint  Committee  is  ultraconservative  in  this  requirement. 

Distribution  of  the  Total  Moment. — The  question  as  to  the  amount  of  total  moment  to  be  specified  in  design 
is,  as  I  view  it,  one  of  conservative  vs.  idtraconservative  opinion.  The  distribution  of  the  total  moment,  however, 
does  not  admit  of  so  many  opinions.  The  J.  C.  report  makes  a  rigid  division  of  the  moment  into  62.5  %  negative 
and  37.5%  positive  for  any  or  all  types  of  flat  slab.  The  A.  C.  I.  report  leaves  a  portion  of  the  moment  to  be  as- 
signed in  accordance  with  the  physical  details  of  the  slab  and  its  reinforcement.  I  cannot  see  that  there  is  any  room 
for  debate  on  this  difference.  If  the  J.  C.  division  is  right  for  a  flat  slab  with  a  drop  and  supported  by  stiff  columns, 
it  is  wrong  for  a  flat  slab  without  a  drop  and  supported  by  relatively  slender  columns.  The  evidence  of  the  tests 
also  is  positive  and  conclusive  on  this.    For  four  panels  loaded  uniformly,  the  tests  show  a  distribution  of  approxi- 


486 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-19 


mately  —  and  H  +,  with  individual  cases  in  which  as  high  as  70%  of  the  total  moment  has  been  negative 
(see  Table  V).  These  figures  are  for  buildings  with  a  much  deeper  drop  than  the  J.  C.  permits.  "With  other  con- 
ditions of  loading,  certainly  the  center  or  positive  moment  would  be  greater  and  the  ratio  of  negative  moment  to 
total  moment  reduced.  And  with  no  drop  present,  the  change  would  be  even  greater  as  shown  in  the  test  of  the 
Bell  Street  Warehouse  at  Seattle  where  only  40  %  of  the  total  moment  was  negative  and  60  %  positive — practi- 
cally a  reversal  of  the  conditions  where  a  large  drop  is  used.  This  data  gives  ample  basis  for  the  A.  C.  I.  recom- 
mendation that  permits  an  extreme  division  of  50%  —  and  50%  +  where  the  drop  is  not  used,  and  also  permits 
from  60  to  70%  negative  where  the  drop  is  used.  This  division  accords  much  more  closely  with  the  facts  than  the 
rigid  J.  C.  distribution,  which  forces  the  designer  to  either  use  an  unbalanced  design  or  employ  additional  material 
where  the  total  material  already  involved  is  more  than  ample  but  improperly  distributed. 


Table  V 


Test 

Steel  area  in  square  inches 

Observed  steel  stress 

Total  tension  carried 

%  of  whole 

Two* 
diagonal 
bands 

Long 
direct 
band 

Short 
direct 
band 

Diagonal 
band 

Long 
direct 
band 

Short 
direct 
band 

Diagonal 
bands 

Direct 
bands 

Diagonal 
bands 

Direct 
bands 

Franks  

Schwinn  

10.00 
11.13 
8.48 
13.89 

3.54 
5.10 
3.45 
5.10 

3.14 
2.55 
2.55 
4. 12 

6,950 
12,900 

4,220 
21,900 

7,350 
10,200 

8,400 
16,000 

10,100 
24,200 
7,200 
18,600 

69,000 
143,800 

36,000 
304,000 

57,000 
113,800 

47,400 
159,000 

54.8 
55.9 
43.2 
65.6 

45.2 
44.1 
56.8 
34.4 

54.9 

45.1 

*  Effective  section. 


The  J.  C.  also  assigns  a  fixed  proportion  of  the  moment — 12.5%  of  the  total  moment — to  the  mid-section  in 
flat  slabs  with  a  drop.  The  whole  report  shows  no  conception  of  the  fact  that  the  distribution  of  the  moment  is 
different  in  two-way  and  four-way  flat  slabs — a  fact  very  clearly  brought  out  in  tests.  In  four-way  flat  slabs 
tested  in  Chicago  as  shown  in  Table  II,  columns  8  and  9,  the  calculated  stress  across  the  mid-section  was  over 
70,000  lb.  per  sq.  in.  and  the  actual  stress  under  10,000  lb.  per  sq.  in.  even  after  a  year.  In  the  test  of  the  Sears- 
Roebuck  Building  at  Seattle,  a  two-way  flat  slab  gives  a  computed  stress  at  this  section  of  27,200  lb.  per  sq.  in.  and 
an  actual  stress  of  23,500  lb.  per  sq.  in.  This  would  indicate  that  the  moment  across  the  mid-section  is  several 
times  as  great  with  the  two-way  arrangement  of  the  steel  as  it  is  with  the  four-way  arrangement.  The  J.  C.  assign- 
ment of  moment  to  this  section  is  too  large  for  four-way  slabs  and  too  small  for  two-way  slabs,  and  again  the  result 
is  unbalanced  design.    The  A.  C.  I.  report  permits  a  distribution  that  will  fit  either  type. 

Customary  practice  in  four-way  design  makes  a  distribution  of  the  steel  between  direct  and  diagonal  bands 
varying  from  a  1  :  1  ratio  to  a  1 .5  :  1  ratio  and  the  results  of  tests  as  shown  in  Table  V  show  that  these  ratios  are  about 
right.  The  average  distribution  of  the  moment  was  about  even  between  direct  and  diagonal  bands  and  this 
would  result  in  a  1.4  :  1  ratio  between  direct  and  diagonal  bands.  The  J.  C.  report  specifies  as  a  minimum  that 
60%  of  the  positive  moment  must  be  taken  by  the  outer  section  and  this  gives  a  minimum  relation  of  2.1  times  as 
much  cross-sectional  steel  area  in  the  direct  as  in  the  diagonal  band.  Just  why  all  previous  practice  is  passed 
over  and  a  novel  arrangement  required,  I  am  at  a  loss  to  know  after  studying  the  available  data. 

Arbitrary  Limitations. — Arbitrary  limits,  established  in  addition  to  the  natural  limitations  of  the  moment 
and  shear  requirements,  should  be  reduced  to  a  minimum.  With  flat-slab  construction  the  moment  at  the  center 
is  too  small  to  establish  a  slab  thickness  such  as  we  deem  advisable  from  the  standpoint  of  deflection  and  some 
arbitrary  limit  is  desirable  here,  as  found  in  all  three  codes  cited  above.  At  the  support,  however,  the  shear 
determines  an  adequate  thickness  and  no  other  limit  is  needed. 

An  investigation  of  the  Chicago  buildings  tested  in  the  past  does  not  appear  to  call  for  the  limitation  of  0.4L 
as  the  minimum  drop  dimension  nor  for  one-half  the  slab  thickness  as  the  maximum  drop  thickness.  These  and 
other  J.  C.  limitations  handicap  the  designer  in  the  economic  use  of  his  materials  and  do  not  seem  to  be  founded 
on  any  experience  in  the  past.    The  A.  C.  I.  report  contains  all  the  limitations  that  seem  necessary  to  safe  design. 

Column  Moment. — The  amount  of  moment  in  the  column  will  depend  on  the  type  of  flat  slab  and  on  the  stiff- 
ness of  the  columns  above  and  below  the  slab.  For  the  Franks  test,  made  on  an  upper  floor  and  with  20-in.  columns 
on  a  20-ft.  span,  the  observed  moment  was  0.0138wZi(^2  —  gc)^.  For  small  columns  in  tipper  stories  of  buildings  the 
A.  C.  I.  specification  of  O.Q22wli{h  —  Qc)^  should  be  ample  even  where  the  drop  type  of  flat  slab  is  used  as  was  the 
case  in  the  Franks  building.  For  lower  stories  the  column  moment  undoubtedly  largely  increases  but  it  would  not 
be  right  to  specify  these  larger  moments  as  a  minimum  for  all  columns.  This  is  a  matter  where  the  judgment 
and  calculations  of  the  engineer  must  decide  on  the  proper  increase  but  the  specification  of  a  definite  minimum 
moment  by  the  A.  C.  I.  Committee  seems  to  me  a  step  in  the  right  direction.  The  J.  C.  report  and  the  Chicago 
Ruling  leaves  this  in  very  indefinite  shape,  with  the  result  that  many  designers  acting  in  good  faith  will  entirely 
overlook  the  design  of  the  columns  for  bending  moment. 


Sec.  11-20] 


BUILDINGS 


487 


20.  Methods  of  Design  and  Problems. — Many  attempts  have  been  made  to  develop  a 
scientific  method  of  analysis  of  the  stresses  which  will  be  developed  in  flat-slab  floors  as  at 
present  constructed.  On  account  of  the  complex  nature  of  the  problem  and  the  various  modi- 
fying factors  which  enter  into  it  no  satisfactory  method  of  design,  so  far  as  the  writer  is  aware, 
has  been  presented. 

A  very  comprehensive  testing  program  of  flat  slabs  has  been  carried  out  in  which  actual 
stresses  have  been  measured  (see  Art.  19).  With  these  results  as  a  foundation,  rules  governing 
the  design  of  such  structures  have  been  adopted  by  various  city  building  departments  and 
technical  societies,  and  the  adequacy  of  these  rulings  has  been  proven  in  turn  by  tests  of  build- 
ings designed  in  accordance  with  their  provisions  (see  Appendix  C).  A  study  of  the  provisions 
of  the  various  rulings  reveals  at  once  the  fact  that  all  methods  of  design  now  in  common  use 
are  to  a  large  extent  empirical. 

The  following  general  remarks  regarding  the  design  of  flat-slab  buildings  may  be  of  aid 
to  those  who  are  inexperienced  in  this  field. 

1.  The  live  load  for  which  the  structure  is  to  be  designed  must  be  established  either  by 
the  architect  or  the  engineer,  or,  if  the  structure  comes  under  the  jurisdiction  of  a  building 
department  of  a  city,  the  Building  Code  will  be  found  to  contain  rules  which  will  apply. 
Frequently,  it  is  necessary  to  obtain  a  special  ruling  from  the  building  department  in  a  particu- 
lar case. 

2.  The  story  heights,  etc.,  having  been  decided  upon  with  due  consideration  of  the  use  to 
which  the  building  is  to  be  put,  the  next  question  to  be  settled  is  the  column  spacing.  Fre- 
quently this  is  decided  by  the  owner  or  the  architect  but  in  industrial  buildings,  the  machinery 
to  be  housed  may  be  the  controlling  factor.  In  garages  and  service  stations  of  moderate  width, 
a  wide  central  span  and  narrow  side  panels  may  be  necessary.  However,  the  following  general 
rules  may  be  stated. 

(a)    In  general  the  short  span  construction  is  the  cheapest,  but  it  is  very  seldom  that 
spans  less  than  16  ft.  are  used,  and  probably  a  20-ft.  panel  represents  the  average. 
(6)  The  ideal  design  has  square  panels. 

(c)  The  next  best  arrangement  consists  of  identical  rectangular  panels. 
{d)  Oblique  panels  have  been  used,  but  their  use  is  not  recommended, 
(e)  The  outer  spans  are  frequently  made  shorter  than  the  interior  spans  in  order  to  make 
the  bending  moment  in  exterior  panels  equal  to  that  in  interior  panels. 

3.  The  method  of  design  to  be  used  for  the  slab  depends  on  whether  the  structure  comes 
under  the  jurisdiction  of  a  city  building  department.  If  it  does,  and  the  department  has 
adopted  a  ruling  on  flat-slab  design,  that  ruling  must  be  followed  in  so  far  as  it  applies.  If  no 
ruling  has  been  adopted,  then  much  time  and  trouble  will  be  saved  by  visiting  the  building 
examiners  and  obtaining  a  statement  as  to  just  what  they  will  accept.  In  cases  where  no  city 
authorities  have  jurisdiction,  the  designer  is  at  liberty  to  use  any  of  the  rulings  which  have  been 
adopted  by  our  larger  cities  or  technical  societies,  but  the  ruling  of  the  American  Concrete 
Institute  is  recommended. 

The  following  recommendations  regarding  designs  of  flat-slab  floors  are  made  by  Arthur 
R.  Lord  after  a  thorough  study  of  all  the  available  test  data  and  an  analysis  of  the  various 
rulings  which  have  been  adopted  (see  paper  by  A.  R.  Lord  entitled,  "  Extensometer  Test  Data  and 
Recommended  Practice  in  the  Design  of  Flat  Slabs,"  read  before  the  Southwestern  Cement 
Association,  Feb.  23,  1917).  The  intimate  connection  which  Mr.  Lord  has  had  with  the  develop- 
ment of  this  branch  of  engineering  and  his  thorough  knowledge  of  the  practical  construction  side 
entitles  him  to  speak  with  authority  and  with  his  recommendations  we  are  thoroughly  in 
accord. 

For  engineers  who  desire  to  be  conservative  and  who  are  designing  for  normal  variations  in  the  conditions 
of  manufacture  of  the  concrete  in  various  localities,  I  would  personally  advise  the  use  of  the  A.  C.  I.  Committee 
report  as  the  best  and  most  thoroughly  considered  design  basis  now  available.  For  engineers  designing  structures 
to  be  erected  by  the  most  improved  means  under  positive  controls,  ensuring  a  superior  grade  of  concrete,  I  would 


488 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  ll-20a 


approve  the  use  of  the  A.  C.  I.  teport  with  a  moment  coefEdent  of  0.08u;^i(/2  5c) 2  instead  of  the  value  given  in 
their  report  0.09w/i(Z2  —  qcy-. 

For  four-way  flat  slabs  with  drops  which  is  the  economical  type  to  use,  I  should  advise  the  following  dis- 
tribution of  the  total  moment: 

Column-head  section   50% 

Mid-section    10  % 

Outer  section  (direct  bands)   20  % 

Inner  section  (diagonal  bands)   20  % 

Where  no  drop  is  used,  I  should  advise  taking  from  6  to  10  %  (depending  on  the  column  stiffness)  of  the  total  amount 
away  from  the  column-head  section  and  distributing  it  equally  over  the  inner  and  outer  sections. 

For  two-way  flat  slabs  with  drops,  I  would  advise  the  following  distribution  of  the  total  moment: 

Column-head  section   50  % 

Mid-section   15% 

Outer  section   23% 

Inner  section   12%. 

The  writer  agrees  with  these  recommendations  and  knows  them  to  be  very  conservative. 
With  first-class  construction  and  supervision,  satisfactory  results  have  been  obtained  with  the 
four-way  system  using  drop  panels  and  concrete  sections  as  given  in  the  tables  of  Art.  21  under 
the  Pittsburgh  Ruling,  and  using  low  steel  stresses  (never  over  16,000  lb.  per  sq.in.).  This 
is  somewhat  less  than  the  minimum  recommended  by  Mr.  Lord,  both  as  regards  concrete  and 
steel,  and  its  universal  adoption  is  not  recommended. 

The  Pittsburgh  Ruling  may  be  regarded  as  giving  the  minimum  design  which  has  been 
used  with  satisfactory  results.  With  a  uniformly  high  grade  of  concrete  assured  and  properly 
seasoned  before  loading,  it  is  the  writer's  opinion  that  the  Pittsburgh  Ruling  would  give 
good  results.  With  conditions  as  they  are,  Mr.  Lord's  recommendations  above  quoted 
represent  the  best  practice. 

A  series  of  designs  of  typical  panels  will  now  be  given  in  order  to  illustrate  the  method  of 
application  of  the  various  rulings. 

It  is  not  the  intention  to  compare  the  relative  economy  of  the  various  systems  and  the 
reader  should  be  slow  to  make  such  comparisons  for,  unless  all  factors  are  considered,  they 
are  sure  to  be  misleading.  As  a  matter  of  fact  there  is  very  little  difference  between  different 
designs  which  are  made  upon  exactly  the  same  basis. 

20a.  Computations  for  Akme  System. — The  following  computations  are 
published  through  the  courtesy  of  the  Condron  Co.  of  Chicago  and  are  based  on  the  Chicago 
Ruling.    For  method  of  analysis  and  moment  distribution  see  Art.  17/;  also  Appendix  C. 

Span  22  ft.  0  in.  by  25  ft.  0  in.  200  lb.  L.L.  91/2-in.  slab  Slab  =  119  lb.  per  sq.  ft. 

„  .  ,      ,  WL^  L.L.  =  200  lb.  per  sq.  ft. 

Col.  head  section  =  -:j-r~  ft.-lb.  w  =  load  per  sq.  ft.  . —  ^ 

^^/^  Total  =  319  lb.  per  sq.  ft. 

Outer  section  =  -g^-  ft.-lb.  W  = 

Inner  &  mid.  section  =  ft.-lb. 

Head  =  (0.225)  (23.5)  =  5.29,  say  5  ft.  6  in.  round  head. 
Plate  =  (22)  (0.35)       =  7.70,  say  8  ft.  0  in.  short  direction. 

Plate  =  (25)  (0.35)       =  8.75,  say  9  ft.  0  in.  long  direction.    Use  9  ft.  0  in.  square 
22  -f  25  ^ 
 2         =  23.5  avg.  span. 

,  u    J  .      (319) (23.5)3  (12)  f       18,000  lb.  per  sq.  in. 

Col.  head  moment  =   =  1,655,980  in.-lb.  7         '  ^ 

(2)  (15)  fc  =       700  lb.  per  sq.  in. 

Cubes 
2'  =  1 
23.5'  =  12,978 


—3  (1,655,980)(15,625)       ,  .  1 

22    =  10,648   ^2  978   ^  1,995,000  in.-lb.,  long  span 


25"  -  15.626  a^|0Kia6«)  .  ,,360,000  in.-lb.,  short  span 


See.  11-206] 


BUILDINGS 


489 


Long  span  Short  span 

Col.  head  section   1,995,000   1,360,000    in. 

Outer  section    997,500   680,000   m  in. 

Inner  &  mid.  section   340,000   498,750 


997,500 
Long  span  (85^)2(141) 


Short  span 


Long  span 


Short  span 


Slab 


Long  bands 


680,000 

(89i)H14l) 


1.995.0C0 

(157;i)-^(108) 


101  =  X  p  =  0.63% 

(0.0063)  (141)  (85^)  =  7.45  sq.  in. 

17  —  Va(I>  =  7.51  sq.  in. 


=  m  =  K  0.42  % 

(0.0042)  (85i) (141)  =  4.96  sq.  in. 

12  —  H(f>  =  5.30  sq.  in. 
=  74  =  X  0.46  % 


SH  in. 

Assume  plate.  .  .  .  7H  in. 
7li  +  m  =  17  in. 

IH  in. 
d  =  15^^  in.,  high  bars 


^4  in. 
15\i  in. 


low  bars 


1.360,000 


(0.0046)  (15^i)  (108)  =  7.88  sq.  in. 
17  -  9i0  +  2  -  y2<f>  =  7.90  sq.  in. 


55 


0.34  % 


(15^^)2(108) 

(0.0034)  (15H) (108)  =  5.56  sq.  in. 
12  -  ^l<^  +  2  -  ^y^(t>  =  5.69  sq.  in 

—  1  in.     =  8H-in.,  short  bands 

—  VA  in.  =  8-in.,  long  bands 
340,000 


(8)  (0.9)  (18,000) 
498,750 
(8}-^)  (0.9)  (18,000) 


=  2.62  sq. 
=  3.63  sq. 


14  -  1.^0  =  2.74  sq.  in. 
19  -  i/2<^  =  3.73  sq.  in. 


Make  long  main  band  10  ft.  0  in. 

Make  short  main  band  9  ft.  6  in. 


Mid. 
Mid. 


band  10  ft.  0  in. 

band  S  ft.  6  in. 


206.  Computations  for  Corr -plate  Floors. 

be  taken  as  typical  of  the  method  used  in  the  design 
of  Corr-plate  floors  based  on  the  Standard  Building 
Regulations  of  the  American  Concrete  Institute,  1917. 
As  will  be  noted,  the  designs  are  for  typical  interior 
panels  only,  and  special  conditions  and  exterior  panels 
will  require  a  different  treatment.  The  computa- 
tions were  furnished  the  writer  through  the  courtesy 
of  the  Corrugated  Bar  Co.  of  Buffalo,  N.  Y. 

The  moment  distribution  usually  adopted  in 
Corr-plate  floors  is  given  in  Fig.  61.  In  the  prob- 
lems here  presented  the  moment  distribution  recom- 
mended by  the  American  Concrete  Institute  is  used. 

Typical  Interior  Panel  (Fig.  62). — 

Data:  Panel  =  20  ft.  4  in.  by  20  ft.  4  in. 
Live  load  =  175  lb.  per  sq.  ft. 

fs  =  18,000       fc  =  750 
^1  =  ^2  =  20.33 

c  =  4.5  qc  =  %(4.5)  =  3  ft.  0  in. 

Assuming  that  a  754 -in.  slab  will  be  required,  we  find  from  the 
thickness  formula  that  the  total  slab  thickness 


-The  following  computations  may 


Va/ues  oFZ  m  fhe  equation  M= 


t  =  0.02  X  20.33  X  \/l75  +  93  -f  1  =  7.65 

Therefore  the  assumption  made  is  satisfactory. 

The  sum  of  the  positive  and  negative  moments  in 
pounds  or  the  total  moment 

=  KO.Og)  (268)  (20.33)  (17.33)2(12) 
-  1.767,500  in.-lb.  , 


inch- 


Disthbution  across  ends  of  pane/ 
Fig.  61. 


490 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-206 


Corr-plate  moment  distribution  to  agree  with  A.  C.  I.  Standards  of  1917 

A.  C.  I.  section 

Negative  moment  in 
%  of  total  moment 

A.  C.  I.  section 

Positive  moment  in 
%  of  total  moment 

Col.  head  section   | 

Middle  section  

2  bands  A  =  31  % 
2  bands  B  =  21  % 
1  band   C  =  13% 

2  bands  A  =  13% 
2  bands  B  =    9  % 
1  band   C  =  13  % 

Negative  Moment  Steel  in  Each  Direction. — 

At  drop  panel,  jdfs  =  (0.875)  (9.5)  (18,000)  =  149,625 
At  outer  section,  jWs  =  (0.895)  (6.5)  (18,000)  =  104,100 
(1.767,500)  (0.31) 


5fr.f5  ctoc. 


—/o'-z"-  ^.^^-^--^il 


c  — - 


I 
I 

 1 


1 
I 
I 


4 


Fig.  62. 


Positive  Moment  Steel  in  Each  Direction. — 

(1.767,.500)(0.13) 


2  bands  A  = 
2  bands  B  = 
1  band  C  = 


104,100 
(1.767,500')(0-09) 

104,100 
(1,767,500)(0.13) 

104,100 


2.21  sq.  in.    Use  12  —  J-i-in.  rounds,  bend  10. 
1.53  sq.  in.    Use  8  —  J^^-in.  rounds,  bend  6. 
2.21  sq.  in.    Use  12  —  Vi-in.  rounds,  bend  6. 


The  area  of  steel  required  for  negative  moment  in  the  several  bands  is  secured  by  bending  up  the  necessary 
number  of  bars  from  the  bottom  of  the  slab  or  by  bending  up  alternate  bars  and  supplying  the  deficiency  in  nega- 
tive reinforcement  by  introducing  straight  bars  in  the  top  of  the  slab. 

(0.3)  (20.33)^268) 

(122)  (0.875)  (9.5)    =  ^"•^ 


The  unit  shearing  stress  u  = 


Sec.  H-206] 


BUILDINGS 


491 


Typical  Interior  and  Exterior  Panel  (Fig.  63). — 

Data:  Panel  =  20  ft.  4  in.  by  22  ft.  6  in. 
Live  load  =  175  lb.  per  sq.  ft. 

fs  =  18,000  fc  =  750 

h  =  20.33  ft.  h  =  22.5  ft. 

c  =  5.0  qc  =  %{5.0)  =  3.33 

L  =  21.42 

Assuming   an  8-in.  slab 


<  =  0.2  X  21.42  X  Vl75  -f-  96+  1  =  8.08. 
The  assumption  made  is  therefore  satisfactory. 
Design  for  the  Long  Span,  h  =  22.5  ft. — 

Total  moment  =  (0.09)(271)(20.33)(19.17)2(12) 
=  2,182,000  in.-lb. 


Fia.  63. 

Note. — The  same  distribution  of  moment  applies  for  the  rectangular  panel  as  that  given  for  the  square  panel. 
Negative  Moment  Steel. — 

At  drop  panel  jdf,  =  (0.875)  (10.5)  (18,000)  =  165,400 
At  outer  section  yd/s  =  (0.895)  (  7.0)  (18,000)  =  112,800 


2  bands  A  = 
2  bands  B  = 

1  band    C  = 
Positive  Moment  Steel. — 

2  bands  A  = 


(2,182,000)  (0.31) 

165,400 
(2,182,000)  (0.21) 

165,400 
(2,182,000) (0.13) 
112,800 

(2,182,000) (0.13) 
112,800 


=  4.08  sq.  in. 
=  2.77  sq.  in. 
=  2.52  sq.  in. 

=  2.52  sq.  in.  Use   9  —  H-in.  square,  bend  up  8 

2  bands  B  =  (^'182,^000)^(0.09)   ^  ^  ^  _  ^^^  .^  square,  bend  up  6 

1  band    C  =  (^•182g)0K0.13)  ^  ^  52  gq.  in.  Use  10  -  H-in.  square,  bend  up  5 


492 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-20C 


Design  for  the  Short  Span,  h  =  20.33  fl. — 

Total  moment  =  (0.09)(271)(22.5)(17)2(12) 
=  1,903,000  in.-lb. 

Negative  Moment  Steel. — 

At  drop  panel  jd/^  =  (0.875)  (11)  (18,000)  =  173,200 
At  outer  section  jd/s  =  (0.895)  (6.5)  (18,000)  =  104,700 
(1,903,000)  (0.31) 

173,200 
(1,903.000)  (0.21) 


2  bands  D  = 
2  bands  E  = 


1  band    F  = 
Positive  Moment  Steel. — 

2  bands  D  = 

2  bands  E  = 
1  band    F  = 


173,200 
(1,903,000)  (0.13) 
104,700 

(1,903,000)  (0.13) 

104,700 
(1,903.000)  (0.09) 

104,700 
(1,903.000)  (0.13) 


3.41  sq.  in. 
2.31  sq.  in. 
2.36  sq.  in. 


2.36  sq.  in.  Use  10  —  yi-xn.  square,  bend  up  7 
1.63  sq.  in.  Use  6  —  J^-in.  square,  bend  up  5 
2.36  sq.  in.    Use  10  —  M-in.  square,  bend  up  5 


104,700 

Note. — For  exterior  panels — provided  the  span  lengths  remain  unchanged — the  positive  moment  steel,  and 
the  negative  moment  steel  at  the  first  row  of  interior  columns,  in  the  bantis  normal  to  the  wall  is  to  be  increased  by 
20%. 

20c.  Computations  Based  on  Pittsburgh  Ruling. — The  following  design  of  a 
typical  panel  according  to  the  Pittsburgh  Ruling  is  here  inserted  to  illustrate  this  method  of 


1- 


 .  L  -.-  -r 


Fig.  64. 


computation  and  it  is  not  recommended  for  universal  adoption.  In  order  to  give  a  design 
the  equal  of  that  recommended  by  the  American  Concrete  Institute,  the  value  of  M  and  M' 
will  have  to  be  increased  or  a  lower  steel  stress  used.  It  will  be  observed  that  the  concrete 
sections  required  are  thinner  and  the  amounts  of  steel  computed  are  less  than  that  required 
by  either  the  Chicago  Code  or  the  American  Concrete  Institute  Rulings. 


Panel  =  20  ft.  10  in.  by  22  ft.  2}4  in. 
Assume  SJ-i-in.  slab  and  a  4y2-in.  drop. 
Column  cap  =  4  ft.  9  in.  diameter.  • 


Live  load  =  250  lb.  per  sq.  ft. 
Dead  load  =  106  lb.  per  sq.  ft. 
Total  load  =  356  lb.  per  sq.  ft. 


Using  the  Pittsburgh  Ruling  which  is  based  on  the  radial  distribution  of  stress  theory,  the  total  bending  moment 

WL 

in  the  center  of  the  suspended  slab  ia  M  =  "yg"'  where  W  is  the  total  live  and  dead  load  on  the  panel  and  L  is  the 

pa^iel  side  (Fig.  64).  fs  =  16,000  lb.  per  sq.  in. 

For  the  short  direct  bands,  /c  =  750  lb.  per  sq.  in. 

^  _   (3561.20.83)H20.83)a2)  ^ 
lb 

d  =  8Vi  in.  —  1  in.  =  7}'^  in.    Area  of  steel  =  22.54  sq.  in. 

113  —  J-i-in.  round  rods 


Sec.  ll-20c] 


BUILDINGS 


493 


113 

This  steel  is  distributed  among  eight  bands  and  the  proportion  for  one  short  direct  band  is  — g-  =  14  — 

in.  round  rods  per  band. 

For  the  long  direct  bands  we  have 

^  _  (356)(22.18)^(22.18)(12)  _ 
lb 

d  =  7y2  in.    Area  =  26.90   sq.in.  =  135  -  Vz-in.  rounds 
135 

— g-  =  17  —  J'^-in.  rounds  per  band 

The  diagonal  bands  in  an  oblong  panel  are  calculated  on  the  basis  of  the  average  panel  length. 

(20.83)  (22.18) 
Average  panel  =   2  —  ^1.5  ft. 

(356)  (21 .5)^)  (21. 5)  (12)  „ 
M  =  =  2,650,000  in.-lb. 

d  =  7^2  in.    Area  of  steel  =  24.52  sq.  in.  =  123  —  J^-in.  round  rods 
1 23 

— g-  =  16  —  y2-in.  round  rods  per  band. 

Check  of  steel  over  column  head. 

Using  the  same  ruling  as  before,  the  bending  moment  at  the  column  head  to  be  resisted  by  eight  bands  is 
W'L' 

M  =  where  W  is  the  total  panel  load  exclusive  of  that  over  the  column  capital  and  L'  is  the  span  measured 

from  edge  of  cap  to  edge  of  cap.    In  this  case,  as  the  difference  of  spans  is  small,  we  can  use  the  average  span  for  L' 

Area  of  slab  =  (20.83)  (22. 18)  =  462.0 
Area  of  col.  cap.  =  17.7 

444.3 

W  =  (444.3)  (356)  =  158,000.       L'  =  21.5  -  4.75  =  16.75  ft. 

(158,000)  (16.75)  (12)  „^  ^       .  „ 

M  =  -^^   =  2,892,000  in.-lb. 

d  =  13  in.  —  2  in.  =  11  in.    Area  of  steel   =  18.77  sq.  in.  =  94  —  i-^-in.  round  rods 

The  total  band  width  is  0.4  of  the  average  span,  which  is  8.6  ft.  The  94  —  Vz-xn.  round  rods  are  not  to  be  dis- 
tributed over  the  whole  band  width  but  over  the  width  of  the  column  cap  plus  twice  the  effective  depth.  This  is  4 
ft.  9  in.  +  2  X  11  in.  =  6  ft.  7  in. 

The  code  specifies  that  over  the  column  head  the  computed  spacing  must  be  maintained  for  the  full  band  width 

The  steel  required  then  in  the  eight  bands  radiating  from  the  column  capital  will  be  (94)  =  123  —  }^-in.  round 
rods 

We  actually  have 

2  short  direct  bands  14  =  28 
2  long  direct  bands  @  17  =  34 
4  diagonal  bands       @  16  =  64 

126  —  Yz-in.  round  rods 
which  gives  a  margin  of  safety  over  the  required  amounts. 

Shear  at  the  edge  of  the  column  cap  =  (179)^]^)  =  80  lb.  per  sq.  in.  with  an  allowable  punching  shear  of 
120  lb.  per  sq.  in. 

Stirrups  are  not  necessary  in  this  form  of  construction  as  all  the  slab  rods  are  in  the  top  of  the  slab  over  the 
drop  head  and  are  in  the  bottom  at  the  center  of  the  span. 

18.77 

V  =         X  11  ^  0.0069  (allowable  =  0.0097  for  16,000  and  750)  O.  K.  for  fc 

The  percentage  of  steel  in  the  center  of  the  span  is  always  low  and  compression  of  that  point  is  never  a  con- 
trolling factor.  * 

If  standard  concrete  sections  are  used,  it  will  seldom  be  necessary  to  check  other  portions 
of  the  slab  design,  except  under  special  conditions.  When  such  is  not  the  case,  the  compres- 
sion in  the  concrete  should  be  checked  at  the  edge  of  the  drop  head.  Where  a  smaller  depth  of 
drop  head  is  used  or  is  omitted  altogether,  the  compression  around  the  edge  of  the  column  cap 
will  be  the  controlling  feature  and,  in  order  to  keep  to  the  allowable  stress,  compression  steel 
may  have  to  be  inserted. 

Where  continuity  cannot  be  secured,  as  for  example  at  the  exterior  columns,  the  direct 
and  diagonal  bands  ending  at  the  exterior  columns  should  be  increased  20%.. 


494 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  ll-20d 


20d.  Computations  Based  on  Chicago  Ruling. — The  computations  of  a  simple 
panel  which  follow  are  inserted  to  illustrate  the  method  of  applying  the  Chicago  Ruling  to  a 
four- way  system.  Results  by  this  method  are  very  similar  to  those  obtained  by  the  A.  C.  I. 
Ruling.  The  across  direct  bands  which  are  called  for  under  this  ruling  are  not  required  under 
the  Pittsburgh  Ruling  and  many  designers  who  use  the  Chicago  method  do  not  put  these  rods 
in  the  top  of  the  slab  across  the  column  center  lines.  While  a  small  amount  of  reinforcement  is 
required  at  this  point,  it  is  doubtful  whether  its  omission  would  entail  serious  cracking  along 
the  edge  of  the  panel  in  the  drop-head  type  of  construction  where  conservative  concrete  sections 
are  used. 


Panel  24  ft.  8  in.  by  24  ft.  8  in. 

Assume  a  lOJ'i-in.  slab 

and  a  63^-in.  drop. 
Drop  head  8  ft.  9  in.  by  8  ft.  9  in. 
Col.  cap  5  ft.  9  in.  diameter. 


Live  load    =  200  lb. 
Finish        =    12  lb. 
Dead  load  =  138  lb.  per  sq.  ft. 
350 

fs  =  16,000  lb.  per  sq.  in. 
fc  =  750  lb.  per  sq.  in. 


The  formula  for  the  minimum  thickness  of  slab  as  given  by  the  Chicago  Code  is  t  =  0.023  L-\J w  where  t  is 
the  total  thickness  of  slab  in  inches,  L  is  the  panel  length  in  feet  and  mo  is  the  total 
1^  ,  I  live  and  dead  load  in  pounds  per  square  foot. 

t  =  0.023  X  24.67  \/350  =  10.6  in.  so  our  assumption  is  satisfactory,  = 

9.25  in.,  the  other  code  requirement,  is  exceeded. 

The  column  cap  must  be  at  least  0.225  X  L  =  5.56  ft.  which  the  assumed  dimen- 
sion of  5  ft.  9  in.  satisfies. 

The  width  of  strips  A  and  B  (Fig.  65)  as  used  in  the  moment  computations  will 
be  12  ft.  4  in.    W,  used  in  the  formulas,  will  be  (12.33)  (350)  =  4315  lb. 
Negative  moment  for  strip  A. 

WL'^  _  (4315)  (24.67)''  (12) 
15  ~ 


1 — 

<•  

\— 

.1, 

 i  

h 

M 


15 


=  2,103,000  in.-lb. 


Fig.  65. 
Positive  moment  for  strip  B 


Positive  moment  for  strip  A 

ELI  _ 
40 


M  = 


(4315) (24.67)2  (12) 


Negative  moment  for  strip  B 


M 


M 


60 


TFL2 
60 


(4315) (24.67)2  (12) 
60 

525,700  in.-lb. 


40 

=  525,700  in.-lb 


=  787.500  in.-lb. 


The  negative  moment  in  strip  A  is  resisted  by  one  diagonal  and  one  direct  band. 

2,103,000 

Area  of  steel  =  (o.87)(l7  -  2)(16,o"00)  =  ^^"^^ 

40  —  V2-\r\.  sq.  rods. 

which  are  not  necessarily  divided  equally  between  one  direct  and  one  diagonal  band.  For  distribution  see  the 
following  computation: 

The  positive  moment  in  each  strip  A  is  resisted  by  the  steel  in  one  cross  or  direct  band. 

d  =  lOJ-i  in.  -  1  in.  =  9}i  in. 
787,500 


Area  of  steel  = 


(0.91)  (9.5)  (16,000) 


5.70  sq.  in. 


23  —  H-in.  sq.  rods. 

The  positive  moment  of  each  strip  B  shall  be  resisted  by  the  steel  in  one  diagonal  band. 
Area  of  steel 


525,700 


(0.91)(9.5)(16,000) 


3.785  sq.  in. 
16  —  I'^-in.  sq.  rods. 


The  negative  moment  of  strip  B  is  resisted  by  the  across  direct  bands  which  are  short  rods  placed  in  the  top 
of  the  slab  over  and  at  right  angles  to  the  direct  bands. 

Area  of  steel  =  3.785  sq.  in. 

=  16  —  Vi-'m.  sq.  rods. 


Sec.  ll-20e] 


BUILDINGS 


495 


The  proper  steel  distribution  will  then  be: 
24  —  H-in.  sq.  rods  in  direct  bands. 
16  —  Vi-in.  sq.  rods  in  diagonal  bands. 
16  —  H-\n.  sq.  rods  across  direct  bands. 

For  exterior  panels  the  amount  of  reinforcement  is  to  be  increased  by  the  use  of  the  moment  coefficients 
specified  for  this  case. 

If  sections  given  in  the  tables  are  used,  it  will  not  be  necessary  to  check  the  shears  or  concrete  stresses  except 
in  special  cases. 

The  methods  of  computation  used  for  rectangular  panels  are  clearly  explained  in  the  text  so  that  the  detailed 
method  will  not  be  given  here.  In  fact  the  entire  ruling  is  very  clearly  written  and  covers  the  vital  points  of  design 
very  well. 

20e.  Computations  Based  on  Ruling  of  American  Concrete  Institute. — The 

following  design  of  a  simple  panel  of  a  four-way  flat  slab  under  the  A.  C.  I.  Ruling  will  serve  to 
make  clear  the  wording  of  the  ruling.  As  in  all  other  problems  in  this  chapter,  the  ordinary 
straight  line  stress  variation  is  assumed  and,  as  in  other  cases,  the  critical  sections  so  far  as 
compression  in  the  concrete  goes  are  either  around  the  column  capital  or  at  the  edge  of  the  drop 
panel.  This  method  gives  a  very  similar  steel  distribution  and  general  results  much  like  those 
obtained  by  the  Chicago  Ruling. 

Given  an  interior  panel  25  ft.  6  in.  by  25  ft.  6  in.  to  be  designed  to  carry  a  live  load  of  175  lb.  per  sq.  ft. 
plus  a  1-in.  cement  finish.  Assume  a  slab  thickness  t  =  10?4  in.  and  a  drop  G\i  in.  thick  and  9  ft.O  in.  by  9  ft. 
0  in.    The  column  capital  will  be  5  ft.  9  in.  diameter.    (Refer  to  Fig.  3,  Appendix  C,  page  858.) 

Testing  the  assumed  dimensions  by  the  ruling  we  have  as  follows: 

t  =  0.02L  v^"-  +  1  in.  Live  load  =  175  lb.  per  sq.  ft. 

t  =  0.02  X  25.5\/3T6  +  1  in.  Dead  load  =  129  lb.  per  sq.  ft. 

t  =  10.07  in.  .  Finish  load  =    12  lb.  per  sq.  ft. 

Total  load  w  =  316  lb.  per  sq.  ft. 
~=  =  ^-"^^"^       =  ^•^'^  =  10,000  lb.  per  sq.  in. 

fc  =  750  lb.  per  sq.  in. 
The  assumption  of  i  =  lOH  in.  is  thus  seen  to  be  satisfactory. 

The  drop  where  used  shall  not  be  less  than  0.3L  =  (0.3)  (25.5)  =  7.65  ft.  and  the  assumed  size  of  drop  9 
ft.  by  9  ft.  need  not  be  changed. 

The  sum  of  the  positive  and  negative  moments  shall  not  be  less  than  O.OQwhih  —  qc)-,  where  w  is  the  unit 
live  and  dead  load  in  pounds  per  square  foot,  li  is  the  span  in  feet  center  to  center  of  columns  parallel  to  sections 
at  which  moments  are  considered,  ^2  is  the  span  in  feet  center  to  center  of  columns  perpendicular  to  sections 
at  which  moments  are  considered,  c  the  average  diameter  of  column  capital  in  feet  at  the  point  where  its  thickness 
is  l}'Hn.,and  q  is  the  distance  from  center  line  of  capital  to  the  center  of  gravity  of  the  periphery  of  the  half 

capital  divided  by  |  (for  our  case  q  = 

Total  moment  =  (0.09)  (316)  (25.5)  (25.5  -  %X  5.75)2(12)  =  4,086,600  in.-lb. 

Under  the  ruling  50  %  of  this  must  be  resisted  by  the  steel  over  the  column  head.   (Refer  to  Fig.  3,  page  858.) 
Not  less  than  10  %  shall  be  resisted  in  the  mid-section,  not  less  than  18  %  shall  be  resisted  in  the  outer  sections, 
and  not  less  than  12%  of  the  total  moment  shall  be  resisted  on  the  inner  section. 
The  following  distribution  is  adopted:  ■ 

Column-head  section   50% 

Mid-section   10% 

Outer  section  (direct  bands)   20  % 

Inner  section  (diagonal  bands)   20% 

Total   100% 

The  moments  to  be  taken  by  the  different  sections  will  be  as  follows: 

Column-head  section   2,043,300  in.-lb. 

Mid-section   408,660 

Outer  section   817,320 

Inner  section   817,320 


Total 


4,086,600  in.-lb. 


496 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-20/ 


The  column-head  section  includes  two  diagonal  bands  and  one  direct  band. 

The  effective  depth  is  IGYz  in.  —  2  in.  =  14H  in.  (assuming  2  in.  to  the  center  of  gravity  of  the  steel).  With 
fs  =  16,000  and  fc  =  650,  we  have  the  area  for  three  bands  in  top  of  slab  over  the  column  head 

 2,043,300 

~  (14.5) (0.874) (16,000)    -  10-08  sq.  in. 
which  is  equal  to  40  —  H-in.  sq.  bars. 

For  the  mid-section  d  =  lOH—  IH  =  9  in. 

408,660 
'  ~  (9) (0.91) (16,000)  ~  ^-^^ 

which  is  equal  to  13  —  J-^-in.sq.  bars  in  the  across  direct  bands  located  in  the  top  of  the  slab  across  the  sides  of 
the  panel. 

In  the  outer  section  d  =  9  in. 

_         817,320  _     o.,  . 

~  (9) (0.89) (16,000)  -  ^-^^  ^"^^ 

which  is  equal  to  26  —  H-in.  sq.  rods  for  each  direct  band. 

Under  this  system  of  moment  distribution,  the  effective  area  of  steel  for  the  inner  section — i.e.,  the  two  diag- 
onal bands — will  be  the  same  as  that  for  the  direct  band  or  6.23  sq.  in.    The  actual  area  then  of  each  diagonal 

band  must  be  ('2)(o  707)  ^  ^-'^'^  which  is  18  —  J-^-in.  sq.  rods. 

Assuming  that  all  the  diagonal  rods  are  bent  up  over  the  head  to  form  negative  reinforcement,  the  amount 
of  steel  in  a  direct  band  which  will  have  to  be  bent  up  will  be  10.08  —  6.33  (effective  area  of  two  diagonal 
bands)  =  3.75  sq.  in.,  which  is  equal  to  15  —  }^-in.  sq.  rods.  As  there  ai;e  26  —  H-in.  sq.  rods  in  each  direct  band, 
1 1  may  be  stopped  at  the  edge  of  the  column  capital  or  carried  through  as  compression  reinforcement.  Another 
allowable  arrangement  would  be  to  bend  up  all  the  bars  in  the  direct  band  over  the  column  head,  which  would  re- 
quire an  effective  area  of  10.08  —  6.33  =  3.75  sq.  in.  in  the  two  diagonal  bands  to  be  bent  up,  which  equals 
3.75 

(2)  (0  707)  ~  2.65  sq.  in.,  or  11  —  J'^-in.  sq.  rods  per  diagonal  band.  These  rods  should  be  carried  (0.35)  (25.5)  = 
8.92  ft.,  or  8  ft.  11  in.  past  the  center  line  of  the  column. 

The  balance  of  the  rods  in  the  diagonal  band  should  extend  (0.35)  (25.5)  =  8  ft.  11  in.  on  either  side  of  the 
center  of  panel — that  is,  they  must  be  at  least  17  ft.  10  in.  long  in  this  case. 

It  is  common  practice  to  use  rods  in  the  direct  bands  which  are  long  enough  to  cover  two  spans  and  when 
this  is  done  the  laps  should  be  staggered.  Since  they  are  spliced  over  the  column  head,  each  bar  should  extend 
40  diameters  or  20  in.  past  the  center  line  of  splice  in  this  case. 

Still  another  possible  arrangement  of  steel  would  be  to  arrange  the  diagonal  bands  as  just  outlined  and  then 
to  only  bend  up  half  the  bars  in  the  direct  bands,  lapping  them  8  ft.  11  in.  past  the  center  line  from  each  side  so  as 
to  make  up  the  necessary  area  over  the  head.  This,  of  course,  only  applies  where  the  steel  in  the  direct  bands 
extends  for  one  span  only.  Where  rods  covering  two  spans  are  used  in  the  direct  bands,  this  arrangement  will 
have  to  be  modified  or  extra  short  rods  will  have  to  be  added  over  the  column  head. 

20/.  Roof  Design. — In  the  design  of  flat-slab  roofs  it  should  be  remembered 
that  the  deflection  rather  than  the  strength  may  be  and  usually  is  the  controlling  factor.  For 
this  reason  very  thin  slabs  should  not  be  used.  The  Chicago  and  A.  C.  I.  Rulings  limit  the 
thickness  of  the  roof  slab  to  one-fortieth  of  the  span  as  a  minimum.  For  a  20-ft.  span  this 
would  give  a  thickness  of  6  in.  which  has  been  found  by  experience  to  be  about  right  for  a  roof 
slab  of  this  span. 

There  are  two  methods  of  constructing  roofs  in  common  use.  The  first  method  is  to  pitch 
the  slab,  laying  the  roofing  surface  directly  on  the  concrete.  The  second  method  is  to  cast 
the  roof  slab  level  and  obtain  the  required  pitch  by  means  of  a  cinder-concrete  fill  (of  varying 
depth)  which  is  surfaced  with  a  cement  finish  and  upon  which  the  roofing  membrane  is  laid. 
The  first  method  involves  a  comparatively  small  dead  load  and,  as  the  roof  live  load  is  small, 
— generally  40  lb.  per  sq.  ft. — the  total  load  for  which  the  slab  will  be  designed  is  small.  In  the 
second  case  the  dead  load  may  be  very  considerable  in  certain  parts  of  the  slab  where  a  deep 
cinder  fill  is  necessary.    This  matter  should  obviously  receive  consideration  in  the  design. 

The  writer  has  made  it  a  practice  in  the  first  case  mentioned — i.e.,  a  pitched  slab  roof — 
to  never  design  for  a  lighter  live  load  than  75  lb.  per  sq.  ft.  This  means  a  total  load  of  75  lb. 
plus  the  dead  load  of  the  slab  and  roof  finish.  Some  other  engineers  use  even  more  than  this. 
The  reason  for  such  a  rule  is  that  the  roof  slab,  being  subjected  to  the  maximum  temperature 
variation,  both  daily  and  seasonal,  is  very  apt  to  crack  if  the  percentage  of  steel  is  too  small  and 
designing  with  light  loads  will  not  give  sufficient  reinforcement  to  resist  these  stresses. 


Sec.  Il-20g7] 


BUILDINGS 


497 


Frequently  in  roof  design  the  question  of  the  best  design  to  accommodate  sawtooth  sky- 
Hghts  will  arise.  An  economy  in  the  use  of  concrete  and  a  more  rational  design  will  often 
result  if  a  beam-and-girder  design  is  used  instead  of  the  flat-slab  type  for  such  cases.  Some 
designers  prefer  the  older  type  for  the  roofs  of  all  flat-slab  buildings. 

20g.  Beams  in  Flat-slab  Floors. — Two  general  cases  of  the  design  of  beams 
forming  a  part  of  fiat  slabs  arise.  The  first  is  that  of  beams  located  between  the  exterior 
columns  and  supportmg  the  edge  of  the  slab  and  carrying  either  a  low  wall  under  the  windows, 
or,  where  no  windows  occur,  a  wall  extending  from  the  floor  to  the  underside  of  the  beam  above. 
The  stresses  to  be  withstood  are  torsional,  due  to  the  deflection  of  the  panel,  and  tension,  due 
to  bending  under  applied  vertical  load.  For  this  reason  a  wide  shallow  beam  as  nearly  square 
in  section  as  possible  is  to  be  preferred.  Where  a  drop  panel  is  used,  it  is  advantageous  to 
make  the  beams  the  same  depth  as  the  drop.  Lighting  consideration  make  it  advisable  to. 
keep  the  depth  as  small  as  possible.  Parallel  and  adjacent  to  the  beam  there  is  a  half  band  of 
steel  in  the  bottom  of  the  slab  which  has  a  smaller  effective  depth  than  the  reinforcement  of 
the  wall  beam.  It  is  evident,  therefore,  that  a  part  at  least  of  this  band  cannot  be  stressed 
to  its  full  value  until  the  steel  in  the  bottom  of  the  beam  is  overstressed. 

It  is  the  practice  of  some  designers  to  calculate  the  steel  in  the  wall  beams  for  the  wall 
load  and  beam  dead  load  only,  and  there  are  several  cases  where  such  a  practice  has  given 
satisfactory  results.  With  this  method,  however,  there  is  every  chance  of  having  cracked 
beams  and  exterior  walls.  The  writer  believes  that  in  addition  to  the  load  above  specified, 
the  live  load  on  a  portion  of  the  floor  should  be  included.  It  is  recommended  that  in  addition 
to  the  weight  of  the  beams  and  wall,  the  exterior  beams  be  calculated  to  carry,  as  a  uniform 
load,  the  live  load  of  a  strip  of  floor  adjacent  to  the  beam,  of  length  equal  to  the  span,  and  width 
equal  to  one-sixth  the  span  at  right  angles  to  the  exterior  wall  of  the  building. 

For  the  second-class  beams  located  in  interior  panels,  the  same  rule  may  be  used,  except 
that  where  the  beam  carries  concentrated  or  stair  loads  these  must  be  provided  for  in  addition. 
Some  designers  prefer  the  wide,  shallow  type  of  beam  with  a  depth  equal  to  the  drop  head  which 
has,  besides  the  advantage  of  increased  clearance,  the  added  advantage  of  less  liability  of 
unsightly  cracking  under  excessive  deflection.  As  will  be  evident  from  a  study  of  any  building 
design,  cases  of  this  kind  are  bound  to  arise  which  are  indeterminate.  Under  these  conditions 
the  application  of  such  theoretical  analysis  as  will  apply  must  be  modified  by  experience  based 
on  former  designs,  successful  or  otherwise. 

Continuity  should  be  secured  in  all  beams  whenever  possible,  particularly  in  the  wall 
beams.  Adequate  temperature  reinforcement  in  exposed  concrete  surfaces  should  always 
be  provided.  Where  the  wall  beams  do  not  extend  below  the  floor  slab,  it  is  usually  possible 
to  utilize  the  entire  wall  below  the  window  as  a  beam  and  a  very  stiff  construction  can  be  secured. 
The  danger  of  cracking,  due  to  torsional  stresses,  is  greater,  however,  in  this  type  of  design. 

20h.  Columns. — The  calculation  of  the  columns  supporting  a  flat  slab  is  one 
of  the  most  important  parts  of  the  entire  design  and  is  more  frequently  overlooked  than  any 
other  portion  of  the  work. 

Tests  have  shown  conclusively  that  both  interior  and  exterior  columns  below  and  above 
the  loaded  floor  are  stressed  by  an  unbalanced  live  load  in  the  panel  which  they  support.  This 
point  is  well  covered  by  the  A.  C.  I.  Ruling  and  was  also  covered  in  a  way  by  the  Chicago  and 
Pittsburgh  Rulings,  but  in  many  cases  little  consideration  has  been  given  to  it. 

There  is  a  provision  in  the  Chicago  Ruling  that  no  column  shall  be  less  than  one-twelfth 
the  panel  length  or  one-twelfth  the  clear  height  in  thickness.  For  the  interior  columns  in  all 
stories  below  the  roof  story,  this  rule  is  good  and  should  be  used  even  though  it  will  often  give 
a  larger  section  than  the  direct  load  will  require.  An  exception  may  be  made  where  structural- 
steel  cores  are  used.  In  the  story  below  the  roof  somewhat  smaller  columns  may  be  used  as 
there  is  little  possibility  of  unbalanced  live  load  on  the  roof,  but  it  is  the  writer's  opinion  that 
12  in.  diameter  should  be  the  minimum  size  for  an  interior  column. 

For  the  exterior  columns  the  Chicago  Ruling  will  frequently  give  rather  thicker  sections 
32 


498  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  ll-20i 

than  are  necessary,  particularly  when  wide  columns  are  desired  on  account  of  the  exterior 
appearance  of  the  building.  The  following  minimum  thicknesses  are  recommended  for  exterior 
reinforced-concrete  columns: 

16-ft.  span   14  in. 

20-ft.  span   16  in. 

24-ft.  span   18  in. 

28-ft.  span   20  in. 


The  method  of  computing  the  moment  in  and  designing  columns  supporting  flat-slab 
buildings  as  recommended  by  the  American  Concrete  Institute  will  give  conservative  results 
and  should  meet  with  universal  adoption.  At  present  commercial  competition  has  led  to  a 
slighting  of  the  reinforcement  to  resist  bending  in  the  exterior  columns  in  many  cases,  with 
the  result  that  hair  cracks  have  developed  on  the  outside  of  the  column  at  the  base  of  the 
bracket.  No  serious  consequences  accompany  such  cracks,  but  if  the  adjacent  panels  were 
overloaded,  a  dangerous  condition  would  probably  develop. 

As  a  practical  minimum  for  vertical  reinforcement  in  columns,  the  equivalent  of  four  ^^-in. 
round  rods  has  been  adopted  by  some  designers  and  is  a  safe  minimum  for  general  use. 

The  bending  stresses  in  columns  will  be  found  to  be  more  important  in  the  upper 
stories  than  in  the  lower  floors  on  account  of  the  increase  in  the  direct  load  as  the  footings  are 
approached. 

For  moments  in  columns  in  fiat-slab  construction,  see  also  Art.  7,  Sect.  10.  The  methods 
of  computing  stresses  in  columns  due  to  bending  and  direct  stress  are  given  in  Sect.  9. 

20i.  Brick  Exterior  Wall  Supports. — Several  of  the  building  codes  allow  the 
use  of  brick  bearing  walls  for  the  exterior  support  of  flat-slab  floors.  The  fact  that  such  a 
support  cannot  develop  a  large  negative  moment  is  offset  by  providing  an  excess  of  40%  of 
steel  in  the  adjacent  slabs  as  against  20%  where  reinforced-concrete  columns  are  used.  Some 
structures  of  this  class  have  not  given  entire  satisfaction  and  one  failure  is  attributed  to  the 
weakness  of  the  brick  supporting  walls  {Engineering  News,  vol.  76,  page  262).  Two  difficulties 
arise  in  this  connection ;  one  is  to  determine  what  thickness  of  wall  is  necessary  and  the  other 
is  to  secure  first-class  brickwork.  Another  element  which  is  almost  certain  to  cause  trouble 
is  that  the  interior  columns  and  brick  exterior  walls  settle  at  different  rates  which,  in  a  multi- 
story building,  will  introduce  serious  strains  in  the  slabs.  Where  such  a  construction  must 
be  used,  it  is  recommended  that  pilasters  of  a  total  thickness  at  least  equal  to  one-twelfth  of 
the  span  be  used  and  that  a  heavy  continuous  beam  be  carried  around  the  edge  of  the  floor. 

It  is  inadvisable  to  use  corbels  or  brackets  on  the  brick  pilasters  as  they  will  increase  the 
bending  stress  in  the  pilaster  and  may  actually  endanger  the  structure.  If  they  are  required 
for  shear,  the  slab  drop  or  beam  should  be  increased  in  size  to  take  care  of  it  and  no  attempt 
should  be  made  to  restrain  the  slab  at  a  brick  wall  or  pilaster  bearing.  Usually  there  is  little 
if  any  saving  in  total  cost  by  the  use  of  brick,  and  the  reinforced-concrete  skeleton  building 
veneered  with  brick  is  superior  structurally. 

21.  Tables.  Pittsburgh  Ruling. — The  following  tables  have  been  computed  for  a  standard 
four-way  flat  slab  having  square  panels,  drop  heads,  and  reinforced  according  to  the  Pittsburgh 
Ruling. 

The  stresses  used  are  as  follows : 
/.  =  16,000  lb.  per  sq.  in. 

fc  =  not  more  than  750  lb.  per  sq.  in.  at  the  edge  of  column  capital. 
The  shear  at  the  edge  of  the  drop  head 
V 

V  =  ^  is  not  greater  than  60  lb.  per  sq.  in. 
For  100  lb.  per  sq,  ft.  superimposed  load,  the  drop  head  is  0.35L  square. 


Sec.  11-21] 


BUILDINGS 


499 


For  150  to  400  lb.  per  sq.  ft.  superimposed  load,  the  drop  head  is  0.4L  square,  where  L  is 
the  center  to  center  distance  between  columns. 

The  superimposed  load  means  the  live  or  live  and  dead  load  above  the  structural  slab  and 
may  or  may  not  include  the  weight  of  the  cement  finish,  depending  upon  whether  it  is  laid  at 
the  same  time  as  the  slab  or  at  a  later  date  if  it  forms  a  part  of  the  structure  at  all. 

The  computations  are  based  on  a  typical  interior  panel  and  the  amounts  of  steel  given 
in  the  tables  must  be  increased  in  exterior  panels  of  the  same  span  in  accordance  with  the  Pitts- 
burgh Code  requirements.  Where  concrete  exterior  columns  are  used  and  are  so  constructed 
and  reinforced  that  they  will  withstand  the  bending  stresses  developed  by  the  unbalanced  load, 
the  amount  of  steel  given  in  the  tables  should  be  increased  20%  for  all  the  bands  which  end  at 
the  outside  of  the  building  or  are  parallel  to  and  adjacent  to  the  wall  beam. 

Bands  which  extend  from  wall  to  wall,  such  as  diagonal  bands  at  corner  panels,  should 
be  increased  40%  over  the  values  given  in  the  tables.  It  is  the  writer's  opinion  that  the  same 
method  should  be  followed  in  treating  exterior  panels  where  brackets  are  not  provided  at  the 
wall  columns  and  insufficient  vertical  steel  is  used  in  them  to  properly  resist  the  bending  stresses 
due  to  the  unbalanced  loading,  i.e.,  the  slab  reinforcement  should  be  increased  40%. 

Where  reinforced-concrete  interior  columns  are  used  and  the  exterior  panels  are  carried 
on  brick  piers  or  walls,  the  Pittsburgh  Ruling  recommends  that  the  steel  in  the  exterior  panels 
be  increased  40%. 

Where,  as  is  frequently  the  case,  the  span  of  the  exterior  panels  is  greater  or  less  than  that 
of  the  interior  panels,  due  consideration  must  be  given  to  these  conditions,  and  the  preceding 
remarks  regarding  exterior  panels  will  be  modified  thereby. 

These  tables  are  given  here  principally  as  a  check  on  design  and  as  an  aid  to  estimating, 
and  it  is  not  the  intention  that  they  should  take  the  place  of  a  carefully  considered  design  in 
any  special  case.  Particularly  is  this  true  where  conditions,  due  to  irregular  panels,  openings, 
or  concentrated  loading  make  an  accurate  analysis  of  actual  stresses  imperative. 

Where  panels  are  not  square  and  where  the  angles  between  column  center  lines  are  not 
right  angles,  the  tables  do  not  apply  and  cannot  be  used  without  modification. 

For  intermediate  spans  and  loads  the  proper  values  (for  square  panels)  may  be  obtained 
from  the  tables  approximately  by  interpolation. 


Flat-slab  Panels — Pittsburgh  Regulations 
Interior  Panels — Superimposed  Load  100  lb.  per  sq.  ft. 


Panel 

Capi- 
tal 

Head 

T 

Total 
drop 

t 

Concrete 
in  cu.  ft. 

Steel  in  each  band 

Steel 
in.  lb. 

diame- 
ter 

Slab 

per 
sq.  ft. 

Direct 

Diagonal 

per 
sq.  ft. 

16'  X  16' 

3'-6" 

5'-7"  X  5'-7" 

8" 

5" 

0.465 

11-% '> 

1.460 

17'  X  17' 

3'-9" 

6'-0"  X  6'-0" 

5>^" 

0.492 

12-%  "0 

1.491 

18'  X  18' 

4'-0" 

6'-4"  X  6'-4" 

9" 

5M" 

0.513 

14-^r'<^ 

14-%"</> 

1.510 

19'  X  19' 

4'-3" 

6'-8"  X  6'-8" 

6" 

0.535 

15-M"<^ 

15-%"<^ 

1.610 

20'  X  20' 

4'-6" 

7'-0"  X  7'-0" 

6M" 

0.559 

17-%  "(^ 

1.700 

21'  X  21' 

4'-9" 

7'-4"  X  7'-4" 

lOM" 

6M" 

0.580 

15-% 

15-%  "□ 

1.780 

22'  X  22' 

5'-0" 

7'-8"  X  7'-8" 

lOM" 

7" 

0.622 

17-%  "□ 

17-% 

1.980 

23'  X  23' 

5'-3" 

8'-l"  X  8'-l" 

0.644 

19-%  "□ 

19-%  "□ 

2.140 

24'  X  24' 

5'-6" 

8'-5"  X  8'-5" 

0.669 

15->^> 

15->^"0 

2.190 

25'  X  25' 

5'-9" 

8'-9"  X  8'-9" 

12M" 

0.691 

16-K"</> 

16->^"</> 

2.260 

26'  X  26' 

5'-9" 

9'-2"  X  9'-2" 

0.740 

18-H"</> 

18->^"</> 

2.430 

27'  X  27' 

6'-0" 

9'-6"  X  9'-6" 

13M" 

0.763 

19-K"<A 

19->^"</> 

2.480 

500 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-21 


Interior  Panels — Superimposed  Load  150  lb.  per  sq.  ft. 


Capi- 

T 

Concrete 

Steel  in  each  band 

Steel 

Panel 

tal 

Head 

Total 
drop 

t 

in  cu.  ft. 

in  lb. 

diame- 

Slab 

per 

per 

ter 

sq.  ft. 

Direct 

Diagonal 

sq.  ft. 

16' 

X 

16' 

or  ntt 
6  — O 

o  — / 

X 

5'-7" 

y 

0.4/0 

11-^^ 

11-^^ 

1  '70 

1 .  7o 

17' 

X 

17' 

3'-9" 

6'-0" 

X 

6'-0" 

9>^" 

0.518 

12-^^  "□ 

1.84 

18' 

X 

18' 

4'-0" 

6'-4" 

X 

6'-4" 

10" 

6" 

0.543 

13-^r'n 

13-^r'a 

1.91 

19' 

X 

19' 

4'-3" 

7'-0" 

X 

7'-0" 

lOH" 

6M" 

0.571 

15-^^  "□ 

i5-M"a 

2.06 

20' 

X 

20' 

4'-6" 

7'-4" 

X 

7'-4" 

11" 

0.594 

17-^r'n 

2.15 

21' 

X 

21' 

4'-9" 

7'-8" 

X 

7'-8" 

ny2" 

7" 

0.635 

18-^^  "□ 

2.21 

22' 

X 

22' 

5'-0" 

8'-l" 

X 

8'-l" 

0.662 

15->^"<^ 

2.44 

23' 

X 

23' 

5'-3" 

8'-5" 

X 

8'-5" 

0.705 

16^3^  "0 

16-H''<^ 

2.50 

24' 

X 

24' 

5'-6" 

8'-9" 

X 

8'-9" 

13>^" 

8K" 

0.744 

17-^^  "0 

2.52 

25' 

X 

25' 

5'-9" 

9'-2" 

X 

9'-2" 

13^^" 

83^" 

0.770 

19-3^  "<A 

19-K"0 

2.70 

26' 

X 

26' 

5'-9" 

9'-8" 

X 

9'-8" 

14M" 

8M" 

0.800 

17-3^  "□ 

i7->^"n 

2.91 

27' 

X 

27' 

6'-0" 

10'-6" 

X 

10'-6" 

15>^" 

9" 

0.830 

18-3^  "□ 

i8->^"n 

2.98 

Flat-slab  Panels — Pittsburgh  Regulations 


Interior  Panels 


Superimposed  load 

200  lb.  per  sq.  ft. 

250  lb.  per  sq. 

ft. 

Side 
of 
panel 

Capi- 
tal 
diam- 
eter 

Side 
of 
head 

T 
Total 
drop 

t 

Slab 

Con- 
crete 
in 

cu.  ft. 
per 

sq.  ft. 

Steel  in  each  band 

Steel 
in  lb. 

per 
sq.  ft. 

T 
Total 
drop 

t 

Slab 

Con- 
crete 
in 

cu.  ft. 
per 

sq.  ft. 

Steel  in  each  band 

Steel 
in  lb. 

per 
sq.  ft. 

Direct 

Diag- 
onal 

Direct 

Diag- 
onal 

16' 

3'-6" 

6'-5" 

10" 

6" 

0.555 

12-%  "□ 

12-%  "□ 

2.00 

10%" 

0.600 

i3-%"n 

13-%"  □ 

2.16 

17' 

3'-9" 

6'-10" 

mi" 

6H" 

0.578 

13-% 

13-% 

2.02 

mi" 

7" 

0.645 

14-%"  □ 

14-  %"□ 

2.18 

18' 

4'-0" 

7'-3" 

mi" 

w 

0.620 

i5-%"n 

15-%"D 

2.19 

12" 

IM" 

0.684 

16-%"  □ 

16-%"n 

2.34 

19' 

4'~3" 

7'-8" 

iw 

7" 

0.645 

]6-%"n 

16-%  "□ 

2.27 

12M" 

7%" 

0.710 

18-%"  □ 

18-%"  □ 

2.92 

20' 

y-6" 

8'-0" 

12" 

7>i" 

0.665 

18-%  "□ 

18-%  "□ 

2.34 

mi" 

8\i" 

0.755 

14-H"<A 

14-M"<^ 

2.54 

21' 

4'-9" 

8'-5" 

mi" 

iVi" 

0.696 

mH"4> 

15-M"</> 

2.56 

mi" 

8M" 

0.778 

16-M",/, 

16->^"0 

2.74 

22' 

5'-0" 

8'- 10" 

mi" 

7H" 

0.720 

17-K"<A 

17-M"<A 

2.78 

mi" 

9" 

0.825 

17-H"<^ 

17-M"</. 

2.78 

23' 

5'- 3" 

9'-3" 

14" 

8}i" 

0 . 765 

18-K'V 

18-H"<A 

2.88 

15" 

9M" 

0.867 

19-M'V 

19-M"</' 

2.99 

24' 

5'-6" 

9'-8" 

iw 

8H" 

0.81] 

i6-M"n 

i6-H"n 

302 

15%" 

10" 

0.908 

i6-K"n 

16-1^^"  □ 

3.02 

25' 

5'-9" 

lO'-O" 

mi" 

9K" 

0.849 

i7-M"n 

17-H"a 

3.06 

16>^" 

10>^" 

0.955 

i8-M"n 

18-3-^"  □ 

3.24 

26' 

5'-9" 

10'-5" 

mi" 

OH" 

0.901 

i8-K"n 

i8-H"n 

3.08 

171^^2" 

11" 

1.010 

i9-H"n 

i9-M"n 

3.28 

27' 

6'-0" 

lO'-lO" 

mi" 

mi" 

0.946 

20-K"n 

20-H"n 

3.30 

18H" 

iiM" 

1.050 

2i-M"n 

2i-H"n 

3.48 

Sec.  11-21]  BUILDINGS  501 

Flat-slab  Panels — Pittsburgh  Regulations 


Interior  Panels 


Superimposed  load 

300  lb.  per  sq.  ft. 

350  lb.  per  sq. 

ft. 

Side 
of 
panel 

Capi- 
tal 
diam- 
eter 

Side 

ot 
head 

T 
Total 
drop 

t 

Slab 

Con- 
in 

cu.  ft. 
per 

sq.  ft. 

Steel  in  each  band 

Steel 
in.  lb. 

per 
sq.  ft. 

ToUl 
drop 

t 

Slab 

Con- 
in 

cu.  ft. 
per 

sq.  ft. 

Steel  in  each  band 

steel 
in  lb. 

per 
sq  ft 

Direct 

Diag- 

Direct 

Diag- 
onal 

16' 

3'-6" 

6'-5" 

113-^" 

0.665 

13-%"  □ 

i3-M"n 

2.16 

8" 

0.725 

13-%  "□ 

i3-%"n 

O  Id 
^  .  ID 

17' 

3'-9" 

6'-10" 

12" 

0.702 

15-%"  □ 

i5-%"n 

2.33 

o>2 

0.765 

15-%  "□ 

15-%"  □ 

z .  OO 

18' 

4'-0" 

7'-3" 

12H" 

8K" 

0.750 

16-M"n 

16-%"  □ 

2.34 

13>^" 

9" 

0.810 

17-%"  □ 

17-%  "□ 

2.49 

19' 

4'- 3" 

7'-8" 

ISH" 

SH" 

0.790 

18-?^  "  □ 

18-%"  □ 

2.48 

1*>4 

y>2 

0.860 

14-M"<^ 

2 . 69 

20' 

4'-6" 

S'-O" 

U}4" 

0.840 

15-M"</> 

15-H"<f> 

2.72 

15" 

10" 

0.900 

15^>^"</, 

2.72 

21' 

4'-9" 

8'-5" 

15" 

9^i" 

0.882 

16-M"<p 

2.75 

15%" 

lOM" 

0.945 

i7-y2"<i> 

17->^"</> 

2.92 

22' 

5'-0" 

S'-IO" 

15>^" 

lOK" 

0.928 

i8-y2"<i> 

3.03 

16M" 

11" 

0.995 

iB-yu 

18-M"«^> 

2.94 

23' 

5'-3" 

9'-3" 

16" 

loy^" 

0.970 

15-H"D 

i5-M"n 

2.98 

17>i" 

11%" 

1.058 

i6-K"n 

]6->^"n 

3.16 

24' 

5'-6" 

9'-8" 

17" 

mi" 

1.020 

i7-M"n 

3.20 

18" 

12M" 

1.115 

i7-K"n 

i7-i,^"n 

3.20 

25' 

5'-9" 

lO'-O" 

17M" 

iw 

1.055 

i8-M"n 

3.26 

18%" 

13>i" 

1.180 

18-1^^"  □ 

i8-M"n 

3.24 

26' 

5'-9" 

10'-5" 

18^" 

12H" 

1.105 

2o-M"n 

2o-M"n 

3.46 

20" 

14" 

1.250 

2o-i.^"n 

2o-H"n 

3.46 

Flat-slab  Panels — Pittsburgh  Regulations 


Interior  Panels 


Superimposed  load 

400  lb.  per  sq.  ft. 

Side 
of 

Capi- 
tal 

diam- 
eter 

Side 
of 

T 
Total 

t 

Slab 

Con- 
crete 

in 
cu.  ft. 

per 
sq.  ft. 

Steel  in  each  band 

steel 
in  lb. 

panel 

head 

drop 

Direct 

Diag- 
onal 

per 
sq.  ft. 

16' 

3'-6" 

6'-5" 

12%" 

8^4" 

0.785 

14-%  "□ 

14-%  "□ 

2.31 

17' 

3 '-9" 

6'- 10" 

13M" 

9M" 

0.828 

i5-%"n 

15-%  "□ 

2.33 

18' 

4'-0" 

7'-3" 

UH" 

9%" 

0.878 

17-%"  □ 

17-%"  □ 

2.49 

19' 

4 '-3" 

7'-8" 

mi" 

0.924 

14->^",^ 

14-K'V 

2.69 

20' 

4'-6" 

8'-0" 

16" 

mi" 

0.968 

16-M"</> 

16-H''0 

2.90 

21' 

4'-9" 

8'-5" 

16%" 

iiM" 

1.025 

17-M"</> 

17-H"«A 

2.92 

32' 

5'-0" 

8'-10" 

171.^2" 

mi" 

1.090 

i5-K"n 

15->^"D 

3.10 

23' 

5 '-3" 

9 '-3" 

183^" 

13" 

1.155 

16-1^"  □ 

16-M"a 

3.16 

24' 

5'-6" 

9'-8" 

19" 

13%" 

1.220 

i7-M"n 

i7-H"n 

3.20 

25' 

5'-9" 

10 '-0" 

19%" 

14M" 

1.280 

i9-M"n 

i9-M"n 

3.44 

26' 

5'- 9" 

10'-5" 

21" 

15" 

1.333 

2i-M"n 

2i->^"n 

3.63 

Chicago  Ruling. — The  following  tables  have  been  computed  for  a  four-way  flat  slab  having 
square  panels,  drop  heads,  and  reinforced  according  to  the  Chicago  Ruling.  They  include 
designs  for  from  100  to  400  lb.  per  sq.  ft.  live  load  and  spans  of  from  16  to  27  ft.  in  some  cases. 
Being  based  on  square  interior  panels  they  will  not  apply  without  modification  to  other  con- 
ditions and  are  useful  mainly  for  estimating  and  as  a  check  on  actual  designs.  The  general 
remarks  given  under  the  head  of  Pittsburgh  Ruling  apply  in  this  case. 

For  methods  of  computation  see  Art.  20(i  and  Appendix  C. 

The  stresses  used  are:  /«  =  18,000  and  fc  =  not  over  750  lb.  per  sq.  in. 


502 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec,  11-21 


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Sec.  11-211  BUILDINGS  503 

Flat-slab  Panels — Chicago  Regulations 


Interior  Panels — Superimposed  Load  300  lb.  per  sq.  ft. 


Panel 

Capital 
diam- 

Head 

T 
total 
drop 

t 

Concrete 
in  cu.  ft. 
per  sq.  ft. 

Steel  in  each  band 

Steel 
in  lb. 

slab 

Direct 

Across 
direct 

Diagonal 

per 
sq.  ft. 

16'  X  16' 

3'-6" 

5'_7"  X  5'-7" 

1 1 14  " 

IVa" 

0  648 

19-%"  □ 

12-%"  □ 

i3-%"n 

17'  V  17' 
Li     a  i ' 

3'— 9" 

fi'-o"  V  6'— n" 

123,';" 

8" 

0  715 

20-%"n 

13-%  "□ 

14-%  "□ 

0  on 

18'  X  18' 

4'-0" 

6'-4"  X  6'-4" 

13^" 

SH" 

0.766 

3.  13 

19'  X  19' 

4 '-3" 

o  -8    X  o  -8 

14>^" 

9" 

0 . 810 

18-H"<A 

12-1.-2 

13-H"<^ 

3.23 

20'  X  20' 

4 '-6" 

7'-0"  X  7'-C" 

15M" 

0.854 

2O->^"0 

13-M"<^ 

14->^"0 

3.27 

21'  X  21' 

4'-9" 

7'-4"  X  7'-4« 

163^^" 

10" 

0.899 

22->^"<^ 

15-K"<A 

16-M"0 

3.57 

22'  X  22' 

5'-0" 

7'- 8"  X  7'-8" 

16H" 

lOM" 

0.945 

20-M"n 

i3->^"n 

i3-M"n 

3.71 

23'  X  23' 

5'-3" 

8'-l"  X  8'-l" 

18" 

11" 

0.990 

2i-K"n 

i4-M"n 

i5-M"n 

3.88 

24'  X  24' 

5'-6" 

8'-5"  X  8'-5" 

19" 

11%" 

1.055 

23-M"n 

i5-M"n 

i6-M"n 

4.00 

25'  X  25' 

5'-9" 

8'-9"  X  8'-9" 

20" 

12K" 

1.100 

25-K"n 

i6->^"n 

i7-M"n 

4.11 

26'  X  26' 

5'-9" 

9'-2"  X  9'-2" 

20^" 

12H" 

1.153 

27->^"n 

i8-M"n 

i9-M"n 

4 . 34 

Interior  Panels- 

—Superimposed  Load  350  lb.  per  sq.  ft. 

Panel 

Capital 
diam- 
eter 

Head 

T 
total 
drop 

t 

Concrete 
in  cu.  ft. 
per  sq.  ft. 

Steel  in  each  band 

bteel 
in  lb. 

slab 

Direct 

Across 
direct 

Diagonal 

per 
sq.  ft. 

16'  X  16' 

3'-6" 

5'-9"  X  5'- 9" 

12>^" 

8" 

0.718 

i9-%"n 

13-%"  □ 

13-%"  □ 

2  91 

17'  V  17' 

3'-9" 

6'-l"  X  6'-l" 

13^^" 

8M" 

0.768 

2i-%"n 

14-%"  □ 

15-%"  □ 

2  97 

18'  X  18' 

4'-0" 

6'-6"  X  6'-6" 

9" 

0.810 

my2"<}> 

12->^"<^ 

3.10 

19'  X  19' 

4' -3" 

6'-ll"  X  6'-ll" 

15M" 

9>^" 

0.855 

19-M"<^ 

13-K"0 

14-M"<A 

3.48 

20'  X  20' 

4'-6" 

7'-4"  X  7'- 4" 

10" 

0.905 

21-K"0 

14-1.^  "0 

15-M"0 

3.53 

21'  X  21' 

4'-9" 

7'-5"  X  7'-5" 

mi" 

mi" 

0.965 

i9-M"n 

\2-y2"n 

13-K"n 

3.77 

22'  X  22' 

5'-0" 

8'-0"  X  8'-0" 

18" 

mi" 

1.010 

21-1.^"  □ 

i3-M"n 

3.92 

23'  X  23' 

5'-3" 

8'-4"  X  8'-4" 

19" 

12" 

1.075 

22-M"n 

my2"n 

15-H"n 

4.00 

24'  X  24' 

5'-6" 

8' -9"  X  8'-9" 

20>i" 

mv 

1.130 

24-H"n 

mH"o 

17-M"n 

4 . 12 

25'  X  25' 

5'-9" 

9'-3"  X  9'-3" 

21" 

13" 

1.175 

27-H"n 

i8->^"n 

i8-M"n 

4.40 

26'  X  26' 

5'-9" 

9'-5"  X  9'-5" 

22>r' 

13%" 

1.240 

28-M"n 

.i9-M"n 

20-M"n 

4.54 

Interior  Panels- 

—Superimposed  Load  400  lb.  per  sq.  ft. 

Panel 

Capital 
diam- 
eter 

Head 

T 

total 
drop 

t 

Concrete 
in  cu.  ft. 
per  sq.  ft. 

Steel  in  each  band 

Steel 
in  lb. 

slab 

Direct 

Across 
direct 

Diagonal 

per 
sq.  ft. 

1  A'  N/   1  A' 
ID    A  lO 

3'-6" 

6'-l"  X  6'-l" 

13" 

8M" 

0.746 

20-%  "□ 

14-%"  □ 

14-%"  □ 

3 .09 

17'  S/  17' 
1  <     A   1  # 

3'-9" 

6'-4"  X  6'-4" 

143^" 

9" 

0.814 

22-%  "□ 

i5-%"n 

16-%  "□ 

3  24 

18'  X  18' 

4'-0" 

6'-9"  X  6'-9" 

15" 

0.855 

25-%  "□ 

17-%  "□ 

18-%  "□ 

3.47 

19'  X  19' 

4'-3" 

7'-2"  X  7'-2" 

mi" 

10" 

0.905 

21-M"<> 

13-K"</, 

14-M"0 

0  .  Do 

20'  X  20' 

4'-6" 

7'-6"  X  7' -6" 

17M" 

10%" 

0.978 

22-H"0 

15-H"<^ 

16-H"0 

3.77 

21'  X  21' 

4'-9" 

8'-0"  X  8'-0" 

mi" 

mi" 

1.022 

25-H"0 

16-K'> 

17-K"0 

3.91 

22'  X  22' 

5'-0" 

8'-4"  X  8'-4" 

mi" 

12" 

1.090 

2i->^"n 

i4->^"n 

14-M"n 

3.98 

23'  X  23' 

5'-3" 

8'-8"  X  8'-8" 

20" 

12K2" 

1.130 

24-M"n 

i6-H"n 

4.29 

24'  X  24' 

5'-  6" 

9'-2"  X  9'-2" 

21" 

mi" 

1.200 

26-<^"n 

i7-K"a 

i8-H"n 

4.52 

25'  X  25' 

5'-9" 

9'-5"  X  9'-5" 

22 1.^" 

14" 

1.270 

28-H"n 

i8-H"a 

i9-H"n 

4.60 

26'  X  26' 

5'-9" 

9'-ll"  X  9'-ll" 

23>i" 

14M" 

1.315 

3o-H"n 

20-H"O 

20-wn 

4.71 

Corr-plate  Floors. — The  following  table  gives  data  regarding  designs  which  are  based  on 
the  Corr-plate  method  of  computation  for  square  interior  panels  and  apply  only  to  such  cases. 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-21 


ft' 

H 

51 


35315 

6  6  6  6  <6 

mil 


>  > 

Hill 

iifii 


18565 

6  6  6  6  6 

m 


 _ 


o  o  o  o  o 


b  b  b  b  b 


;;;;; 


o  o  o  o  o 


5;8SS§2 


;;;;; 


o  o  o  o  o 


Why 

S  2  2  S  2 
iiiii 

mil 


I 


llili 


inn 


fffff 


T — in; — 

fffff 


\  «  o  w  ^ 

illl 


Hill 


fffff 


fffff 


Hill 

nisi 


illll 


Illll 
Illll 


f-    f.  E.  f. 

fffff 

Hill 


Illll 

iim 


>>>>> 

mil 
Illll 


1. 1, 

XX  XXX 

«  Bo  Bo  00  00 
X  X  X  X  X 

Bo  QO  00  X  « 


X  X  X  X  X 

00  00  00  Bo  Bo 

X  X  X  X  X 

Bo  Bo  Bo  00  Bo 


I.     ^  S 
X  X  X  X  X 

b  b  b  b  b 

X  X  X  X  X 

nm 


HI 


ml 


ml 


I 


b 

X 

b 


? 

X 

? 

Bo 


X 


X 


X 


Sec.  11-21] 


BUILDINGS 


505 


The  stresses  used  are 

Ss  =  18,000  lb.  per  sq.  in. 
fc  =      700  lb.  per  sq.  in. 

They  are  based  on  the  Corr-plate  method  of  moment  distribution  and,  of  course,  will  not 
apply  where  other  rulings  are  in  force.  The  main  value  of  tables  of  this  kind  is  for  estimating 
and  as  a  check  on  design.  The  general  remarks  under  the  head  of  Pittsburgh  Ruling  apply 
in  this  case. 

For  methods  of  computation  see  Arts.  17 g  and  206. 

Akme  System. — The  designs  given  in  the  following  tables  were  not  computed  by  the 
Condron  Co.,  but  were  worked  out  by  one  of  the  construction  companies  who  have  used  the 
Akme  system  extensively.  As  given  here  the  steel  stresses  govern,  the  compression  in  the 
concrete  being  always  less  than  the  allowable. 

The  data  here  given  is  useful  for  estimating  and  as  a  check  on  design,  and  applies  only  to 
square  interior  panels  using  the  stresses  specified.  For  any  other  conditions  special  treat- 
ment will  be  required. 

The  stresses  used  are 

fs  =  18,000  lb.  per  sq.  in. 
fc  =      750  lb.  per  sq.  in. 

These  tables  should  be  used  in  connection  with  Figs.  47  and  48,  pp.  467  and  468.  For 
method  of  computation  see  Arts.  17/  and  20a. 


Akme  System — Flat  Slab 


100  lb.  per  sq.  ft. 

150  lb.  per  sq.  ft. 

Size  of 
panel 

Capi- 
tal 

diam- 
eter 

Side 

Reinforcing  steel 

Con- 
crete, 

Reinforcing  steel 

Con- 
crete, 

drop 
head 

Drop 

Slab 

Band  A 

Band  B 

cu.  ft. 

per 
sq.  ft. 

Drop 

Slab 

Band  A 

Band  B 

cu.  ft. 

per 
sq.  ft. 

15'  X  15' 
16'  X  16' 
17'  X  17' 
18'  X  18' 
19'  X  19' 
20'  X  20' 
21'  X  21' 
22'  X  22' 
23'  X  23' 
24'  X  24' 
25'  X  25' 

3'-6" 
3'-9" 
4'-0" 
4'-3" 
4'-6" 
4'-6" 
4 '-9" 
5'-0" 
5'-3" 
5'-6" 
5'-9" 

5'-3" 
5'-9" 
6'-0" 
6'-6" 
6'-9" 
7'-0" 
7'-6" 
7'-9" 
8'-0" 
8'-6" 
8'-9" 

4" 
4" 
4" 
4" 
4" 
4" 
4" 

w 

5" 
5" 
5" 

6" 
6" 

6M" 
7" 

7y2" 

7>^" 

8" 

8M" 

9" 

9" 

9>^" 

12->^<^ 

15-^g<^ 
12-H<f> 

5-  y2<f> 

6-  M</. 

10-  >^</> 

11-  M<^ 

12-  >'2> 

9-  ys<i> 

10-  ys<t> 

0.541 
0.543 
0.583 
0.626 
0.667 
0.666 
0.709 
0.755 
0.800 
0.802 
0.843 

4" 

.4" 
*4" 

4" 
4" 
4" 
4" 

4>^" 
6" 
5" 
5" 

6" 
6" 

6M" 
7" 

73-^" 
7M" 
8" 

8H" 

9" 

9" 

9M" 

10-^^0 

I2^ys<^ 
10-?4  4> 

12-  ^4  <i> 

13-  ^4  </. 

14-  ^4  <A 

15-  K<^ 
12-Ii<t> 

6-  H<t> 

7-  y2<t> 
s-y2  4> 

9-  y2<f> 

10-  M<^ 

i2-y2<i> 

l2-%<t> 

0.541 
0.543 
0.583 
0.626 
0.667 
0.666 
0.709 
0.755 
0.800 
0.802 
0.843 

200  lb.  per  sq.  ft. 

250  lb.  per  sq.  ft. 

15'  X  15' 
16'  X  16' 
17'  X  17' 
18'  X  18' 
19'  X  19' 
20'  X  20' 
21'  X  21' 
22'  X  22' 
23'  X  23' 
24'  X  24' 
25'  X  25' 

3'- 6" 
3'-9" 
4'-0" 
4'-3" 
4'-6" 
4'- 6" 
4'-9" 
5'-0" 
5'-3" 
S'-e" 
5'-9" 

5'-3" 
5'-9" 
6'-0" 
6'-6" 
6'-9" 
7'-0" 
7'-6" 
7'-9" 
8'-0" 
8'-6" 
8'-9" 

4" 
4" 

4H" 
4H" 
4>^" 
4>^" 
5" 

6" 

6H" 
W 
7" 

7H" 

8" 

8" 

8>^" 
9" 

93-^" 
9>^" 
10" 

\i-H<i> 

\2~y<t> 
\o-y4^4> 
n-yi<j> 
is-yi<t> 

14-  ^8  (A 

15-  ^^0 

7-y2<t> 

9->^0 
10-H<A 

n-H<t> 

9-  ys<i> 

10-  H<t> 

10-^0 

12-  ^0 

13-  ^^0 

14-  ^ 

0.533 
0.584 
0.630 
0.674 
0.714 
0.713 
0.756 
0.802 
0.847 
0.849 
0.895 

4" 
4" 

4H" 

5" 

5" 

5" 

5" 

5>^" 

6" 

6" 

W 

W 
7" 

7H" 
8" 

83-^" 

9" 

9" 

9>^" 
10" 
10>^" 
11" 

11-  %4> 

12-  %4> 

n-y4.<i> 

12-  H<t> 

13-  M<^ 

16-^4 

is-Vs<t> 
1^%<I> 

9-  y2<t> 
n-y2<i> 

12- H</. 

10-  ^^0 

i2-ys<}> 

0.583 
0.626 
0.672 
0.721 
0.761 
0.801 
0.803 
0.846 
0.892 
0.938 
0.983 

506 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-22 


300  lb.  per  sq.  ft. 

350  lb.  per  sq.  ft. 

Size  of 
panel 

Capi- 
tal 
diam- 
eter 

Side 

Reinforcing  steel 

Con- 
crete, 

Reinforcing  steel 

Con- 
crete, 

drop 
head 

Drop 

Slab 

Band  A 

Band  B 

cu.  ft. 

per 
sq.  ft. 

Drop 

Slab 

Band  A 

Band  B 

cu.  ft. 

per 
sq.  ft. 

15'  X  15' 
16'  X  16' 
17'  X  17' 
18'  X  18' 
19'  X  19' 
20'  X  20' 
21'  X  21' 
22'  X  22' 
23'  X  23' 
24'  X  24' 
25'  X  25' 

3'-6" 
3'-9" 
4'-0" 
4'-3" 
4'-6" 
4' -6" 
4'-9" 
5'-0" 
5'-3" 
5'-6" 
5'-9" 

5'-3" 
5'-9" 
6'-0" 
6'-6" 
6' -9" 
7'-0" 
7'-6" 
7'-9" 
8'-0" 
8'-6" 
8'-9" 

4" 

43-^" 
4M" 
5" 

5M" 
5H" 
5M" 
6" 

6>^" 

7" 

7" 

7" 
8" 

8K" 
9" 

9H" 

10" 

10>^" 

11" 

iiM" 

i2-ys<t> 

12-  Ii4, 
11-^^0 

13-  1 

9->^0 
9-M<A 
10-M<A 
12-3-^  0 
9-^^<A 

10-  ^^  <A 

11-  M</> 

12-  ^^  <A 
10-M<A 
1 

0.624 
0.673 
0.713 
0.763 
0.808 
0.848 
0.850 
0.895 
0.941 
0.990 
1.030 

4>^" 
5" 
5" 
5" 

5>^" 

5>^" 

6" 

6" 

7" 

73-^" 
73-^" 

73-^" 
8" 

W2" 
9" 

93-^" 
10" 
10" 
10>^" 

11" 

113-^" 
12" 

I3-H0 

10-  ^^0 

11-  ^^0 

10-^80 

12-  7:^0 

13-  ^^0 

14-  ^:^0 

15-  7:i0 

12-  10 

13-  10 

9->^0 

10-  3-^0 

11-  3-^0 

12-  3-^0 

9-  M0 

12-^0 

10-  ^^0 

10-  %  0 

11-  M0 

12-  ^0 

0.671 
0.721 
0.760 
0.840 
0 .849 
0.889 
0.897 
0.937 
0.982 
1.037 
1.076 

400  lb.  per  sq.  ft. 

15'  X  15' 
16'  X  16' 
17'  X  17' 
18'  X  18' 
19'  X  19' 
20'  X  20' 
21'  X  21' 
22'  X  22' 
23'  X  23' 
24'  X  24' 
25'  X  25' 

3'-6" 
3'-9" 
4'-0" 
4'-3" 
4'-6" 
4'-6" 
4'-9" 
5'-0" 
5'-3" 
5'- 6" 
5'-9" 

5'-3" 
5'-9" 
6'-0" 
6'-6'' 
6'-9" 
7'-0" 
7'- 6" 
7'-9" 
8'-0" 
8'-6" 
8'-9" 

5" 
5" 

5H" 

6" 

6" 

6M" 
7" 

8" 

8" 

8>^" 
9" 

W 
10" 

mi" 
11" 

iiM" 

12" 

12H" 

10-  M0 

12-  M0 

13-  M«A 

11-  Ji<> 

12-  7:^0 

13-  ^i<A 

l5-7:^<^ 

12-  1./. 

13-  l.A 

14-  l</> 

9-K2  <A 
10->^  0 
12-M<A 

9-^^<A 

9-K<A 

10-  H<P 

11-  %0 

12-  M0 
I2-M0 

0.718 
0.762 
0.807 
0.851 
0.896 
0.936 
0.944 
0.984 
1.029 
1.078 
1.123 

22.  Construction  Methods  and  Safeguards. — The  care  with  which  the  actual  construction 
of  a  reinforced-concrete  building  is  carried  out  has  more  to  do  with  its  success  than  any  other 
part  of  the  operation  and  is  certainly  far  more  important  than  the  design.  This  is  just  as 
true  of  the  flat-slab  type  as  of  any  other.  The  present  practice,  therefore,  of  several  of  the 
larger  bar  companies  in  furnishing  design  without  inspection  is  to  be  regretted. 

The  more  important  features  regarding  construction  as  they  appear  to  the  writer  may  be 
summarized  as  follows: 

1.  Column  Forms. — The  present  practice  is  to  use  metal  forms  for  the  interior  columns, 
including  the  column  capital,  which  are  commonly  leased  from  one  of  the  steel  form  com- 
panies. Forms  for  the  exterior  columns  are  commonly  built  of  wood,  although  in  some  cases 
metal  forms  are  also  used.  Great  care  should  be  taken  to  see  that  these  forms  are  tight, 
particularly  around  the  capital,  as  leakage  at  this  point  always  results  in  a  poor  casting  which 
never  can  be  properly  repaired.    The  same  is  true  where  beams  join  the  interior  columns. 

2.  Pouring  Columns. — Columns  should  be  cast  to  the  bottom  of  the  column  capital  and 
allowed  to  set  24  hr.  before  casting  the  capital  and  slab.  Otherwise,  there  is  likely  to  be  a 
separation  at  this  point. 

3.  Floor  Forms. — Both  matched  and  edged  lumber  is  used  for  floor  forms  with  satisfactory 
results.  In  the  latter  case,  however,  more  care  must  be  exercised  to  prevent  leakage  which  is 
always  attended  with  serious  consequences. 

4.  Methods  of  Securing  Reinforcing  Steel  in  Position. — In  all  reinforced-concrete  construction 
the  accurate  location  and  securing  of  the  reinforcing  steel  in  its  proper  position  until  the  cast- 
ing of  the  concrete  is  completed  is  of  the  utmost  importance.  Until  recently,  this  fact  was  not 
generally  realized  and  some  of  the  older  constructions,  which  have  been  lately  demolished, 


Sec.  11-22] 


BUILDINGS 


507 


exhibit  a  remarkable  displacement  of  both  major  and  secondary  reinforcement.  Beam  bars 
were  crowded  together  in  one  side  of  the  beam  or  forced  up  several  inches  above  their  correct 
position  and  stirrups  were  in  almost  all  conceivable  positions. 

The  necessity  of  the  positive  anchoring  of  the  reinforcement  in  position  during  the  cast- 
ing period  is  even  greater  in  the  case  of  flat-slab  floors  than  with  other  forms  of  construction, 
because  a  small  amount  of  vertical  displacement  will  have  a  much  greater  relative  effect. 

This  fact  has  been  well  understood  by  engineers  engaged  in  this  class  of  construction 
and  the  result  has  been  the  development  of  numerous  special  devices  for  spacing  rods  uniformly 
and  maintaining  them  at  the  proper  distance  above  the  forms.  Cuts  of  some  of  these  devices 
are  shown  in  Art.  73,  Sect.  2.  These  are  carried  in  stock  by,  or  can  be  quickly  obtained  from, 
their  various  makers  and  are  all  of  proven  merit.  It  is  strongly  recommended  that  devices  of 
this  type  or  of  equal  efficiency  be  specified  and  their  use  insisted  on  as  experience  has  shown 
that  slipshod  methods  have  no  place  in  this  class  of  construction. 

5.  Casting  Floor  Slab. — The  ideal  floor  is  one  that  is  cast  at  a  single  operation.  It  is  not 
always  possible  to  do  this  but  the  fewer  construction  joints  in  the  floor,  the  better.  It  is  usual 
to  make  these  in  the  center  of  panels  and  it  is  the  practice  of  some  engineers  to  use  extra  short 
steel  rods  across  these  joints.  A  thorough  cleaning  of  the  finished  surface  together  with  the 
liberal  use  of  neat  cement  on  this  surface  before  casting  the  adjoining  section  is  advantageous. 
Care  should  be  taken,  by  the  frequent  use  of  grade  points,  to  see  that  the  slab  is  cast  to  the 
thickness  specified.    Variations  of  an  inch  or  more  have  frequently  been  observed  in  practice. 

6.  Floor  Finish. — Two  methods  of  applying  the  cement  finish  to  the  floor  slab  are  in 
common  use.  The  first,  known  as  the  monolithic  method,  consists  in  smoothing  down  the 
structural  slab  and  applying  a  thin  finish  before  the  concrete  has  thoroughly  set.  In  this 
case  the  finish  is  properly  considered  as  a  part  of  the  slab  in  the  computations  for  strength. 

In  the  second  method,  more  commonly  used  in  cold-weather  work,  the  finish  to  a  thick- 
ness of  %  in.  or  more  is  applied  after  the  structural  slab  has  set  and  cannot  be  considered  as 
an  integral  part  of  it  for  in  many  cases  it  does  not  bond  uniformly  with  it  but,  of  course,  adds 
to  the  dead  load. 

7.  Wall  Beams. — Where  the  wall  beams  do  not  extend  above  the  slab  they  are  cast  with 
it,  but  in  some  cases  where  they  extend  above  they  are  cast  part  with  the  floor  and  the  balance 
afterward.  When  this  is  the  case,  it  is  advisable  to  provide  additional  stirrups  to  bond  the 
two  sections  together. 

8.  Concrete. — Very  wet  concrete  should  not  be  permitted  and  the  remarks  on  this  subject 
in  Sects.  1  and  2  apply  here  with  full  force.  A  mixture  no  leaner  than  1:2:4  should  be  used  in 
the  slabs  with  an  aggregate  not  coarser  than  1  in.  For  columns  the  writer  prefers  a  richer 
mixture  and  has  recommended  1  :  IJ^  :3  wherever  possible. 

9.  Steel. — Deformed  or  square  twisted  bars  are  to  be  preferred  for  all  flat-slab  work  on 
account  of  their  superior  bonding  qualities.  Where  market  conditions  permit,  hard-grade 
steel  is  recommended  for  slabs  on  account  of  its  higher  elastic  limit.  It  has  been  the  usual 
practice  in  four-way  flat  slabs  to  specify  the  exact  points  of  lapping  of  the  various  bars.  Just 
as  good  results  may  be  secured  by  allowing  the  splices  to  come  where  they  will  but  so  arrang- 
ing the  bars  that  the  splices  are  well  staggered.  The  ability  to  use  steel  of  random  lengths 
frequently  results  in  a  considerable  saving. 

10.  Removal  of  Forms. — It  is  not  advisable  to  remove  the  support  from  a  flat-slab  floor  as 
soon  after  casting  as  with  the  beam-and-girder  type.  Especial  care  must  be  exercised  in  this 
respect  in  cold-weather  work.  Yielding  of  the  green  concrete  in  the  slab  may  be  sufficient  to 
crack  the  exterior  columns,  a  thing  which  has  happened  in  the  past. 

It  is  usually  possible  to  so  arrange  the  floor  forms  that  they  may  be  removed  without 
disturbing  some  of  the  props  which  support  the  slab,  and  this  practice  should  be  followed.  It 
is  unwise  to  leave  this  matter  to  the  judgment  of  an  inexperienced  contractor,  who  will  likely 
as  not  pull  out  the  forms  and  put  in  the  props  afterward.  No  rule  can  be  given  but  it  may  be 
said  that  the  time  that  the  slab  should  be  supported  is  a  function  of  the  mean  temperature, 


508 


CONCRETE  ENGINEERS'  HANDBOOK 


fSec.  11-23 


provided  it  has  been  prevented  from  actually  freezing,  and  cases  are  on  record  where  40  days 
was  insufficient. 

In  winter  work  heating  must  frequentlj'"  be  resorted  to,  both  of  the  materials  before  mixing 
and  of  the  slab  after  pouring,  but  unless  the  heated  air  can  pass  over  the  top  of  the  slab,  but 
little  benefit  will  be  derived  from  the  latter  method. 


UNIT  CONSTRUCTION 


23.  Method  of  Construction  in  General. — The  two  main  systems  of  ''unit"  construction 
for  buildings  are  the  Unit-hilt  system  and  the  Ransome  Unit  system.  In  the  first  system 
mentioned,  all  members  are  cast  in  forms  on  the  ground  and  set  in  place,  when  hard,  by  a 
derrick.  The  Ransome  system  differs  principally  in  that  the  slab  is  poured  in  place  after  the 
unit  beams,  girders,  and  columns  have  been  erected.  In  the  Unit-hilt  system  all  the  units  are 
tied  together  by  virtue  of  bars  projecting  into  pockets  or  open  spaces  in  which  concrete  is 
poured. 

24.  Advantages  of  the  Unit  Method. — The  greatest  advantage  obtained  from  the  use 
of  separately  molded  members  occurs  when  a  large  number  of  the  same  size  of  beams,  columns, 

and  girders  are  to  be  employed.  The  same  forms  can 
then  be  used  over  and  over  again.  From  this  it 
follows  that  the  unit  type  of  construction  is  not  likely 
to  have  universal  application  due  to  the  multiphcity 
of  shapes  in  complex  structures.  Study  of  designs, 
however,  should  in  most  cases  reduce  the  number  of 
shapes  to  a  workable  minimum.  Restriction  in  sizes 
of  discontinuous  members  is  also  likely  to  be  a  con- 
trolling factor  and,  under  some  conditions,  narrow  the 
application  of  this  system  to  certain  layouts  governed 
by  the  capacities  of  the  handling  apparatus. 

Where  a  large  number  of  members  of  the  same 
^lui  sys^;m^o7reTntTced-oo""f^^^^^  ^re  required,  «m(  construction  is  likely  to 

be  cheaper  than  monolithic  construction  for  three 
main  reasons:  (1)  the  greatly  reduced  amount  of  falsework  required  as  compared  with  the 
monolithic  type,  (2)  the  reduction  in  the  number  of  men  required  for  the  work  of  construc- 
tion, and  (3)  the  chance  to  carry  on  the  work  under  cover  in  all  kinds  of  weather. 

Shrinkage  cracks  do  not  usually  occur  in  buildings  of  unit  construction  since  all  the  shrink- 
age has  taken  place  in  the  individual  units  before  their  incorporation  into  the  structure.  Every 
element  may  be  inspected  and  approved  before  it  is  placed,  or,  if  desired,  a  given  percentage 
of  the  units  may  be  tested  before  erection. 


Side  Eleva-1-ion 
Fig.  67. — Typical  girders  for  Unit-bilt  system. 


25.  "Unit-bilt"  System. — Figs.  66  to  69  inclusive,  and  Plate  VI  show  the  principle  of 
construction  of  the  Unit-hilt  system  used  by  the  Unit  Construction  Co.  of  St.  Louis.  The 
columns  are  provided  with  brackets  for  the  support  of  the  girders,  and  the  girders  are  set 
on  a  mortar  bed  at  a  distance  back  from  the  center  of  column  sufficient  to  allow  the  column 


Sec.  11-26] 


BUILDINGS 


509 


rods  to  overlap.  The  girder  rods  to  take  negative  moment  over  supports  project  into  the  space 
over  the  columns — the  girders  being  cut  back  so  as  to  give  the  necessary  length  for  embedment 
(Fig.  67  and  Plate  VI).  The  ribbed  slabs  rest  on  shelves  or  ledges  on  the  sides  of  the  girder, 
with  the  top  of  slab  above  the  top  of  girder  so  as  to  permit  the  slab  reinforcing  rods  to  project 
into  the  space  thus  formed  and  provide  for  negative  tensile  stresses.  The  outer  face  of  each 
side  rib  of  slab  has  a  groove,  so  that  the  two  grooves  of  adjacent  slabs  will  form  a  key  for  the 
grout  filling.  No  attempt  is  made  in  the  field  to  obtain  a  complete  bond  between  the  filled 
concrete  and  the  concrete  of  the  separately  molded  members,  since  the  filled  concrete  is  used 
either  in  direct  shear  or  in  compression,  or  as  a  means  for  bonding  the  projecting  rods  in  the 
space  between  the  units. 

It  would  be  impossible  to  enumerate  all  constructions  that  have  been  carried  out  by  Unit- 
hilt  methods,.  The  more  important  applications  are  as  follows:  sea  walls,  caissons,  docks, 
retaining  walls,  tunnel  linings,  culverts,  pipe,  sewers,  fences,  fence 
posts,  telegraph  posts,  piles,  lamp  posts,  warehouses,  factories, 
elevators,  cotton-handling  plants,  cotton  mills,  bridges,  and  via- 
ducts, fireproof  residences,  school  buildings,  railroad  stations, 
roundhouses  and  train  sheds. 

Railroad  work  offers  a  wonderful  field  for  the  development  of 
the  ''unit"  method.  If  it  were  possible  to  standardize  such  struc- 
tures as  engine  houses,  freight  sheds,  snowsheds,  train-sheds  and 
small  stations,  the  construction  of  these  by  the  Unit  method  on 
a  factory  basis  at  central  locations  would  effect  great  economies. 


i^""rTi  


1~ 





Longi+udinaf  Sec-tlon ' 
Fig.  68. — Typical  floor  slab  for  Unit-hilt  system. 


Bottcm  Plan  SecTion 

Fig.  69. — Details  of  column  con- 
struction, Unit-hilt  system. 


26.  Ransome  Unit  System. — The  main  details  of  the  Ransome  Unit  system  are  shown  in 
Plate  VII.  The  usual  reinforcement  is  placed  near  the  sides  of  the  columns  and,  in  addition, 
a  longitudinal  rod  is  inserted  in  a  central  cored  hole  extending  lengthwise  through  the  column. 
The  grouting  of  the  column  is  done  from  the  top  after  the  setting  of  the  girders  and  beams. 
The  cored  hole  is  enlarged  and  flared  out  at  the  bottom  in  order  to  insure  an  even  bed  for  the 
column.  The  main  column  reinforcement  is  not  continuous  from  story  to  story  and  the  caps 
and  bases  of  the  columns  are  enlarged  so  that,  at  these  points,  the  concrete  alone  will  be  able 
to  transfer  the  weights. 

The  main  girders  are  placed  on  top  of  the  columns— the  ends  of  each  girder  being  enlarged 
so  as  to  almost  cover  the  cap  of  the  column.  The  beams  are  made  with  dove-tailed  ends  and 
fit  into  pockets  in  the  girders  (Plate  VII).    In  the  design  of  this  system,  the  vertical  stirrups 


510 


CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  11-26 

Plate  VI 


Plate  VII 


^  U-bar  exTencf/n^ 
from  co/umn 


Recess  to  receJv^e 
■f/oor  s/ab 


i'    II!    !i|  ''' 

Hr--i!r"i— CT^Ir 


Sec-rional  P\an. 


in  F/oor  concre^ 


Sectional  Ellevai-ion 


-Top  afShb 


■Pane/ . 


Derails  of 
Construction  of  the 
'Ransome  Unit  System* 


•~  Bo/rs  ■■  ■^ 

Section  through  SlaO  find  Beam  showing  arrangement  of  centering 


Sec.  11-27] 


BUILDINGS 


511 


must  be  so  arranged  as  to  thoroughly  bind  the  slab  and  beam,  and  make  these  members  act 
as  a  unit.  The  beams  and  girders  are  usually  cast  of  a  depth  equal  to  the  distance  from  the 
bottom  to  the  neutral  axis  only  (Plate  VII).  The  slab  forms  are  erected  between  the  beams 
(which  are  usually  spaced  about  4  ft.  on  centers)  and  rest  upon  ledgers  bolted  to  the  sides  of 
the  beam.  The  beam  and  girders  are  joined  to  the  slab  with  a  beveled  joint,  giving  a  slight 
draft  to  the  forms,  thus  affording  considerable  concrete  around  the  connecting  rods. 

There  is  no  shoring  placed  under  the  floor  during  construction  so  that  the  beam-and-girder 
units  should  be  designed  strong  enough  to  carry  their  own  weight  plus  that  of  forms  and  wet 
concrete  slabs,  in  addition  to  an  allowance  for  impact  from  buckets  and  so  forth.  The  slab 
panels  may  be  removed  in  a  much  shorter  time  than  would  be  permitted  on  monolithic  con- 
struction, since  the  previously  molded  beams  and 
girders  take  care  of  the  entire  load  up  to  the  time 
when  the  full  live  load  is  brought  on  the  floors. 

The  beams  in  some  buildings  have  been  con- 
nected by  means  of  tie  bars  as  shown  in  Fig.  70.  At 
about  the  quarter  points  and  in  the  top  of  each  beam 
and  girder  a  hole  was  cast,  extending  down  into  the  L 
beam  about  3  in.  From  this  to  the  end  of  beam  a 
slot  was  formed.  With  two  beams  end  to  end,  a  rod 
with  a  right-angle  bend  at  each  end  could  then  be 
slipped  in  place  before  the  slab  was  poured.  In  the  more  recent  developments  of  the  system 
(Plate  VII),  the  ends  of  the  reinforcing  rods  project  above  the  tops  of  the  beam  and  girder 
units  and  a  loose  rod  is  inserted  in  the  slab  to  provide  for  negative  moment.  The  beams 
and  girders  are  figured  as  simply  supported  although,  with  proper  design,  the  continuity 
might  probably  be  taken  advantage  of  to  some  extent. 


STEEL-FRAME  CONSTRUCTION  WITH  CONCRETE  SLABS 

27.  Types  of  Construction. — The  steel  skeleton  consists  of  columns,  girders  and  cross- 
beams— the  same  arrangement  as  in  the  monolithic  beam-andrgirder  construction — the  beams 
usually  being  spaced  about  6  ft.  on  centers.  The  many  types  of  this  form  of  construction 
differ  from  each  other  in  the  form  of  slab  steel  used,  the  position  of  the  concrete  relative  to  the 
beam,  and  in  the  use  of  curved  or  flat  slabs. 

28.  Wrapping  of  I-beams. — I-beams  completely  enclosed  in  concrete  should  be  wrapped 
with  wire,  wire  mesh,  or  metal  lath,  to  prevent  the  concrete  below  the  bottom  flange  from  crack- 
ing and  dropping  off.  The  material  used  should  be  of  sufficient  size  to  render  efficient  service 
even  though  it  should,  by  some  accident,  become  corroded.  It  should  be  wrapped  securely  to 
the  I-beam  flange,  and,  at  the  same  time,  sufficient  space  should  be  left  to  effect  a  concrete 
clinch  between  the  wrapping  material  and  the  beam. 

29.  Types  Illustrated. — Fig  71  shows  the  floor  slab  placed  directly  on  the  tops  of  the  steel 
beams.    The  reinforcement  of  the  slab  may  be  either  small  rods,  a  wire  fabric,  or  sheet  re- 

^    inforcement.    The  slab  as  shown  must  be  calculated  as  a  simple 

jk^^^jt.;:^^^^;^>^^^       beam,  since  reinforcement  is  not  provided  for  negative  moment 
±  1        over  the  supports. 

Fia.  71.  Fig.  72  is  a  very  common  form  of  concrete  floor  supported  by 

steel  girders.  The  form  for  constructing  same  is  also  shown. 
The  haunches  of  the  slab  are  carried  down  to  the  lower  flange  of  the  I-beam,  the  under 
surface  of  which  may  be  covered  with  metal  lathing  and  plaster  for  fire  protection  (see  Figs. 
73  and  74).  The  I-beam  is  sometimes  entirely  encased  in  the  concrete  but  it  is  difficult  to 
place  the  material  under  the  lower  flange. 

Concrete  floors  are  sometimes  laid  as  continuous  slabs  with  only  the  upper  part  of  the  I- 
beams  in  the  concrete,  and  sometimes  the  slab  is  so  located  with  reference  to  the  I-beams  that 


512 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-30 


the  metal  is  placed  between  the  beams  instead  of  running  over  them,  as  in  Figs.  75  and  76. 
Still  another  type  of  floor  consists  of  arches  sprung  between  the  lower  flanges  of  the  I-beams 
and  filled  to  the  floor  level  with  cinders. 


^     ■■  B'e"c  foe 


nana  nu-r 

6* iVooci washer 

Fig.  72. 


•  f^laster 


Fig.  73. 


Fig.  74. 


The  Roebling  slab  floor  is  of  many  types,  a  common  form  being  shown  in  Fig.  77.  The 
reinforcement  is  flat  bars,  which  are  bent  at  the  beams  so  as  to  connect  with  the  flange  as 

shown.  Spacers,  which  supply  the  place  of  dis- 
tributing rods,  are  fitted  into  slots  in  the  bars.  A 
m  16-ft.  span  may  be  constructed  with  this  type  of 
floor.  A  flat  ceiling  is  obtained  by  suspending 
metal  lathing  from  beam  to  beam  and  plaster- 


FiG.  75. 


FiG.  76. 


ing.    A  Roebling  segmental  concrete  arch  floor  is  shown  in  Fig.  78. 


Sfee/  rorf.  spacer 


,F/at  bar 


4 


,-Sleeper 


Part  Plan 


Plastering 

Part  Longitudinal  Sectiort 

Fig.  77. — Roebling  slab  floor. 


ROOFS 

30.  Structural  Design. — Concrete  roofs  of  the  usual  type  are  designed  in  the  same  manner 
as  floors.  Any  likelihood  of  vapor  condensing  on  the  underside  of  roofs  in  buildings  where 
steam-laden  or  moist  air  is  to  be  found  may  be  avoided  by  proper  insulation  and  good  ventilation. 

When  roof  girders  or  frames  are  built  monolithic  with  the  columns  in  order  to  reduce 
sizes  of  members,  the  method  and  formulas  given  in  Sect.  10  may  be  employed  to  determine  the 
resulting  moments. 

31.  Loading. — The  roof  of  a  reinforced-concrete  building  should  be  designed  to  carry  the 
weight  of  roof  covering  and  snow  which  may  come  upon  it.  If  the  roof  has  considerable  pitch, 
wind  pressure  should  also  be  considered.  A  roof  load  commonly  assumed  in  temperate 
climates  for  flat  roofs  is  40  lb.  per  sq.  ft.,  in  addition  to  the  weight  of  the  concrete  itself. 

.  The  snow  load  varies  with  the  latitude  and  the  humidity.  As  a  maximum  it  is  approxi- 
mately 30  lb.  per  horizontal  sq.  ft.  in  Canada  and  northern  Wisconsin,  20  lb.  in  the  City  of 
Chicago,  10  lb.  in  Cincinnati,  and  rapidly  diminishes  southward. 


Sec.  11-32] 


BUILDINGS 


513 


The  wind  load,  which  acts  horizontally,  varies  with  the  velocity  of  the  wind.  A  pressure 
of  30  lb.  per  sq.  ft.  of  vertical  surface  is  usually  assumed.  Several  formulas  are  in  existence  for 
determining  wind  pressure  on  inclined  surfaces.  Duchemin's  formula  which  follows,  is  pre- 
ferred by  many  engineers  as  it  is  based  upon  carefully  conducted  experiments : 

2  sin  A 
'l  +  sin2A 

where  P  =  normal  pressure  of  wind  in  pounds  per  square  foot  of  inclined  surface. 
Pi  =  pressure  of  wind  in  pounds  per  square  foot  on  a  vertical  surface. 
A  =  angle  of  inclination  of  the  roof. 

'  The  dead  load  of  any  roof  may  be  estimated  quite  closely  from  the  following  data — weights 
are  per  square  foot  of  roof  surface : 

Five-ply  felt  and  gravel  roof,  6  lb. 
Four-ply  felt  and  gravel  roof,  5H  lb. 
Three-ply  ready  roofing,  0.6  to  1  lb. 

Slates,  ViQ  in.  thick,  7/4  lb,;  ]'i  in.  thick,  9.6  lb.  (the  common  thickness  is  Vie  in.  for  sizes  up  to  10  by  20  in.). 


Shingle  clay  tiles,  11  to  14  lb. 
Spanish  tile,  8  lb. 

Vitrified  roofing  tile,  1  in.  thick,  9  lb.  (including  asphalt  and  five  thicknesses  of  felt,  11^^  lb.). 
Slate  tile,      to  1  in.  thick,  13  lb.  (including  asphalt  and  felt,  Id^i  lb.). 
Tin  roofing,  sheets  or  shingles,  1  lb. 
Copper  roofing,  sheets,  V/z  lb.;  tiles  IVi  lb. 
Corrugated  iron,  1  to  3  lb. 

Skylights  with  galvanized-iron  frames,  H-in.  glass,       lb.;  Me-in.,  5  lb.;  %-m.,  6  lb. 
Plaster,  5  lb. 

Suspended  ceilings,  10  lb. 
Cinders,  45  lb.  per  cu.  ft. 
Cinder  concrete,  112  lb.  per  cu.  ft. 

32.  Prevention  of  Condensation  on  Concrete  Roof  Slabs. ^ — In  storage  warehouses  and 
buildings  of  a  similar  nature,  where  no  artificial  heating  is  required,  condensation  can  be 
almost  eliminated  by  proper  ventilation.  Buildings  of  this  type  may  be  classed  among  those 
requiring  little  or  no  insulation  for  concrete  roofs.  Power  houses,  paper  mills,  roundhouses 
and  similar  structures  with  concrete  roofs,  however,  are  a  class  of  buildings  which  require  the 
best  of  insulation  and  ventilation  to  prevent  condensation.  Between  these  two  extremes  lie 
many  manufacturing  and  industrial  buildings  which,  if  built  of  concrete,  will  require  a  more 
or  less  positive  type  of  insulation  for  the  roof  slab. 

With  these  facts  in  mind  it  can  be  seen  at  once  that  it  would  be  folly  to  use  the  same  kind 
of  insulation  for  all  classes  of  buildings  and  expect  to  obtain  good  results  and  at  the  same  time 
exercise  economy.  In  one  case,  a  certain  method  of  insulation  may  meet  all  the  requirements, 
while  in  another,  on  account  of  different  conditions,  the  results  may  be  entirely  unsatisfactory. 

1  By  Albert  M.  Wolf,  C.  E.,  in  Concrete-cement  Age,  May,  1914, 
33 


514 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-32 


For  this  reason  the  writer  will  refer  so  far  as  possible  to  the  particular  kind  of  condensation 
insulation  which  is  applicable  to  each  type  of  building. 
The  types  of  insulation  to  be  discussed  are  as  follows : 

1.  Roofing  felts  and  quilts. 

2.  Cinder  fill  (with  cement  finish  upon  which  the  roofing  is  laid). 

3.  Cinder-concrete  fill  (covered  with  roofing). 

4.  Hollow  tile  (with  mortar  top  coat  upon  which  roofing  is  laid). 

5.  Combination  hollow  tile  and  cinder  fill. 

6.  Double  concrete  roof  (light  concrete  slab  above  the  main  roof  slab). 

7.  Suspended  ceilings. 

Roofing  Felts  and  Quilts. — If  the  concrete  roof  is  pitched  or  sloped  to  provide  for  drainage 
and  the  building  is  to  be  used  for  ordinary  light  manufacturing,  warehouse  or  storage  purposes 
and  very  little  steam  or  moisture  is  present,  a  heavy  roofing  quilt  or  insulator  placed  under  the 
tar-and-gravel  or  prepared  waterproof  roofing,  will  furnish  sufficient  insulation.  Such  insu- 
lation is  easily  applied,  is  of  light  weight  and  low  first  cost.  The  cost  in  general  amounts  to 
about  1}4:  cts.  per  sq.  ft.  in  place.  It  has  a  disadvantage  which  somewhat  offsets  the  low  cost, 
that  of  being  soft  and  cellular  and  therefore  easily  pierced  or  broken  down,  thus  destroying 
its  insulating  value  and  necessitating  a  renewal. 

Cinder  Fill. — One  of  the  most  common  methods  of  insulating  roofs  is  to  place  a  fill  of 
steam-boiler  cinders  on  the  roof  pitched  to  provide  for  drainage  and  covered  with  a  coating  of 
cement  mortar  about  1  in.  thick  upon  which  the  roofing  is  placed.  This  method  of  insulation 
permits  the  use  of  a  level  roof  slab,  which  in  itself  is  quite  a  saving.  The  extra  cost  of  form- 
work  with  a  roof  sloped  in  one  general  direction  amounts  to  about  3^  to  1  ct.  per  sq.  ft.,  while 
if  the  surface  is  warped  this  extra  cost  will  amount  to  3  or  4  cts.  per  sq.  ft. 

The  cinders,  which  should  be  a  porous  grade  of  steam-boiler  cinders,  free  from  refuse  or 
slag,  should  be  wet  down  thoroughly,  then  placed  on  the  roof,  arranged  to  the  proper  slopes  and 
tamped'  to  an  even  surface.  The  minimum  thickness  of  cinders  at  any  place  should  be  not 
less  than  3  in.  Before  the  cinders  have  had  a  chance  to  dry  out  a  1  :  3  cement  mortar  coat, 
mixed  quite  wet,  should  be  placed  on  the  cinders  to  a  depth  of  about  1  in.  and  given  a  smooth 
float  finish.    After  the  mortar  has  thoroughly  set  the  roofing  may  be  placed. 

It  is  essential  that  the  cinders  be  wet  down  before  hoisting  to  the  roof,  for  if  this  is  done 
after  placing  on  the  roof  slab  the  excess  water  will  stand  on  the  slab  and  cause  trouble  by  seeping 
through  the  ceiling.  If  the  cinders  are  not  wet  down  before  placing,  they  do  not  tamp  well  and 
when  the  surface  finish  of  cement  mortar  is  applied,  the  dry  cinders  will  take  up  the  water  in 
the  mortar  and  decrease  its  strength  and  value. 

With  insulation  of  this  sort  it  is  necessary  to  provide  for  expansion  of  the  top  surface. 
The  top  portion  of  the  fill  and  the  mortar  finish  should  therefore  be  kept  1  in.  or  so  from  all 
parapet  walls  to  allow  for  expansion  joints  to  be  filled  with  some  bituminous  or  asphalt  paving 
pitch. 

A  cinder  fill  weighs  on  an  average  from  65  to  75  lb.  per  cu.  ft.  and  it  is  therefore  important 
that  the  downspouts  be  so  arranged  as  to  keep  the  average  depth  to  a  minimum,  which  will 
usually  be  about  12  in.  The  cost  of  this  type  of  insulation  for  an  average  depth  of  12  in.  is 
ibout  9  or  10  cts.  per  sq.  ft. 

This  insulation  is  solid  enough  to  bear  all  the  usual  weights  coming  upon  it,  gives  no  trouble 
'rom  expansion  and  can  be  readily  used  on  concrete  slabs  which  are  designed  as  future  floors 
m  case  of  the  desire  for  the  addition  of  future  stories  because  of  the  ease  with  which  it  can  be 
torn  up  and  re-used.  It  has  been  used  extensively  on  concrete  warehouses  and  manufacturing 
buildings  and  is  a  very  satisfactory  insulation  for  any  type  of  building  except  power  houses, 
paper  mills  and  other  similar  buildings  where  much  steam  is  present. 

Cinder-concrete  Insulation. — A  porous  cinder  concrete  mixed  in  proportions  of  1  part  by 
volume  of  cement  to  8  parts  or  10  parts  of  porous  screened  steam-boiler  cinders  has  been  used 
to  a  considerable  extent  as  an  insulator.    It  should  be  placed  carefully  so  as  not  to  lose  the 


Sec.  11-32] 


BUILDINGS 


515 


porosity,  in  much  the  same  manner  as  a  cinder  fill,  and  finished  off  with  a  mortar  coat  on  which 
to  lay  the  roofing.  Expansion  joints  should  be  provided  at  all  walls  the  entire  depth  of  the 
fill,  since  on  hot  days  such  a  fill  expands  and  exerts  considerable  pressure.  Many  parapet 
walls  have  been  pushed  out  of  place  because  of  failure  to  observe  this  rule.  A  cinder-concrete 
fill  insulation  should  primarily  be  very  porous,  with  a  rich  mortar  finish  to  seal  the  dead  air 
space  in  the  fill. 

A  cinder-concrete  fill  is  not  so  efficient  an  insulator  as  a  cinder  fill,  the  cost  is  higher  and 
the  danger  of  expansion  is  greater.  The  excessive  weight,  about  100  lb.  per  cu.  ft.,  is  the  main 
disadvantage,  which  means  that  the  roof  construction  must  be  considerably  heavier  in  order 
to  carry  the  load.  The  cost  of  the  cinder-concrete  fill  with  an  average  depth  of  12  in.  will  vary 
from  13  to  15  cts.  per  sq.  ft.,  depending  on  the  height  of  building  and  the  cost  of  cinders. 

Hollow-tile  Insulation. — Hollow  clay  tile  laid  on  a  concrete  roof  slab  and  covered  with  a 
cement-mortar  finish  upon  which  the  roofing  is  laid  forms  a  good  insulation  against  heat  and 
cold  and  resulting  condensation.  The  tile  used  are  3  or  4  in.  thick,  of  the  ordinary  soft  clay 
partition-tile  variety,  with  scratched  surfaces  to  furnish  a  key  for  the  cement-mortar  surfacing 
about  ^-i  or  1  in.  thick.  The  tile  should  be  laid  end  to  end  to  form  continuous  air  spaces, 
with  tar  or  asphalt  expansion  joints  at  all  walls. 

This  insulation  can  be  used  on  sloping  roofs  only  and  in  fact  is  the  ideal  one  for  such  roofs, 
since  it  combines  the  advantages  of  light  weight  (32  to  35  lb.  per  sq.  ft.)  comparatively  low 
cost  and  positive  insulation.  It  can  be  constructed  very  rapidly  and  easily  and  can  be  used 
for  almost  any  type  of  structure.  The  average  cost  of  this  construction  will  be  about  10  to 
12  cts.  per  sq.  ft. 

Combination  Hollow  Tile  and  Cinder  Fill. — Without  doubt  the  best  insulator  is  the  com- 
j  bination  hollow  tile  and  cinder  fill,  for  it  combines  and  augments  the  advantages  of  each  method 
'  considered  separately.    It  is  constructed  in  the  same  manner  as  the  cinder  fill  except  that 
'  the  hollow  tile  are  first  placed  end  to  end  on  the  roof  slab,  and  the  cinders  and  mortar  finish 
placed  thereon.    The  weight  of  this  construction  for  an  average  depth  of  12  in.  amounts  to 
from  70  to  75  lb.  per  sq.  ft.  and  the  cost  is  about  12  to  13  cts.  per  sq.  ft. 

This  insulation  is  as  nearly  perfect  as  can  be  made  without  the  use  of  expensive  cork  insu- 
lation combined  with  tile,  etc.  For  power  houses,  paper  mills,  roundhouses  and  structures  of  a 
similar  nature  it  is  as  nearly  positive  as  can  be  constructed,  and  with  proper  ventilation  no 
trouble  should  be  experienced  from  condensation.  The  dead  air  space  directly  over  the  roof 
slab  afforded  by  the  tile,  and  the  protecting  covering  of  cinders  (which  at  the  same  time  forms 
the  roof  slopes)  to  keep  the  temperature  of  the  air  in  the  dead  air  space  at  the  normal  tempera- 
ture, allow  little  chance  of  condensation  except  when  the  ventilation  is  insufficient.  The 
principal  objection  is  the  weight  of  this  type  of  insulation,  but  where  a  positive  insulator  is 
I  required  the  advantages  cited  overcome  the  disadvantages  of  weight. 

;  Double-roof  of  Concrete  Slabs. — A  somewhat  new  and  little-used  type  of  construction  is 
j  that  of  secondary  concrete  roof  slab  pitched  for  drainage,  supported  on  a  wooden  framework 
I  resting  on  the  concrete  roof  slab.  The  framework  can  be  built  up  of  2  by  6-in.  stringers  set 
'  on  edge  on  the  slab  and  in  turn  supporting  by  means  of  short  struts  and  braces,  2  by  6-in. 

rafters  directly  above  at  the  required  height  and  slope.    The  several  frames  thus  formed  are 

tied  together  with  longitudinal  and  diagonal  braces  at  such  distances  apart  as  can  be  spanned 
'  by  the  thin  concrete  slab  to  be  placed  on  the  stiffened  metal  lath  fastened  to  the  top  of  frames. 

The  ribbed  metal  lath  should  be  lapped  at  the  sides  and  the  ends,  and  securely  fastened  together. 
.  It  will  be  found  most  economical  to  use  the  maximum  span  allowable  for  the  heaviest  metal 
I  lath  obtainable.    This  is  a  No.  24-ga.  stiffened  metal  lath  which  will  support  without  other 

centering  a  2-in.  concrete  slab  before  the  same  has  set  on  a  span  of  6  ft.    After  hardening, 

such  a  slab  will  readily  carry  a  live  load  of  25  lb.  per  sq.  ft. 

The  concrete  of  a  1  :  2  :  4,  or  better  still,  a  1  :  13^2  :  3  mixture  should  be  mixed  rather  dry, 
'  for  if  there  is  an  excess  of  water  some  of  the  cement  will  be  carried  away  when  the  water  drips 

through  the  mesh.    The  coarse  aggregate  used  should  be  a  crushed  stone  or  gravel  passing  a 


516 


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[Sec.  11-33 


^-in.  mesh.  The  slab  should  be  given  a  smooth  float  finish  ready  to  receive  roofing  or  water- 
proofing, which  should  be  of  the  best,  for  if  any  moisture  reaches  the  metal  mesh  it  will  soon 
rust  and  the  wood  supports  rot  out  and  the  roof  be  destroyed.  This  construction  weighs  about 
30  to  35  lb.  per  sq.  ft.  and  will  cost  on  an  average  about  16  cts.  per  sq.  ft. 

This  construction  gives  a  continuous  dead  air  space  over  the  roof  slab  and  if  the  work  is 
well  done  and  the  ends  effectively  closed  it  provides  a  very  effective  insulation  for  any  type  of 
building.  It  has  the  disadvantages  of  high  first  cost  and  the  use  of  a  woodeii  framework,  which 
does  not  bring  the  construction  within  the  fireproof  classification. 

Suspended  Ceilings. — Suspended  ceilings  are  used  quite  frequently  to  prevent  heat  radiation 
and  condensation  on  concrete  roofs.  In  beam-and-girder  construction  good  insulation  can  be 
obtained  by  fastening  a  metal  lath  to  the  bottoms  of  the  beams  with  wires  or  expansion  bolts 
and  applying  a  cement  plaster.  Where  the  spans  are  short  an  ordinary  metal  lath  will  suffice 
but  for  long  spans  (over  2  ft.)  a  stiffened  metal  lath  should  be  used.  The  lath  should  be  lapped 
and  wired  together  at  sides  and  ends  so  as  to  form  a  stiff  surface.  The  type  of  ceiling  just 
described  will  cost  about  6  to  7  cts.  per  sq.  ft. 

For  flat-slab  roofs  without  beams  or  girders  a  different  type  of  suspended  ceiling  is  used. 
This  construction  consists  mainly  of  a  No.  26-ga.  stiffened  metal  lath  ceiling  wired  at  every  rib 
to  3^  by  13^-in.  flats  or  l>^-in.  channels,  5  ft.  c.  to  c,  running  at  right  angles  to  the  ribs,  the 
flats  or  channels  being  supported  by  No.  7  wire  hangers  or  by  ^  by  1-in.  flats  spaced  about  5 
ft.  c.  to  c.  hung  from  the  concrete  roof  slab  and  placed  at  the  time  of  pouring  the  latter.  If  a 
lighter  or  No.  24-ga.  stiffened  metal  lath  is  used,  the  supports  should  be  not  more  than  4  ft. 
c.  to  c.    Such  a  ceiling  will  cost  on  an  average  103'^  cts.  per  sq.  ft. 

These  ceilings  should  be  plastered  with  a  1:5:  12  plaster  consisting  of  hydrated  lime, 
Portland  cement  and  sand,  respectively,  thoroughly  mixed  while  dry  before  adding  water. 
Long  cow-hair  should  be  used  in  the  plaster. 

On  account  of  the  dead  air  space  between  roof  and  ceiling  this  type  of  construction  gives 
a  very  positive  insulation.  The  metal  lath,  however,  has  a  tendency  to  rust  and  experience 
has  shown  that  suspended  ceilings  will  break  down  in  hot  fires.  Then  again  the  roof  slab  must 
be  sloped  or  other  provision  made  for  drainage,  which  adds  to  the  cost.  Suspended  ceilings 
have  been  used  as  insulators  in  nearly  every  class  of  buildings  including  power  houses,  mills 
and  roundhouses  and  have  in  general  given  good  service. 

33,  Concrete  Roof  Surfaces. — Although  concrete  roofs  have  been  designed  to  be  impervious 
without  a  covering  of  any  other  material,  it  seems  to  be  the  general  opinion  that  it  is  difficult  to 
secure  absolute  imperviousness  in  this  type  of  roof  because  of  the  likelihood  of  shrinkage  cracks. 
Some  engineers,  however,  believe  that  the  cracks  may  be  kept  so  minute,  by  properly  reinforcing 
against  all  the  tensile  stresses  due  to  expansion  and  contraction,  that  the  roof  will  stay  water- 
proof. In  fact,  some  large  buildings  have  been  erected  on  this  theory,  and  have  shown  no 
signs  of  leakage.  There  is  no  doubt,  however,  that  a  concrete  roof  without  a  special  covering 
of  any  sort  is  at  least  well  adapted  to  all  structures  where  absolute  imperviousness  is  not  essen- 
tial, as  in  train  sheds,  reservoir  roofs,  and  in  out-of-door  structures  in  general. 

Shrinkage  joints  are  sometimes  introduced  in  concrete  roof  slabs.  These  joints  are  made 
water-tight  by  the  introduction  of  a  trough-shaped  strip  of  copper  or  lead  which  will  take  con- 
traction and  expansion.  If  a  sufficient  number  of  joints  of  this  nature  are  made,  shrinkage 
cracks  will  undoubtedly  be  reduced  to  a  minimum.  To  make  shrinkage  joints  the  slab  must 
be  poured  separately  from  the  beams  and  girders,  and  no  bond  should  be  allowed  between  the 
slab  and  the  roof  framing.  If  steel  beams  are  used,  there  is  no  danger,  but  in  all-concrete  con- 
struction, galvanized  strips,  well  oiled,  or  some  equivalent  should  be  introduced. 

A  maximum  amount  of  reinforcement  against  shrinkage  cracks  will  be  of  little  avail  in  a 
vioncrete  roof  unless  the  concrete  itself  is  impervious.  Methods  of  waterproofing  concrete 
may  be  roughly  classified  as  follows:  (1)  Use  of  a  rich-concrete  mixture  of  such  proportions  of 
sand  and  stone  as  to  produce  maximum  density;  (2)  use  of  waterproof  coatings  or  washes; 


Sec.  11-34] 


BUILDINGS 


517 


(3)  admixture  of  substances  designed  to  produce  impermeability.  It  is  often  advisable  to 
combine  two  or  more  of  these  methods. 

Methods  of  proportioning  concrete  for  maximum  density  are  given  in  Sect.  2.  Plastering 
a  concrete  roof  surface  with  a  layer  of  rich  mortar  has  been  found  effective  when  care  has  been 
taken  to  place  the  same  before  the  concrete  has  taken  its  final  set.  If  such  care  is  not  exercised, 
variation  in  temperature  and  moisture  between  the  concrete  and  plaster  will  be  almost  certain 
to  cause  a  separation.  Troweling  concrete  to  a  dense,  hard  surface,  in  the  same  manner  that 
granolithic  work  is  troweled,  makes  concrete  impervious  and  nearly  equal  to  a  surfacing  of  rich 
mortar. 

The  methods  employed  to  waterproof  concrete  by  using  washes  or  by  introducing  foreign 
ingredients  into  the  mixture  are  given  in  chapter  on  "Waterproofing  Concrete"  in  Sect.  2. 
The  general  remarks  made  there  apply  to  roofs  as  well  as  to  other  types  of  structures. 

A  hard  wearing  surface  is  sometimes  required  in  roof  construction — for  example,  when  it 
forms  the  floor  of  a  roof  garder.  The  roof  surface  in  such  a  case  should  have  a  granolithic 
finish  the  same  as  in  floors,  and  a  form  of  bitumen  emulsion  mixed  with  cement  mortar  may  be 
used  in  making  the  surface  impervious. 

It  is  not  good  practice  to  use  a  concrete  roof  without  covering  on  steep  slopes,  as  the 
slabs  must  then  either  be  laid  quite  dry  (which  does  not  favor  imperviousness)  or  else  top 
forms  must  be  used  to  retain  the  concrete.    The  latter  method  is  slow  and  expensive. 

34.  Separate  Roof  Coverings. — The  felt  and  gravel  roof  is  the  most  common  and  efficient 
form  of  roof  covering.  The  covering  is  composed  of  layers  of  waterproof  felt,  cemented  to- 
gether and  to  the  concrete  by  coal-tar  pitch  or  asphalt.  The  method  followed  is  to  lay  from 
four  to  eight  thicknesses  of  felt  over  the  roof  surface,  each  ply  being  cemented  to  the  preceding 
layer,  and  the  entire  surface  then  floated  with  a  heavy,  flowing  coat  of  pitch  or  asphalt,  in 
which  (while  hot)  clean,  dry,  uniformly  screened  gravel  or  slag  is  embedded,  sufficient  in 
quantity  to  cover  the  surface  thoroughly. 

Asphalt  has  in  the  past  been  preferred  to  coal-tar  pitch  as  a  binding  medium,  but  at  the 
present  time  coal-tar  products  appear  to  be  satisfactory  when  made  to  contain  a  large  percent- 
age of  carbon,  and  are  being  used  by  many  in  preference  to  asphalt.  Asphalt,  however,  seems 
to  be  much  superior  to  coal-tar  pitch  in  ready  roofings. 

The  following  specification  for  a  five-ply  tar  and  gravel  or  slag  roof  has  been  taken  from 
the  Proceedings  of  the  American  Railway  Engineering  Association,  1910  and  is  essentially 
the  Barrett  Co.'s  specification. 

There  shall  be  used  five  (5)  thicknesses  of  saturated  felt  weighing  not  less  than  fourteen  (14)  lb.  per  one 
hundred  (100)  sq.  ft.,  single  thickness;  not  less  than  two-hundred  (200)  lb.  of  pitch;  and  not  less  than  four  hun- 
dred (400)  lb.  of  gravel  or  three  hundred  (300)  lb.  of  slag  from  H  to  size,  free  from  dirt,  per  one  hundred 
(100)  sq.  ft.  of  completed  roof. 

The  material  shall  be  applied  as  follows:  First,  coat  the  concrete  with  hot  pitch  mopped  on  uniformly. 
Second,  lay  two  (2)  full  thicknesses  of  tarred  felt,  lapping  each  sheet  seventeen  (17)  in.  over  the  preceding  one,  and 
mop  with  hot  pitch  the  full  width  of  the  seventeen  (17)  in.  lap,  so  that  in  no  case  shall  felt  touch  felt.  Third,  coat 
the  entire  surface  with  hot  pitch,  mopped  on  uniformly.  Fourth,  lay  three  (3)  full  thicknesses  of  felt,  lap- 
ping each  sheet  twenty-two  (22)  in.  over  the  preceding  one,  mopping  with  hot  pitch  the  full  width  of  the 
twenty-two  (22)  in.  lap  between  the  piles,  so  that  in  no  case  shall  felt  touch  felt.  Fifth,  spread  over  the  entire 
surface  of  the  roof  a  uniform  coat  of  pitch,  into  which,  while  hot,  imbed  the  gravel  or  slag.  The  gravel  or  slag 
in  all  cases  must  be  dry. 

The  coal-tar  pitch  or  asphalt  is  the  life  of  the  roof,  particularly  in  the  topcoating.  The 
gravel  or  slag  should  be  applied  liberally,  in  order  to  completely  bury  the  coat  of  waterproof 
material  and  protect  it  from  injury  due  to  walking  on  the  roof,  and  from  the  action  of  the  sun. 
In  the  following  statements  asphalt  only  will  be  mentioned,  but  it  must  be  understood  that 
the  same  statements  will  apply  to  coal-tar  pitch. 

In  waterproofing,  the  object  of  using  saturated  felt  is  merely  to  provide  a  medium  to 
hold  the  asphalt  together,  and  thus  allow  for  expansions,  contractions  and  settlings.  The 
greatest  care  and  judgment  must  be  exercised  in  laying  felt  to  see  that  it  is  properly  stretched. 


518 


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[Sec.  11-35 


laid  smoothly,  and  that  no  wrinkles  appear.  All  of  the  roofing  felts  on  the  market  are  made  of 
wool  or  flax,  saturated  with  a  preserving  material  that  will  harmonize  with  the  asphalt.  Satu- 
rated wool  roofing  felts  are  compact,  and  although  they  absorb  little  of  the  asphalt,  they  hold 
it  in  repeated  layers  to  constitute  the  body  material  of  the  roof.  The  flax  felt  is  porous  and 
of  strong  texture,  and  absorbs  the  asphalt,  holding  it  within  its  fibers.  Unsaturated  burlap 
or  canvas  can  be  made  to  hold  asphalt  if  first  run  through  a  bath  of  liquid  asphalt  or  tar. 

The  greater  the  amount  of  felt  and  asphalt  used,  the  greater  the  life  of  the  roof.  How- 
ever, if  too  much  asphalt  is  used  on  top,  it  will  run;  hence  the  flatter  the  roof,  the  greater  the 
life.    No  roof  should  have  less  than  100  lb.  of  asphalt  per  100  sq.  ft. 

What  is  known  as  a  felt  and  gravel  roof  should  not  be  used  in  cold  climates,  on  a  surface 
of  greater  pitch  than  about  3  in.  to  the  foot.  In  hot  climates  1  in.  to  the  foot  is  about  the 
proper  maximum.  Where  the  roof  is  of  greater  pitch,  the  gutters  may  be  put  in  with  galvanized 
iron,  copper,  tin  or  piles  of  felt  and  asphalt,  and  the  steeply  pitched  surface  covered  with 
clay  tile  or  slate  shingles  with  lap  joints.  Vitrified  clay  tile  are  made  in  a  great  variety  of 
forms,  flat;  ribbed,  and  corrugated;  but  those  of  some  interlocking  pattern  are  best.  Nailing 
strips  (1  by  2  in.)  should  be  inserted  in  the  concrete  under  each  row  of  tile  or  slate,  but  it  is 
important  that  they  should  be  so  placed  as  not  to  affect  the  strength  of  the  roof  slab.  Slate 
or  tile  should  not  be  used  on  a  surface  with  a  pitch  of  less  than  6  in.  to  the  foot. 

A  most  durable  roof  covering  for  flat  surfaces  (slope  not  exceeding  3^  in.  to  the  foot)  is 
vitrified  roofing  tile  embedded  in  asphalt.  The  tile  consists  of  flat  rectangular  terra-cotta 
tile  about  1  to  13-^  in.  thick,  bedded  in  hot  asphalt,  on  top  of  four  to  six  thicknesses  of  felt  of 
the  kind  mentioned  above.  The  joints  between  the  tiles  should  be  filled  with  asphalt.  Slate 
tiles  also  make  a  good  wearing  surface.  They  are  usually  %  to  1  in.  thick,  by  12  by  12  in.  in 
area. 

Tin,  corrugated  iron,  and  copper  roofings  are  sometimes  placed  on  reinforced-concrete 
buildings.  These  roofings  do  not  have  a  long  life  if  laid  directly  on  the  concrete,  but  seem  to 
give  satisfaction  when  a  wooden  sheathing  is  used  as  a  separator.  Copper  is  expensive  as 
compared  with  other  types  of  roofing  and  is  usually  employed  only  on  very  costly  buildings. 

There  are  many  roofings  on  the  market  which  come  ready  to  lay,  made  on  the  principle 
of  the  built-up  roof.  These  roofings  are  especially  valuable  for  use  in  small  and  isolated  build- 
ings, as  they  do  not  require  the  expert  help  which  is  necessary  for  a  built-up  roof.  In  a  prepara- 
tion which  comes  rolled,  however,  it  is  impossible  to  obtain  a  great  deal  of  waterproof  material, 
and  there  is  an  additional  weakness  in  some  coverings  of  this  type  due  to  the  fact  that  the 
waterproofing  sheets  are  nailed  together  with  a  short  exposed  lap.  Expansion  and  contraction 
of  the  body  material  in  the  course  of  time  opens  holes  alongside  the  nails  and  permits  water  to 
enter.  In  spite  of  adverse  criticism,  however,  there  are  many  ready  roofings  which  seem  to 
give  satisfaction  and  are  used  frequently  on  pitched  surfaces,  and  to  some  extent  on  flat  slopes. 

A  number  of  types  of  metal  and  composition  shingles  are  on  the  market.  Reinforced- 
concrete  slabs  from  5  to  6  ft.  long  have  been  used  for  this  purpose. 

35.  Drainage. — Felt  and  gravel  roofs  should  have  a  pitch  of  at  least  in.  to  1  ft.  in  order 
to  provide  proper  drainage.  Flat  tile,  however,  may  be  employed  on  surfaces  with  a  very 
slight  pitch — preferably  not  over      in.  per  ft. 

Gussets  in  flat  roofs  are  generally  formed  by  placing  a  well-tamped  cinder  filling  over  the 
concrete  slab  and  then  laying  a  1  to  2-in.  surface  of  cinder  or  stone  concrete.  This  type  of 
roof  generally  permits  the  use  of  the  floor  forms  without  much  change  and  there  is  the  ad- 
vantage of  having  all  the  column  heights  of  the  top  story  the  same.  Stone-concrete  surfacing 
seems  to  be  the  most  satisfactory  but  a  cinder  mixture  is  sometimes  specified. 

If  a  flat  ceiling  is  not  required,  or  if  it  is  the  intention  to  employ  a  suspended  ceiling  (Fig. 
79),  the  roof  beams  and  roof  girders  may  be  so  inclined  as  to  give  the  required  roof  pitch.  This 
method  is  advantageous  when  cold  weather  is  likely  to  overtake  the  work  before  it  can  be 
closed  in,  for,  with  the  use  of  cinders  as  a  filling,  there  is  delay  in  placing  the  final  roof  surface. 

Where  concrete  walls  project  above  the  roof  proper,  grooves  or  reglets  about  1  by  1)^  in. 


Sec.  11-35] 


BUILDINGS 


519 


mast  be  left  in  the  concrete  wall  in  which  to  insert  the  edge  of  the  flashing  (see  Fig.  80).  To 
make  a  reglet,  a  strip  of  wood  is  nailed  to  the  forms  and  the  strip  is  taken  out  when  the  forms 
are  removed.  The  flashing  is  keyed  with  the  reglet,  as  shown,  and  cemented  up  with  a  rich 
cement — sometimes  rubber  cement. 

When  metal  standing  flashing  is  specified  on  felt  roofs,  it  is  necessary  to  nail  through  the 
metal  and  felt  into  wooden  strips  embedded  in  the  concrete  slab  in  order  to  hold  the  flashing 
in  place  (see  Fig.  80).  Since  expansion  and  contraction  will  soon  loosen  the  nails,  the  nails 
and  the  flange  of  the  flashing  should  be  covered  with  a  felt  strip  prior  to  coating  the  roof  with 
the  top  coat  of  asphalt  and  gravel.  A  reinforce- 
ment of  flax  felt,  mopped  on  solidly,  appears  to  be  ^-^--m^^m 

as  satisfactory  as  metal  flashing  in  every  way  (see 
Fig.  81).    All  such  felt  flashings  should  be  turned 


— ^i^y. — . 
Fig.  79. 


Air//  rf7rouff/f  A7o/e 
/n  hanc^er 


•z''.;^'  Hanger 


Mefa/'Lafh  and  fVaster  ' 


....^.4'-o'.  

-Suspended  ceiling  construction. 


up  at  the  parapet  walls  and  curbs  at  least  4  in.  at' 
the  highest  points  of  the  roof,  and  not  less  than  12 
in.  high  as  the  outlets  are  approached,  in  order  to 
avoid  overflows  should  the  outlets  become  clogged. 

Fig.  80  shows  the  method  employed  in  apply- 
ing a  galvanized-iron  flashing  for  a  felt  and  gravel  roof  on  a  large  reinforced-concrete  ware- 
house. The  reglet  was  made  to  taper  slightly — that  is,  wider  at  the  outside — in  order  to  per- 
mit the  easy  withdrawal  of  the  wood  strip  that  was  nailed  to  the  forms.  The  groove  was 
made  10  in.  above  the  roof  line.  When  the  concrete  was  being  poured  for  the  roof  floor,  a 
heavy  strip  of  wood  was  laid  with  its  upper  surface  flush  with  the  top  surface  of  the  concrete, 
and  6  in.  from,  and  parallel  with,  the  parapet  wall.  This  strip  was  employed  to  nail  the  edge 
of  the  flashing  to  the  roof  after  the  roof  had  been  covered  with  felt  and  asphalt.  The  nails  and 
the  flange  of  the  flashing  were  covered  with  a  felt  strip  prior  to  coating  the  roof  with  the  top 
coat  of  asphalt  and  gravel. 

Croove  to  be  -f/h'ed 
yyifh  cement  mortar 


•'  _^Gafvan/zecl  irorj 


Nailing  h  1 
Strip 


J/a///nj  strip 
Fig.  80. 


7b  be  mecf  with 
f  cement  mortar 

•^Counterf /ashing 
Felt  and  Gravel 


The  flashing  was  secured  in  the  reglets  by  band-iron  clips,  as  shown.  These  bands  (2  in. 
long)  were  bent  midway  to  an  angle  of  about  30  deg.  After  insertion  they  were  struck  with 
the  hammer  on  the  bend,  which  straightened  them  out  and  jammed  them  in  place,  thereby 
holding  the  flashing.  The  reglet  was  pointed  up  with  a  rich  cement  to  insure  a  water-tight 
connection.  Figs.  81  to  84  inclusive,  show  different  methods  of  flashing  which,  may  be  employed 
(see  also  Figs.  89  and  90,  and  Art.  36). 

In  flat-roof  construction  with  parapet  walls,  all  valleys  in  the  roof  surface  should  lead  to 
drain  boxes.  Fig.  85  shows  the  drainage  scheme  for  part  of  the  roof  of  a  shoe  factory  at  Cam- 
bridge, Mass. 

Drain  boxes,  or  conductor  boxes  as  they  are  usually  called,  have  been  made  in  many  ways — 
lead  or  copper  being  generally  used.  Fig.  86  shows  a  double  copper  box  for  conductors  used 
on  a  factory  building  at  Roxbury,  Mass.    Fig.  87  is  a  sketch  of  a  conductor  box  installed  in  a 


520 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-35 


warehouse  at  Portland,  Maine.  Wire  screens  or  strainers  should  always  be  specified  since  they 
prevent  the  downspouts  from  becoming  clogged  by  leaves,  etc.    The  downspouts  may  be 


F/crt  nie 


'"-■i^.  Nailing  Strips 


Fig.  82. 


carried  down  inside  or  outside  the  building — depending  upon  preference  and  sewer  conditions. 
The  conductors  should  be  cast  iron  when  carried  inside  the  buildings,  while  corrugated  iron, 


Stab 


/     \       71  •  \'i  *• 

/         Na///nq   '  '  •  '  ••'••I 


•strips 
Fig.  83. 


6/atecf  Tile  Copin^.,^ 
Brick  W/-.... 


Composition 
roofing-. 


Fig.  84. 


due  to  its  ability  to  expand  without  breaking,  is  better  on  the  outside  of  the  building  where 
freezing  of  water  in  the  conductors  may  be  expected.    All  vapor  and  soil  pipes  extending 


■Sky fight  over  E/evator 


Fig.  85. 


through  the  roof  should  have  an  expansion  sleeve  soldered  on  and  counterflashed  with  an  in- 
verted copper  cone  attached  to  pipe.  For  discussion  of  conductor  heads  for  roof  drainage,  see 
article  by  A.  M.  Wolf  in  Engineering  News,  May  11,  1916,  page  901. 


Sec.  11-36] 


BUILDINGS 


521 


Fig.  88  shows  the  method  of  draining  a  roof  surface  of  considerable  pitch — a  condition 
under  which  parapet  walls  could  not  be  used.  This  is  called  hanging-gutter  construction. 
The  gutters  should  have  a  slope  of  about  1  in.  in  16  ft. 


Copper  wire  basket 
Copper  box  .. 


Copper  wire  basket--'' 


Outside  funne/' 
inside  fwnnel 


Cast  Jron  ,^..> 
Conductor  pipe 


Plastic  slate 

Cinder  conctefe 


■••  H'oof  slab 

Brass  sleeye  soldered 
to  outside  copper  casing 


Fig.  86. 


The  following  table  will  serve  as  a  guide  by  which  to  proportion  the  size  of  gutters  and 
downspouts : 


Span  of  roof 

Gutter 

Conductor 

Up  to  50  ft. 
50  to  70  ft. 
70  to  100  ft. 

6  in. 

7  in. 

8  in. 

4  in.  every  40  ft. 

5  in.  every  40  ft. 

6  in.  every  40  ft. 

Copper  Strainer  , 


There  is  wide  variation  in  practice  in  the 
number  of  square  feet  of  roof  surface  to  1  sq. 
in.  of  leader  opening,  but  the  above  table 
should  give  some  idea  of  the  general  practice. 


pis 

"^"Copper 

Caiicin^  Joint 


Downspout 
Fig.  87. 


Head  coyensd 
with  voider 


I'xS"  Nailing  strip  Spikes 
■•.  used  for  anchors 


S'-l&oz.  Copper 
OuTter 


^  i",/'  m>od  Screed 


Fig.  88. 


36.  Parapet  Walls. ^ — Parapet  walls  are  of  two  general  types,  brick  or  reinforced  concrete, 
or  a  combination  of  both,  the  type  used  depending  upon  the  architectural  treatment  desired. 
Where  a  roof  is  enclosed  by  parapet  walls,  overflow  openings  in  the  latter  should  be  provided 
at  suitable  points  to  prevent  flooding  of  the  roof  in  case  the  downspouts  become  stopped  up. 
Such  openings  can  be  provided  by  simply  leaving  a  hole  in  the  parapet,  or  better  still,  the 


By  Albert  M.  Wolf,  C.  E.,  in  Concrete,  Dec,  1916, 


522 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-36 


openings  (4  to  8  in.  square)  can  be  lined  with  sheet  metal  or  a  pipe  projecting  at  least  1  in. 
beyond  the  face  of  the  wall. 

Brick  Para-pet  Walls. — Brick  parapet  walls  have  been  used  extensively,  but  unless  properly 
built,  they  are  very  likely  to  give  more  or  less  trouble,  and  if  built  to  avoid  this,  the  usual 
economy  over  concrete  (in  localities  where  brick  are  comparatively  cheap)  is  lost.  This  has 
given  rise  to  the  use  of  concrete  parapets  either  exposed  or  covered  with  a  veneer  of  brick  or 
terra-cotta. 

The  vital  part  of  the  brick  parapet  wall  is  the  inner  side,  and  usually  this  is  made  up  of 
common  brick  laid  up  in  ordinary  lime  mortar.  As  a  result,  many  brick  parapets  in  a  few 
years  become  a  crumbling  mass,  owing  to  the  freezing  of  the  brick  just  above  the  roof  flashing, 
after  being  saturated  with  water  splashing  up  on  them  during  rains,  or  from  snow  piled  on  the 
roof.  Such  a  condition  increases  the  cost  of  maintaining  the  roof  in  proper  condition,  for 
once  the  brick  start  crumbling,  the  flashing  becomes  loosened,  water  finds  its  way  back  of  the 
roofing  and  down  through  the  slab.  This  means  that  the  parapet  must  be  rebuilt,  the  flashing 
and  probably  the  roofing  also,  must  be  replaced. 

Since  the  life  of  a  good  roofing  is  materially  shortened  by  the  conditions  cited  above,  first- 
class  roofers  now  recommend  that  the  inner  side  of  the  brick  parapets  be  built  of  hard-burned 
vitrified  or  paving  brick  laid  up  in  cement  mortar,  and  covered  with  a  waterproof  coping.  In 
addition  to  this,  the  coating  of  the  parapet  (on  roof  side)  with  roofing  tar  or  pitch  up  to  the 
underside  of  the  coping  will  do  much  toward  making  it  more  permanent. 

Where  cinder  or  cinder-concrete  fills  are  used  to  form  the  drainage  slope,  special  attention 
should  be  paid  to  the  anchoring  of  parapet  walls  to  the  concrete  slab  and  the  provision  of  expan- 
sion joints  between  walls  and  roof  filling.  When  cinder  fills  are  used,  a  coating  of  cement 
mortar  from  1  to  IH  in.  thick  is  placed  on  the  top  after  grading  the  cinders  to  the  proper  slopes, 
to  produce  a  firm  foundation  for  the  roofing.  The  mortar  coat  expands  considerably,  as  does 
cinder-concrete  filling,  which  is  sometimes  used,  and  expansion  joints  from  1  to  2  in.  wide  should 
therefore  be  placed  at  all  walls  extending  down  through  the  mortar  topping  or  cinder  concrete. 
These  joints  should  be  filled  with  a  tar  or  asphalt  paving  pitch  which  will  perform  its  function 
of  completely  filling  the  joint  under  all  conditions  of  weather. 

Lack  of  proper  provision  for  expansion  of  roof  fills  has  been  the  cause  of  the  pushing  out 
of  line,  and  rendering  dangerous  many  brick  parapets.  For  this  reason,  in  addition  to  the 
expansion  joints,  it  is  well  to  anchor  the  brick  walls  to  the  spandrel  slabs  or  girders  by  means  of 
stub  bars  bent  up  from  the  roof  slab  or  spandrel.  No  rules  for  exact  size  and  spacing  of  such 
anchor  bars  can  be  given,  but  in  general  J-^  in.  diameter  bars  projecting  up  into  the  wall  for 
about  2  ft.  at  a  spacing  of  from  18  in.  to  2  ft.  will  do  the  work.-  Of  course  it  is  highly  essential 
that  the  wall  be  built  in  solid  around  the  rods  with  good  cement  mortar. 

Another  detail  of  importance  is  the  flashing  slot  and  strip  left  in  the  parapet  to  provide 
a  means  of  fastening  the  flashing  and  counterflashing  and  making  waterproof  the  roofing  at 
the  parapets.  A  very  satisfactory  detail  for  flashing  of  ordinary  tar  and  gravel  roofing  at 
parapets  is  shown  in  Fig.  89.  This  detail,  recommended  as  good  practice  by  the  American 
Railway  Engineering  Association,  makes  use  of  a  2  by  4-in.  timber  with  one  edge  beveled,  laid 
continuous  in  the  parapet  at  the  proper  height  in  place  of  a  stretcher  course  of  brick.  This 
serves  as  a  nailing  strip  for  a  light  wooden  strip  holding  the  flashing  and  counterflashing  in 
place.  After  placing  the  flashing  the  slot  is  completely  sealed  up  with  cement  grout  or  roofing 
cement. 

Concrete  Parapets. — For  the  proper  flashing  of  concrete  parapet  walls  the  detail  shown  in 
Fig.  90  can  be  recommended.  A  2  by  4-in.  piece  of  lumber  is  ripped  on  the  diagonal  as  shown 
and  then  placed  in  the  forms  at  the  desired  height,  the  upper  strip  being  securely  nailed  thereto, 
so  as  to  insure  its  removal  when  forms  are  taken  down,  while  the  lower  piece  is  just  tacked  to 
forms  (from  outside)  with  wires  or  nails  driven  into  it  as  shown  to  anchor  it  to  the  concrete. 
The  flashing  and  counterflashing  are  then  placed  in  the  same  manner  as  for  brick  walls. 

As  generally  designed,  concrete  parapets,  in  addition  to  retaining  or  masking  the  drainage 


Sec.  11-36] 


BUILDINGS 


523 


slopes,  carry  a  portion  of  the  roof  load  as  beams,  but  owing  to  the  fact  that  they  are  generally 
much  deeper  than  required  to  simply  carry  the  load,  other  considerations  besides  the  load  must 
be  taken  into  account.  That  is,  enough  reinforcing  must  be  provided  and  distributed  in  a 
manner  which  will  prevent  the  formation  of  expansion  and  contraction  cracks  resulting  from 
the  excessive  changes  of  temperature  to  which  side  walls  are  subjected.  Ordinarily  parapets 
are  at  least  3  ft.  deep  overall,  and  usually  this  depth  is  much  more  than  is  required  to  resist 
the  bending  moments  induced  therein,  especially  in  flat-slab  construction  where  the  portion 
of  the  flat  slab  adjacent  to  the  parapet  carries  most  of  the  roof  panel  load.  This  means  that  a 
very  low  percentage  of  steel  will  be  required  to  resist  the  tensile  stresses  produced  by  bending, 
in  fact,  it  may  be  such  small  amount  as  to  be  incapable  of  resisting  the  stresses  set  up  by  tem- 
perature changes.  For  this  reason,  it  is  always  well  to  so  detail  the  reinforcement  of  the  portion 
of  the  parapet  above  the  roof  as  to  have  not  less  than  25  to  30%  of  longitudinal  reinforcement 
arranged  somewhat  as  shown  in  Fig.  91  with  plenty  of  vertical  reinforcement  in  the  form  of 


Z'xA'Confimous 

^■-Sfrlp 

\-Counfer 
f (ashing 

V' Flashing 
^Sjoofing 

[■Hasfic  cemenf 
or  pitch 

Cinder  fill 

Consf.joinf- 

^'orlaiwrsfn.^  t^- 
Lap  ar  mid  span : 

Z-i"5tr  or  larger 
at  Cols,  only 


l''Clear- 


T  ifori'Sfn^ighf- 

\  i'orm" Stirrups 
■  ltfol8"cfo  c. 


-  -. ,  i  T  ^'oni'Str.  Lap 
'^r^:^-^  --''af  mid  span- 


\Consf  Joinf 
\    Roof  line 


Fig.  89. 


Fig.  90. 


Fig.  91. 


stirrups  to  tie  together  the  portions  of  parapet  poured  at  different  times  (portion  below  and 
above  roof  line). 

Concrete  parapets  should  always  be  designed  and  reinforced  as  fully  or  partially  continu- 
ous beams,  depending  upon  the  location  thereof  and  the  condition  of  end  supports,  for  unless 
this  is  done  unsightly  cracks  are  sure  to  appear  near  the  supports.  If  the  parapet  walls  are  of 
such  form  as  to  require  pouring  in  two  operations  (as  in  Fig.  91)  they  will,  of  course,  not  be  so 
strong  as  if  poured  in  one  operation,  and,  therefore,  if  the  total  depth  is  to  be  considered  effect- 
ive a  bending  moment  coefficient  somewhat  lower  than  used  in  the  formula  for  fully  continuous 

beams,  viz.,  M  =^2'  ^^^^1^  be  used.    In  the  writer's  opinion,  this  should  be,  for  beams  of 

the  type  in  question,  M  =  for  interior  spans  and  M  =  for  end  spans  at  support  and 
mid-span. 

Parapets  seldom  require  very  much  diagonal  tension  reinforcement  owing  to  the  depth 
of  same  and  the  relatively  light  loads  to  be  carried,  and  the  use  of  bent  bars  is  therefore  seldom 
warranted,  since  the  stirrups  used  to  tie  the  portions  of  wall  together  can  be  made  of  sufficient 
number  to  care  for  all  diagonal  tension  stresses  in  excess  of  that  which  the  concrete  alone  will 
resist.  At  corners  extra  horizontal  bars  should  be  provided,  bent  around  the  corner  so  as  to 
lap  with  the  main  bars,  for  unless  this  is  done,  cracks  are  sure  to  develop,  owing  to  expansive 
and  contractive  forces  acting  at  right  angles  to  each  other.    In  large  buildings  it  will  be  found 


524 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-36 


advisable  to  provide  expansion  joints  in  parapets  about  every  200  ft.  over  columns,  the  spans 
adjacent  to  such  joints  being  designed  and  reinforced  same  as  end  spans. 

Where  concrete  parapets  are  covered  with  brick  or  terra-cotta  which  forms  a  part  of  the 
architectural  treatment,  they  must  be  reinforced  to  resist  the  twisting  action  produced  by  the 


Fig.  92.  Fig.  93. 


weight  of  the  material  hung  from  the  concrete  (see  Figs.  92  and  93).  When  the  concrete  wall 
supporting  the  ornamental  part  of  the  parapet  or  cornice  is  not  very  high,  as  in  Fig.  92,  the 
stresses  thus  produced  can  be  taken  care  of  by  placing  vertical  bars  or  stirrups  so  as  to  reinforce 


8  "»  /4  " 3 earns.. .  glp  "  6-4  "e-O^  " 


Section  through  Machine  Shop 


l"'/?oc/s9"c^^p7\  ^^.^  fRods  ll"c.to 


No.  7z  A  Fabric 


Section  B-B 
Fig. 


the  wall  as  a  cantilever  with  sufficient  longitudinal  reinforcement  to  resist  the  tensile  stresses 
due  to  beam  action  in  a  vertical  plane.  If  the  concrete  portion  of  the  parapet  is  relatively 
high,  and  the  ornamental  stonework  or  terra-cotta  projects  a  considerable  distance  beyond 


Sec.  11-36] 


BUILDINGS 


525 


the  face  of  the  wall,  or,  in  other  words,  if  the  center  of  gravity  of  the  entire  parapet  lies  outside 
the  face  of  the  concrete  wall,  buttresses  should  be  used  at  the  columns  and  the  wall  reinforced 
as  a  counterfort  wall  between  the  buttresses.  The  main  reinforcement  in  the  buttresses  (at  the 
back)  should  be  well  anchored  into  the  floor  construction  or  into  the  column  below  and  after 
extending  up  the  back  of  the  buttress  be  bent  down  in  front  of  the  longitudinal  wall  bars,  thus 
giving  a  positive  support  for  the  continuous  wall  slab.  Buttressed  parapet  walls  should  also 
be  reinforced  to  take  care  of  the  ordinary  beam  action  which  may  develop  due  to  the  weight 
of  the  parapet.  The  same  bending-moment  coefficients  are  recommended  as  for  ordinary 
roof  parapets  previously  described. 


Fig.  94B. 

If  the  covering  of  brick  or  terra-cotta  is  only  a  few  inches  thick,  it  can  be  supported  by 
spandrel  angles  anchored  to  the  concrete,  and  placed  wherever  offsets  occur  in  the  veneer. 
In  addition  to  these  angles,  corrugated  metal  brick  ties  set  in  the  concrete  should  be  built 
into  the  brick  joints  to  aid  in  holding  the  brick  in  place.  Terra-cotta  or  stonework  which 
projects  9  in.  or  more  beyond  the  face  of  concrete  should  be  anchored  to  the  parapet  by  bolts 
passing  through  the  webs  of  the  blocks  of  terra-cotta  or  by  bent  plate  anchors  securely  fastened 
into  the  stone  courses.  These  anchors  should  be  used  in  addition  to  the  spandrel  angle  supports 
previously  mentioned  (see  Figs.  92  and  93).  When  a  well-designed  concrete  parapet  is  used, 
there  is  no  danger  of  failure  of  the  main  support  of  the  cornice,  and  if  the  spandrel  angles  and 
anchors  are  properly  placed  and  well  covered  with  mortar  when  placing  the  veneer,  practically 
all  danger  of  part  of  the  cornice  falling  is  removed. 


526 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-37 


37.  Sawtooth  Construction. — Sawtooth  roofs,  in  general,  have  been  found  especially 
well  adapted  for  machine  shops  and  factories,  where  it  is  desirable  to  have  a  uniform  daylight 


Fig.  95. — Cross-section  detail  of  sawtooth  roof. 


illumination  over  the  entire  floor  area.  In  reinforced  concrete,  unfortunately,  this  type  of 
construction  is  expensive  because  of  the  irregularities  of  the  forms,  and  has  been  employed  only 


Fig.  96. 

to  a  limited  extent  on  that  account.  Typical  designs  of  sawtooth  roofs  are  shown  in  Figs.  94A, 
94B,  95  and  96.  The  skylights  are  usually  arranged  to  face  the  north,  as  the  sun's  rays  would 
be  undesirable  and  would  cause  excessive  heat  in  the  building  in  the  summer  time. 


poO>^^>^  \\ 

Frame       ^^^^^  \\ 

fGrouT 

'A 

7/e  beam  ■ 

-f  -1 

Girder-- '' 

Fig.  97. — Cross-section  showing  typical  arrangement  of  units  in  sawtooth  construction,  Unit-hill  system. 

Fig.  96  is  a  sketch  of  a  sawtooth  roof  used  in  a.  cotton  mill  at  East  Boston,  Mass.  The 
girders  supporting  the  sawtooth  were  made  of  sufficient  stiffness  so  that  no  horizontal  tie  rods 


Sec.  11-38] 


BUILDINGS 


527 


were  necessary.  The  lines  of  columns  for  the  sawtooth  span  are  20  ft.  c.  to  c.  and  two  girders 
are  located  in  each  bay. 

A  sawtooth  roof  construction  using  separately  molded  members  has  been  developed  by  the 
Unit  Construction  Co.  of  St.  Louis  (see  Art.  25).  Fig.  97  is  a  cross-section  showing  the  typical 
arrangement  of  units.  The  roof  portion  of  the  sawtooth  rests  at  its  lower  end  on  a  ledge  in 
the  girder  and  at  the  upper  end  on  a  ledge  in  the  skylight  frame.  The  lower  end  of  the  frame 
also  rests  on  a  ledge  in  the  girder  and  the  horizontal,  beams  are  provided  in  order  to  tie  in  the 
building,  and  for  the  possible  support  of  shafting  or  other  installations.  The  skylight  frame 
extends  from  column  to  column  and  consists  essentially  of  a  large  flat  plate  into  which  the 
window  frames  are  cast.  The  connections  are  made  in  practically  the  same  manner  as  the 
floor  connections  for  this  system  of  unit  construction  as  described  in  Art.  25. 


Transverse  sectior>  Typical  elevation 

Fig.  98. 


Sawtooth  skylights  are  usually  glazed  with  wire  glass,  held  in  metallic  frames,  so  that  the 
entire  construction  is  fire-resisting. 

38.  Trainshed  of  "Unit-bilt"  Construction. — A  trainshed  built  by  the  Unit-hilt  system 
is  shown  in  Fig.  98  (see  Art.  25). 

COLUMNS 

39.  Details  of  Design. — Columns  exceeding  15  diameters  in  length  should  be  avoided  as 

but  few  tests  have  been  made  on  columns  of  such  slender  proportions.  Fortunately,  however, 
columns  longer  than  15  diameters  are  quite  rare  except  in  roof  stories  where  a  light  roof  load 
often  requires  very  light  sections.  Where  long  columns  must  be  used,  the  reduction  formula 
given  in  Art.  9,  Sect.  8  may  be  used  in  their  design. 

A  high  percentage  of  longitudinal  reinforcement — say  above  4  to  6% — is  undesirable  on 
account  of  the  uncertainty  of  the  strength  of  such  columns.  In  fact,  increase  in  the  proportion 
of  cement  is  usually  much  to  be  preferred  to  a  high  steel  percentage,  not  only  because  the  cement 
gives  a  more  definitely  known  increase  in  strength,  but  also  because  it  is  a  cheaper  column  rein- 
forcement than  steel.    In  no  case  should  a  leaner  concrete  mixture  than  1  :  2  :  4  be  used. 

All  columns  should  be  reinforced  with  at  least  four  %-in.  round  rods  or  four  ^^-in.  square 
bars  whether  or  not  such  reinforcement  is  theoretically  required.  This  should  be  done  to 
guard  against  the  possibility  of  eccentric  loading  and  for  safety  in  construction. 

Provision  should  be  made  in  all  cases  for  the  bending  moment  which  will  be  developed 


528 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-39 


by  unequally  loaded  panels,  eccentric  loading,  or  uneven  spacing  of  columns.  Especially  is 
this  true  for  wall  columns  and  corner  columns.  Moment  in  columns  due  to  unsymmetrical 
floor  loading  may  be  found  as  explained  in  Sect.  10.  Moments  in  columns  due  to  bracket 
loads  may  be  found  by  the  formulas  of  Art.  10,  Sect.  8.  The  stresses  and  amount  of  reinforce- 
ment required  for  a  column  subjected  to  bending  as  well  as  direct  stress  may  be  found  as 
explained  in  Sect.  9. 

The  maximum  allowable  stress  in  a  column  due  to  bending  and  direct  stress  may  be  taken 
considerably  greater  than  for  direct  stress  only,  since  the  maximum  stress  does  not  occur 
over  the  whole  cross-section  of  the  column  but  simply  at  the  outside  edge.  The  bending 
moment  also  rapidly  diminishes  along  the  column  from  the  maximum  value  used  in  the  stress 
computations.  A  unit  stress  15%  greater  than  for  direct  compression  may  be  permitted  pro- 
vided the  unit  stress  due  to  the  maximum  loading  centrally  applied  is  not  greater  than  the 
allowable  for  direct  compression. 

In  structures  with  inflammable  contents  where  a  special  fireproofing  is  not  provided  around 
concrete  columns,  l}i  in.  on  all  sides  should  be  considered  as  protective  covering  and  then  this 
thickness  should  not  be  included  in  the  calculations  for  strength.  A  less  thickness  than  1^  in. 
should  be  sufficient  where  the  contents  of  a  building  are  not  especially  inflammable.  In  no 
case,  however,  should  the  steel  be  nearer  the  surface  than  1^  to  2  in.  since  it  is  desirable  to 
prevent  any  tendency  of  the  vertical  rods  to  buckle  under  working  loads.  For  square  or 
rectangular  columns  the  corners  should  be  beveled  or  rounded,  as  sharp  corners  are  more  seriously 
affected  by  fire  than  round  ones. 

It  is  advisable  in  all  cases  to  place  occasional  horizontal  hoops  around  the  vertical  steel. 
Although  tests  do  not  show  that  they  are  absolutely  necessary  if  a  1  ^  to  2-in.  concrete  covering 
is  provided,  yet  it  is  good  practice  to  employ  them  as  an  additional  precaution  against  any 
buckling  of  the  rods  under  small  loads.  Such  hoops,  also,  serve  to  keep  the  rods  in  place  during 
the  pouring  of  the  concrete,  and  should  not  be  farther  apart  than  12  in.  nor  exceeding  about 
16  times  the  diameter  of  the  vertical  rods.  For  columns  of  moderate  size,  J^-in.  wire  hoops 
are  generally  used  12  in.  on  centers. 

Bands,  hoops  or  spirals  to  be  considered  effective  should  have  a  clear  spacing  not  greater 
than  one-sixth  (preferably  one-tenth)  the  diameter  of  the  enclosed  column — in  no  case,  however, 
more  than  23^  in. — and  should  be  equal  in  amount  to  at  least  1  %  of  the  volume  of  the  column 
inside  the  hoops  (see  report  of  the  Joint  Committee  in  Art.  7,  Sect.  8).  It  should  be  noted 
that  the  Joint  Committee  recommends  an  increase  in  the  allowable  working  stress  on  the  con- 
crete of  hooped  columns  only  when  the  ratio  of  the  unsupported  length  of  column  to  the 
diameter  of  the  hooped  core  is  not  greater  than  10. 

It  should  always  be  kept  in  mind  that  hoops  and  spirals  are  tension  reinforcement  and 
subject  to  all  the  rules  governing  the  design  of  such  steel.  If  hoops  are  used,  the  ends  should 
lap  a  sufficient  distance  to  secure  the  requisite  grip,  or  else  the  ends  should  be  bent  toward  the 
center  of  the  column  to  accomplish  the  same  purpose.  When  spiral  reinforcement  is  employed, 
it  is  important  to  have  one  continuous  piece  from  top  to  bottom,  or  else  joints  should  be  made 
as  just  explained. 

Hooping  should  extend  from  the  bottom  of  the  column  to  the  under  side  of  the  slab  above 
and  adequate  means  should  be  provided  to  hold  it  rigidly  in  place  so  as  to  form  a  column,  the 
core  of  which  will  be  straight  and  well-centered.  For  ordinary  percentages  of  hooping,  tests 
show  that  wire  of  high-carbon  steel  gives  a  much  larger  increase  in  the  ultimate  strength  of 
column  than  wire  of  mild  steel. 

The  core  of  a  hooped  column  should  preferably  be  circular  in  cross-section,  but  square  and 
rectangular  hoops  are  sometimes  employed  in  practice.  (The  Joint  Committee  recommends 
that  only  circular  hoops  be  employed.)  In  such  cases,  the  hoops  are  probably  less  effective, 
but  it  is  not  known  how  much.  The  ideal  condition,  theoretically,  is  hooped  columns  of  cir- 
cular cross-section  with  circular  cores. 

When  light  vertical  rods  are  used  they  may  be  spliced  by  lapping  a  sufficient  distance  above 


Sec.  11-39] 


BUILDINGS 


529 


the  floor  level  (about  30  diameters)  to  develop  the  requisite  bond  strength.  They  should 
be  bent  slightly  inward  at  the  top  in  order  to  come  just  within  the  rods  of  the  column  above, 
thus  preventing  any  tendency  of  the  load  coming  down  from  the  upper  rods  to  bulge  the 
column.  Rods  much  over  an  inch  in  diameter  should  be  milled  square  and  butted  together 
in  a  secure  manner. 

The  splicing  of  large  rods  may  be  effected  by  joining  them  in  rather  closely  fitting  pipe 
sleeves.  All  such  splices  should  be  made  just  above  the  floor  level  and  not  more  than  12  in. 
above  the  same.  Since  each  rod  should  find  a  bearing  on  a  rod  below,  the  number  of  rods 
increases  downward  in  the  building  and,  unless  the  loading  is  eccentric,  great  care  should  be 
taken  to  have  the  rods  symmetrically  arranged  in  each  story.  A  splice  of  this  kind  is  good 
for  compression  in  the  rods  but  is  of  no  use  when  the  stress  is  tension.  Rods  in  tension  may 
be  spliced  by  using  short  extra  rods  at  the  splice.  These  short  rods  should  extend  above  and 
below  the  joint  far  enough  to  develop  the  requisite  bond  strength.  Rods  may  extend  through 
several  stories  if  so  desired,  but  it  is  difficult  to  hold  them  in  place  while  concreting  the  lower 
lengths. 

At  the  bottom  of  the  columns,  the  loads  from  the  rods  should  be  distributed  over  the 
footing  by  means  of  a  steel  bearing  plate.  In  order  not  to  overstress  the  concrete  in  the  column, 
the  concrete  immediately  below  the  plate  should  be  enlarged  so  as  to  bring  the  average  pressure 
within  the  allowable.  Tests  show  that  if  considerable  lengths  of  the  longitudinal  reinforcing 
rods  are  bent  outward  into  a  reinforced-concrete  footing,  the  strength  of  column  will  be  about 
as  great  as  when  these  rods  are  bedded  on  a  metal  plate.  The  results,  however,  also  show  that 
the  use  of  metal  plates  leads  to  greater  uniformity  and  strength.  Base  plates  should  be  set 
in  a  thin  grout  of  proportions  about  1  :  2  in  order  to  prevent  hollow  places  under  the 
plates. 

In  our  modern  city  buildings  where  the  floor  space  on  the  first  floors  is  valuable,  the  use 
of  a  steel  column  core  presents  a  very  economical  and  efficient  construction.  To  be  able 
to  count  upon  the  concrete  in  such  columns,  the  steel  itself  should  be  sufficiently  rigid  to  act 
as  a  column  and  the  concrete  should  be  well  enclosed  either  by  the  steel  form  itself  or  by  means 
of  bands  or  hooping.  However,  if  the  amount  of  steel  is  very  large,  the  relative  value  of  the 
concrete  is  more  uncertain,  and  its  element  of  strength  should  be  neglected.  The  best  conc^- 
nection  between  column  and  beam  is  a  structural-steel  seat  riveted  to  the  column,  and  of  suffi- 
cient 'size  to  carry  the  entire  load  in  bearing.  These  seats  do  not  appear  in  the  finished  surface 
of  rooms  and  their  stiffness  is  considerably  assisted  by  the  concrete  shell.  Where  structural- 
steel  columns  are  used,  the  floor  beams  and  girders  should  be  figured  as  simply  supported  unless 
the  usual  continuity  rods  are  run  through  the  column. 

Wherever  concrete  walls  are  to  be  built  against  concrete  columns  at  some  later  time, 
weather  breaks  or  key  ways  should  be  formed  in  the  columns.  This  is  accomplished  by  nailing 
small  strips  on  the  inside  of  the  forms.  Where  windows  are  to  be  set  into  column  reveals, 
window  ties  should  be  embedded.  In  order  to  obtain  a  low  cost  for  formwork  it  is  better 
to  vary  square  columns  in  one  dimension  rather  than  in  two,  both  on  account  of  the  columns 
themselves  and  the  beams  framing  into  them. 

For  the  same  reason  it  is  advisable  to  keep  the  story  heights  uniform  so  that  the  forms  will 
not  have  to  be  cut  off  or  spliced  from  story  to  story.  If  the  story  heights  vary  it  is  better  to 
have  the  high  stories  at  the  bottom  as  it  is  cheaper  to  cut  off  the  forms  than  to  splice  them. 

Cinder-concrete  cylinders  have  been  used  to  some  extent  as  a  protective  covering  for  rein- 
forced-concrete  columns  and  also  to  take  the  place  of  column  forms.  In  Factory  No.  1  of  the 
plant  of  the  Bush  Terminal  Co.,  South  Brooklyn,  N.  Y.,  the  interior  columns  are  cylindrical 
and  composed  of  an  outside  shell  of  cinder  concrete  23^  in.  thick.  These  cinder-concrete 
cylinders  were  prepared  in  advance  in  2-ft.  lengths,  in  a  zinc  mold,  with  spiral  hooping  and 
expanded  metal  forming  the  inner  surface.  After  hardening,  they  were  set  one  upon  another 
in  the  building  and  filled  with  concrete. 

Hooped  concrete  columns  with  cast-iron  cores  known  as  the  Emperger  columns  have  been 
34 


530 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-40 


\ 


W 


7^ 


/ 


X 


receiving  some  attention.  It  is  claimed  that  by  using  the  hooped  reinforcement  high  working 
stresses  may  be  used,  thus  reducing  the  size  of  column  (see  Engineering  Record,  March  3,  1917). 

Hollow  reinforced-concrete  columns  have  been  used  in  heating  and  ventilation  systems, 
the  air  heating  and  fan  systems  being  in  a  pent  house  on  the  roof.  The  heated  air  is  forced 
down  the  hollow  columns  and  is  distributed  to  the  different  floors  through  openings  in  the 
columns. 

40.  Loading. — In  addition  to  its  own  dead  weight,  a  column  should  be  designed  to  carry 
the  live  and  dead  loads  of  the  roof  and  floors  above.  The  full  live  load  on  floors  must  be  used 
in  designing  columns  for  warehouses  or  buildings  for  heavy  mercantile  and  manufacturing 
purposes.  In  other  buildings,  however,  of  five  stories  or  more  in  height,  where  it  seems  reason- 
able to  suppose  that  a  full  live  load  will  never  occur  on  all  floors  simultaneously,  reductions 
may  be  made  as  follows: 

The  live  load  on  the  floor  next  below  the  top  floor  may  be  assumed  at  95  %  of  the  allowable  live  load,  on  the 
next  lower  floor  at  90%,  and  on  each  succeeding  lower  floor  at  correspondingly  decreasing  percentages,  provided 
that  in  no  case  shall  less  than  50%  of  the  allowable  live  load  be  assumed. i 

41.  Column  Brackets. — Column  brackets,  such  as  are  shown  in  Fig.  99,  are  serviceable 
in  stiffening  the  building  frame  and  in  decreasing  the  stress  in  the  girders.    They  should  not, 

however,  be  considered  as  decreasing  the  girder  span, 
but  simply  as  so  much  additional  protection  against 
failure. 

Brackets  are  usually  required  in  high  buildings 
in  order  to  brace  the  frame  properly  against  wind 
stresses.  If,  however,  buildings  are  both  high  and 
narrow,  the  stresses  in  the  members  due  to  wind 
should  be  figured  and  proper  provision  made  for 
the  same.  For  method  of  computing  such  stresses, 
see  Art.  9,  Sect.  10. 

A  column  supporting  a  roof  may  also  serve  as  a  crane  post  or  to  carry  a  heavy  load  on  a 
bracket.  For  method  of  computing  the  bending  moment  due  to  such  eccentric  loading  see 
Art.  10,  Sect.  8 

Illustrative  Problem. — In  order  to  show  in  detail  the  method  of  column  design,  the  computation^  will  be 
given  for  the  design  of  a  typical  interior  column  of  a  three-story  building  assuming  that  no  bending  moment  is 
likely  to  be  caused  by  unequally  loaded  panels  or  eccentric  loading.  The  columns  will  be  spaced  21  ft.  on  centers 
both  ways  and  the  two  intermediate  beam  design  of  Plate  I,  page  448,  will  be  adopted  as  the  typical  floor-bay 
design  for  all  three  floors. 

The  height  from  finished  floor  to  finished  floor  will  be  made  13  ft.,  except  the  basement  which  will  be  made 
11  ft.  A  concrete  mixture  of  1  :  1}-^  :  3  will  be  used,  which  will  allow  a  working  stress  of  565  lb.  per  sq.  in.  when  longi- 
tudinal steel  only  is  employed  and  870  lb.  per  sq.  in.  when  eff'ective  hooping  is  provided.  As  recommended  in  the 
final  report  of  the  Joint  Committee  (see  Appendix  B)  the  concrete  will  be  assumed  to  have  a  modulus  of  elasticity 
one-twelfth  that  of  the  steel.    The  size  of  octagonal  columns  will  be  given  in  terms  of  the  short  diameter. 

The  load  coming  from  the  roof  may  be  found  by  multiplying  the  total  shear  on  both  girder  and  cross-beam  by 
2,  and  adding.  Assume  end  reaction  from  roof  beam  at  16,100  lb.  and  from  roof  girder  at  36,200  lb.  Then  the 
roof  load  is 

(2)  (36,200)  +  (2)  (16,100)  =  104,600  lb. 

Similarly,  each  floor  load  is 

(2)  (55,300)  +  (2)  (25,000)  =  160,600  lb. 

The  building  in  question  will  be  considered  as  for  manufacturing  purposes  and  no  reduction  in  live  load  will 
be  m^de.    The  complete  design  of  column  is  given  on  page  531.    Tables  of  Sect.  8  will  be  used  in  the  design. 

The  recommendations  of  the  Joint  Committee  will  be  followed  and  the  amount  of  vertical  steel  is  in  every 
case  less  than  4%  and  more  than  1  %.  The  pitch  of  the  spiral  hooping  is  given  to  the  nearest  \i  in.,  as  the  mills 
that  fabricate  spirals  can  manufacture  them  to  such  a  pitch.  The  weight  of  column  has  been  figured  for  a  length 
2  ft.  less  than  the  story  height  in  order  to  compensate  somewhat  for  taking  the  weight  of  beams  and  girders  as 
extending  from  center  to  center  of  supports.  It  is  the  intention  to  splice  all  rods,  not  lapped,  by  means  of  a  tightly 
fitting  pipe  sleeve  about  12  in.  long. 


Fig.  99. 


From  1916  New  York  City  Building  Code,  Bureau  of  Manhattan. 


I 


Sec.  11-41] 


BUILDINGS 


531 


Third-floor  Columns. — Assume  weight  of  column  at  2700  lb.  Then  the  total  load  is  104,600  +  2700  = 
107,300  lb. 

Taking  the  percentage  of  longitudinal  steel  at  0.025,  Table  1  shows  that  a  column  whose  effective 
diameter  is  14  in.  (total  diameter  17  in.)  is  good  for  111,000  lb.  Table  3  shows  weight  of  column  per  foot  to 
be  (1.66)  (150)  and  the  total  weight  (1.66)  (150)  (11)  =  2740  lb.  Table  1  shows  the  steel  area  to  be  3.9  sq.  in. 
and  from  Table  4  we  get  seven  Ji-in.  round  rods. 

Second-floor  Columns. — Assume  weight  at  3800  lb.,  then  total  weight  is  107,300  +  160,600  +  3800  = 
271,700  lb. 

Table  1  shows  that  with  1%  spiral  and  3.5%  longitudinal  rods,  a  column  whose  effective  diameter  is  17  in. 
(total  20  in.)  is  satisfactory.  Table  3  shows  the  weight  to  be  (2.30)  (150)  (11)  =  3800  lb.  Table  1  gives  the  steel 
area  of  7.9  sq.  in.  and  Table  4  shows  that  fourteen  Ys-in.  round  rods  will  be  sufficient.  From  Table  2  for  pitch  of 
2]^^  in.,  the  area  of  spiral  is  0.106  sq.  in.  (say  H-in.  round)  and  the  length  of  spiral  per  foot  is  256  in.  For  mini- 
mum pitch  of  l^i  in.  the  area  of  spiral  is  0.088  sq.  in.  (say  Vs-in.  round)  and  the  length  per  foot  is  366  in.  The 
11  X  12 


value  of 


d'^  18 

First-floor  Columns.— Total  load  is  271,700  +  160,600  +  6500  =  438,800  lb. 

Table  1  shows  that  a  column  of  26  in.  outside  diameter  and  with  2  %  longitudinal  steel  will  answer.  Weight  is 
(3.89)  (150)  (11)  =  6420  lb.  Steel  area  is  8.3  sq.  in.,  or  fourteen  li-in.  round.  Area  of  spiral  is  0.144  sq.  in.  (say 
^^6-in.  or  ^6-in.  round)  and  length  per  foot  is  347  in.  For  minimum  pitch  of  2^4  in.,  area  is  0.13  sq.  in.  (say  Ji^-in. 
round)  and  the  length  per  foot  is  386  in. 

Basement  Columns. — Total  load  is  438,800  +  160,600  +  7500  =  606,900  lb. 

Size  of  column  from  Table  1  is  31  in.  outside  diameter  or  28  in.  effective  for  p  =  1.5%.  Steel  area  is  9.2  sq. 
in.  Use  fourteen  1-in.  round  rods.  Weight  of  column  is  (5.53)  (150)  (9)  =  7500  lb.  Area  of  spiral  is  0.175  sq.  in. 
(say  H-in.  round)  and  the  length  of  spiral  per  foot  is  422  in. 

Column  Schedule 


=  7H- 


Story 

Kind  of 
load 

Amount 
of  load 

Shape  and 
size  of 
column 
(short 

diameter) 

Vertical 

steel 
(rounds) 

Spiral  (core 
3  in.  less 
than  diameter 
of  column) 

Third.  .  .  . 

Roof 
Column. . 

104,600 
2,700 

17  in. 

octagonal 

7-li  in. 

Total. .  .  . 

107,300 

Second. .  . 

Floor  

Column. . 

160,600 
3,800 

20  in. 
octagonal 

14-Ji  in.  (lap 
above  27  in.) 

dia.    =  in. 
pitch  =  2>^  in. 

Total..  .  . 

271,700 

First 

Floor. . .  . 
Column. . 

160,600 
6,500 

26  in. 
octagonal 

14-%  in.  (lap 
above  27  in.) 

dia.    =  J'ie  in. 
pitch  =  23^^  in. 

Total..  . 

438,800 

Basement 

Floor. . . . 
Column. . 

160,600 
7,500 

31  in. 

octagonal 

14-1  in. 

dia.     =  >2  in. 
pitch  —  2]y^  in. 

Total..  . 

606,900 

Illustrative  Problem. — It  will  be  of  interest  to  investigate  the  columns  in  the  foregoing  problem  concerning 
stresses  due  to  unbalanced  load.  Since  the  columns  just  designed  represent  standard  practice,  the  following  investi- 
gation will  serve  to  point  out  the  effect  of  unbalanced  loading  upon  such  a  design.  AH  diagrams  referred  to  in  this 
problem  will  be  found  in  Sect.  10. 

From  a  comparison  of  Diagrams  6  to  10,  it  may  be  seen  that  the  largest  moments  in  interior  columns  due  to 
unbalanced  loads  will  occur  in  the  second  tier  columns. 

Assuming  the  neutral  axis  of  the  girder  in  Plate  I  to  be  governed  by  the  fact  that  the  beam  is  doubly  rein- 
forced, kd  is  found  to  be  13.1  in. 
I  =  Ic  +  nis 

(15)(13.1)3  (15)(22.9)3 


Ic  = 


71.100  in." 


nia 


47,300  in.* 


532 


CONCRETE  ENGINEERS'  HANDBOOK 


ISec.  11-42 


Whence 


I  =  118,400  in.4  and  Ki  =  ^^^^  =  471  in.3 


For  the  basement  column,  similarly, 

I  =  41,760  in.4  and        =  316  in.3 
For  the  first  tier  column, 

I  =  20,300  in.4  and  K3  =  131  in.^ 
^0'=  0.675       Kz'  =  0.278       Ko'/K/  =  2.42. 

From  an  examination  of  Diagram  10  it  may  be  seen  that,  for  these  values  of  Ka'  and  Ko'      Kz',  the  moment 

F 

at  the  end  of  the  first  story  columns  will  not  exceed  20%  of  -j*    Therefore,  for  the  live-load  moment, 
^      My  2/  (110,250)(21)(11.5)(0.20) 

f^—  =  Wl-j  =   =  262  lb.  per  sq.  in. 

This  is  the  extreme  compressive  unit  stress  in  the  concrete  due  to  unbalanced  loading.  It  may  be  noted  that  the 
panels  either  way  from  the  loaded  one  have  no  live  load.  Thus,  referring  to  the  design  of  this  column  in  the  pre- 
vious problem,  the  total  load  carried  by  the  column  under  present  conditions  is 

438,800  -  (^^^"^^^^Q)  =  383.800  lb. 

Now  for  a  given  column,  in  which  no  load  is  assigned  to  the  spiral  steel,  the  concrete  unit  stress  due  to  direct  load  is 

 I  

A[l  +{n-  1)  p] 

Then  in  the  above  case 

383  800 

•^^  =  (415.5)[1  +  (0.02)(11)]  =  "^^^  ^'5- 
This  stress,  when  combined  with  that  caused  by  the  unbalanced  load,  gives 

/c(max)  =  262  +  757  =  1019  lb.  per  sq.  in. 

A  re-design  is  advised. 

Illustrative  Problem. — The  moment  in  an  outer  column  of  the  same  size  as  the  interior  column  of  the 
preceding  problems  may  be  computed  in  the  following  manner.  The  dead-load  moment  may  be  computed  with 
the  girder-end  fixed,  and  the  live-load  moment  with  the  girder-end  hinged.  The  two  results  may  then  be  added 
together  as  the  most  probable  moment  in  the  column.    For  the  live  load  (Case  XI), 

F  r  3(131)  T     ^  F 

l2(131)-f  471  +  2(48.3). 
=  (0.474) fl  10,250)  (21)=  1,097,000  in.-lb. 


r  r  n^idL)  -1  t 

"  7  L2(131)-f  471  +  2(48.3)J  "  ^-^^  1 
=  {OA 

For  the  dead  load  (Case  XII), 


1-  0.265? 


I  L3(131)  +  2(471)  +  3(48.3)  J        '  I 
=  (0.265)  (50,350)  (21)  =  280,000  in.-lb. 
Total  moment  =  1,377,000  in.-lb. 
^     „  ,       (1,377,000)  (8. 5) 

For  flexure  /  =   300          =  ^'^^       P^^"  sq-  in. 

which  is  the  stress  due  to  flexure  only,  at  the  top  or  bottom  of  the  first-story  column.  The  direct  load  on  this 
outside  column  will  be  438,800  2,  plus,  say,  50,000  lb.  for  the  spandrel  load  above  the  first  floor.  The  direct 
stress  is 

.  269,400 

=  (415.5)  [1  -h  (0.2) (12)]    =  P^'" 

Thia,  added  to  the  flexure  stress  above,  gives  for  a  total  stress 

/c(max)  =  576  +  523  =  1099  lb.  per  sq.  in. 


WALLS  AND  PARTITIONS 

42.  Bearing  Walls. — The  two  principal  types  of  reinforced-concrete  office  and  factory 
buildings  differ  only  in  the  character  of  the  outside  walls.  A  skeleton  type  is  the  common  form 
of  construction  but  bearing  walls  are  built  occasionally. 

Although  the  bearing-wall  type  of  construction  is  naturally  the  only  type  employed  in 
concrete  residences,  it  has  not  been  found  in  much  favor  for  manufacturing  and  commercial 
buildings  in  general.    Of  course,  a  building  with  monolithic  wall  construction  possesses  great 


Sec.  11-43] 


BUILDINGS 


533 


rigidity  when  properly  designed  and  reinforced,  but  it  cannot  be  erected  as  rapidly  as  buildings 
with  other  wall  types,  and,  unless  great  care  is  employed  in  construction,  there  is  a  likeli- 
hood of  defects  occurring  in  casting  the  work.  There  is  also  difficulty  in  obtaining  a  uniform 
color  for  the  wall  surfaces. 

Concrete  walls  are  either  of  single  thickness,  or  of  double  thickness  with  an  air  space 
between.  One  method  of  obtaining  an  air  space  is  by  building  in  a  central  course  of  hollow- 
tile  blocks.  Double  walls  render  the  interior  of  the  building  less  subject  to  changes  in  tem- 
perature and  more  completely  moisture-proof,  but,  in  the  ma- 
jority of  office  and  manufacturing  buildings,  single  walls  are  not 
objectionable  and  make  a  great  saving  in  floor  space.  Occa- 
sional projections  or  pilasters  improve  the  appearance  and  add  to 
the  strength  of  a  single  wall.  Building  codes  usually  specify  that 
concrete  bearing  walls  are  to  be  made  the  same  thickness  as 
brick  bearing  walls. 

Except  in  residences,  bearing-wall  footings  must  usually 
be  reinforced.  A  cantilever  projection  is  formed  on  each  side  of 
the  wall  and  the  amount  of  reinforcement  may  be  determined  as 
for  a  simple  cantilever  beam  (see  Art.  5,  Sect.  12). 

43.  Curtain  Walls. — In  the  usual  type  of  construction,  wall 
girders  are  placed  at  each  floor  and  the  reinforced-concrete  walls 
(called  curtain  walls)  are  designed  merely  to  fill  in  the  panels  be- 
tween the  columns  and  girders  which  form  the  skeleton  frame 
of  the  building.  They  are  not  intended  to  carry  any  weight 
but  need  to  be  strong  enough  to  withstand  wind  pressure  of  30 
lb.  per  sq.  ft.  Such  walls  may  be  designed  as  slabs  carrying  a 
uniformly  distributed  load  and  supported  on  all  four  sides. 
Figuring  in  this  way,  using  the  above  value  for  the  wind  pres- 
sure, a  wall  in  ordinary  building  construction  will  never  exceed 
33^  to  4  in.  in  thickness,  which  is  the  practical  limit  for  ease  in 
construction.  In  fact,  6-in.  walls  will  generally  be  required  in 
order  to  obtain  sufficient  imperviousness  to  moisture.  Also,  a 
6-in.  wall  is  usually  cheaper  than  a  4-in.  wall  owing  to  the  greater 
ease  of  pouring  the  concrete  and  placing  the  reinforcing  steel  in 
position.  A  4-in.  wall,  however,  is  all  that  is  needed  for  fire 
protection.  Building  codes  usually  specify  a  minimum  thickness 
of  8  in. 

In  addition  to  the  consideration  of  wind  pressure,  concrete 
walls  are  reinforced  generally  for  the  purpose  of  preventing  cracks 
and  guarding  against  accidents  during  or  immediately  after  con- 
struction, except,  of  course,  where  lateral  pressures  occur,  when 


Ca/.  7/ 


the 


First  Floor  Plan 

Fig.  100. — Lang  building, 
Haverhill,  Mass. 


beam  action  must  be  considered.  The  reinforcement  gener- 
ally consists  of  yi  to  3'^-in.  rods  placed  both  horizontally  and  ver- 
tically from  12  to  18  in.  apart. 

Slots  in  the  columns  are  made  by  nailing  a  strip  on  the  inside  of  the  column  forms.  In 
this  way  the  curtain  walls  are  mortised  into  the  columns  and  a  contraction  joint  is  formed,  so 
that  the  contraction  to  be  provided  for  is  due  only  to  the  curtain  wall  itself. 

When  curtain  walls  are  employed  with  a  small  percentage  of  window  area,  it  is  customary 
to  use  both  horizontal  and  vertical  reinforcement,  the  same  as  when  the  wall  covers  the  entire 
panel,  and  to  place  one  or  more  rods  near  the  edge  of  the  slab  about  all  openings.  When  wire 
fabric  is  used  for  reinforcement,  the  edges  of  the  openings  are  stiffened  by  bending  back  the 
fabric  into  a  U-shape. 

Where  a  large  percentage  of  the  outside  wall  of  a  building  is  used  for  windows,  as  is  gener- 


534 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-43 


4'/?ffof  S/ab  ■  ^"*^ocfs  9*c  foe. 


/z'.Zo'Cof. 
^'(*  Hoops 


/e'.zo'Co/ 

4-S''<f  Pods  /Z'-3' 


/0-f^//00pS  //'',/7* 


4-/^'P  Rods  /3'-0' 
/0-^'''^//oops  /7'/7' 


zs'-o' 


20'xSO'Co/ 
8-M"<f/?ads  /S^-3" 
J2'i"^/yoops/3^/7^ 


{20'x20'Co/ 
\d-/j"^J?ods/si6 


/e"x26"Co/. 


HOOPS /7^.y7' 


6- ^^Rod^ 

^' *  Hoops /2'cibC 


4- /"^Pods /S'-O^ 
/O'^"^ Hoops  /3{y7^ 


/S"x24'Co/. 

4-$°^Rods/Z'-3'' 

/0-:^'^HoopsJj'My 


/S''x24''Co/ 

4-^''^A;ds/g*r^ 

/0-;^''fiHoopsAfiJ7'^ 


/0-;f'^Hoops  /3!£/^ 


^*,24''Co/. 
4-^'*/?ods/2'-s'^ 

Hoops  /3"m/7" 


/6',24'Co/ 
4-f^/?ods/2'-6" 
/O-^'*  Hoops  /3''*2/' 


^"x24''Co/ 
/2-;l:'^ Hoops  /3'lc/S^' 


F/n/s/7ed  f/rst  f/oor 


Dnvewqy 


Earth  /7// 


TYPICAL   CROSS  SECTION  THROUGH  BUILDING 
Fig.  101. — Lang  building,  Haverhill,  Mass. 


Sec.  11-43] 


BUILDINGS 


535 


ally  the  case  in  factory  buildings,  the  wall  proper  consists  of  little  more  than  columns  with 
deep  wall  beams  or  wall  girders  forming  belt  courses  between  them.  The  spandrels,  or  walls 
directly  beneath  the  window  sills,  may  be  reinforced  so  as  to  act  as  the  upper  part  of  the  wall 
beams,  but  the  usual  method  is  to  consider  this  portion  as  separate  from  the  beam  and  merely 
reinforce  with  small  rods  (in  some  cases  with  wire  fabric)  so  as  to  prevent  cracks  and  to  reinforce 
the  construction  during  the  setting  of  the  concrete.    If  this  is  done,  the  spandrels  may  be  put 


*^      1 1  Finished  BHJ^  F/oor 


F/n.  ^'^r/oar 


l£-I"<f  Hoops        4  ^-^^ 


ffi 

r.,  Section 
\^^E!rL3Lfloor  co(s. 58-49  Ind.SI 
"  53-66 


i  ^Hi! 

Fin  /KiF/oor 


1=^ 


Section  opposite  Windov?3 


Elevation  of 
Typical  Interior  Column 


(27  Cols; 


4'  4" 


'  l"x4  "m-ather  Brea^ 


4  Rods  /g"'^ IS- J"  ^ 
/Z-y^floops  /z"c.foc  is"/S 

Elevation  of  ^C^^XBldg  \Une 

Typical  Exterior  Column        ^  L-^e-'J 

Section  opposite  Panel  Walls 
For  Cols.2-)3  Incl.  21-32  Incl 
72-99  Incl. and  15  (53 Cols.) 


—  *-i 

"^'^7  Foadyyay  Beam 
^\fvt>e  put  in  /afer 


•■^J  BracJfef 

i-  -  ForCois  2-6  inc/ 

:" 
^  tVl 


7-J2 


Bracket 


Fin.  Basement  F/oor 


Details  of  East  Cols 


Cols.  I  &  7/  0pp.  Windows 


■I6-: 


3^ 


-  ~~—f,i 4  Keyyyay 


4"^ifoc>ps 
l-ie'ct^c. 
Cols  I  a  71  Opposite  wall  Panels 
Col.  71  as  shown 
Col.  f  Opposite  Hand 


^^""S/ab  distributing  rods 
y''     Stair  landing  s/ab  rods  ^ 
turn  up  into  pane/  yyaZ/s  S-6 
2--^" conrinuous  rods  at  stair 
/andin^s.  2- to  tar  sides 
■  .-Fin  Bl!^ F/.  of  columns 


i."mod 


Detail  of  "Typical  Wall  Panel 


Fig.  102. — Details  of  Lang  building,  Haverhill,  Mass. 


in  after  the  main  structural  parts  have  been  cast,  in  the  same  manner  as  complete  curtain  walls. 
This  saves  time  in  the  erection  of  the  building  and  allows  the  use  of  more  care  in  obtaining  a 
neat  finish  on  the  spandrel  walls. 

In  Fig.  102  two  spandrel  sections  are  shown,  one  where  wall  beams  are  employed  and 
the  other  where  only  the  floor  slab  and  spandrels  form  the  exterior  belt  course.  Figs.  100  to 
106  inclusive  show  many  of  the  details  of  the  Lang  Building  at  Haverhill,  Mass.  Many  of 
the  details  are  referred  to  elsewhere. 


536 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-43 


£/crsf/c  cement 


4  "Concrete  75p  screecfecf  fo  Xme/ 

yyi7terprc>of/r7£r  and  -SiJ/ic/  ^  "'^^^'^'^ 

£/asf/c  Ce/77e/7f: 


£d^e  of  Concrete  Si// 
PIpn  of  Elevator  Door  Opening 

Bo/red  to  co/omn 
Fig.  103. — Details  of  Lang  building,  Haverhill,  Mass. 


Sec.  11-43] 


BUILDINGS 


ELEVATlOn 


SECTION 


1  I  8  NAILING 


^  ■    %           EDGE  or  5ILL 

'cast 

SLOCK 

5-4'oPETlING 

8'-0i' 

•  POIlTlQH'Or'nWT'n,GDR.'PLAH  ' 

'  jnownie;LOCATioN:orDa5UiJHown'AwvB 


Fig.  104. — Details  of  Lang  building,  Haverhill,  Mass. 


538 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-43 


Sec.  11-44] 


BUILDINGS 


539 


Reinforced  concrete  is  well  adapted  to  the  construction  of  walls  where  considerable  strength 
is  required,  but  in  very  thin  walls,  such  as  curtain  walls,  it  becomes  a  relatively  expensive 
building  material  on  account  of  the  cost  of  forms.  Brick,  concrete  blocks,  or  terra-cotta  are 
often  used  on  this  account,  not  only  for  spandrel  walls,  but  to  cover  entire  wall  panels. 

44.  Brick  and  Other  Veneer. — From  an  architectural  standpoint  it  sometimes  becomes 
necessary  to  cover  the  exterior  columns  and  walls  with  brick,  terra-cotta,  marble,  limestone,  or 
other  material.    The  facing  or  veneer  is  usually  laid  after  the  structural  frame  is  completed. 


•Stairs  at  Rear  of  Building 

PIPE  RAIL  DETAILS 
Fig.  106. — Details  of  Lang  building,  Haverhill,  Mass. 


A  brick  veneer  generally  consists  of  one  thickness  of  brick,  and  this  is  tied  into  the  concrete 
work  by  means  of  copper  or  galvanized-iron  ties.  These  ties  are  usually  about  %  in.  wide 
and  are  tacked  to  the  form  boards  in  such  a  manner  that  about  4  in.  of  the  tie  will  be  embedded 
in  the  concrete  work.  When  the  forms  are  removed,  the  portion  of  the  tie  lying  flat  against  the 
forms  is  bent  out  as  shown  in  Fig.  107.    A  tie  should  be  provided  for  about  every  4  sq.  ft.  of 


540 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-45 


wall  surface.  Brick  facings  should  be  supported,  at  least  at  every  floor,  by  a  ledge  formed  in 
the  concrete.  Angle  irons  are  usually  employed  to  carry  stone  and  brickwork  over  door  and 
window  openings. 

Fig.  108  shows  one  method  of  supporting  a  stone  lintel.  The  anchor  at  the  top  should  be 
noted. 


Fig.  107. 


The  arrangement  of  the  ties  and  supports  for  terra-cotta  varies  greatly  with  the  design. 
The  facing  is  usually  supported  by  projections  in  the  concrete  fitting  into  openings  in  the  terra- 
cotta, forming  a  sort  of  dovetailing.  Iron  anchors  then  tie  the  two  together.  It  is  very  im- 
portant that  suitable  play  be  provided  for,  as  terra-cotta  cannot  be  made  to  exact  dimensions. 
Stone  facings  are  also  supported  by  projections  in  the  concrete,  the  same  as  terra-cotta,  but 
the  stone  can  be  made  to  more  nearly  fit  any  simple  shape  given  to  the  concrete  ledge. 


Fig.  108. 


45.  Window  Openings. — The  arrangement  of  floor  slab  and  wall  beam  in  Fig.  108  makes 
it  possible  to  obtain  the  maximum  amount  of  light  within  the  building;  that  is,  the  window 
frames  are  run  as  close  as  possible  to  the  underside  of  the  floor  slab.  It  should  be  noted  that 
to  accomplish  this,  the  beams  should  either  be  run  parallel  with  the  walls  of  the  building,  so 
that  none  of  the  beams  will  take  bearing  on  the  lintel,  or  else  the  floor  arrangement  should 
be  similar  to  that  shown  in  Fig.  101  where  only  parallel  girders  are  employed  spaced  relatively 
close  together.  If  beams  run  parallel  with  the  walls,  the  spacing  of  the  beams  may  be  returned 
at  the  corners  by  a  diagonal  girder  as  illustrated  in  Fig.  109.  By  so  doing  the  windows  may 
be  made  the  same  height  throughout. 


Sec.  11-45] 


BUILDINGS 


541 


Reinforced-concrete  buildings  to  be  considered  fire-resisting  should  have  windows  of  wire 
glass,  held  in  metallic  frames.  Wire  glass  is  either  ribbed,  rough,  maze,  or  polished  plate 
having  wire  embedded  in  its  center  during  the  process  of  manufacture.  The  wire  netting 
used  for  this  purpose  is  similar  to  ordinary  chicken  netting  with  about  a  1-in.  mesh.  It  is 
embedded  in  the  glass  at  a  very  high  temperature 
which  insures  adhesion  between  the  netting  and  glass, 
and  the  two  materials  become  one  and  inseparable. 

If  the  glass  is  broken  by  shock  or  by  intense  heat,  it  J-^r^  .v.  '^^.T^ 

remains  intact.    It  is  this  property  which  gives  wire 
glass  its  fire-retarding  qualities. 

Metal  frames  are  made  in  a  great  variety  of 
forms  to  meet  all  purposes.  Sashes  may  be  station- 
ary, sliding,  pivoted  either  horizontally  or  vertically, 


GJa^s-. 


\ 


\  T 

\^  L,_ 


Norma/  6/ refer, 

 [_.  

Normal  Beams 


Fig.  109. 


Fig.  110. 


hinged,  or  double  hung  with  weights  like  an  ordinary  window.  Sash  may  also  be  obtained 
which  will  close  automatically  and  lock  under  fire  by  the  fusing  of  a  link  or  other  means  to  ac- 
complish the  same  result.    A  number  of  sections  of  steel-sash  windows  are  shown  in  Figs.  110, 

,         111,  and  112.    These  sections  are  included  to  show 
'  '   ,  '  '        a  few  of  the  different  methods  of  fastening  metal 
frames  to  the  walls  or  wall  columns. 

When  properly  constructed,  a  tin-covered  wood 
shutter  is  a  most  effective  window  protection. 
There  is  one  objection,  however,  to  the  use  of  shutters 
on  window  openings  and  that  is,  they  must  neces- 
sarily be  open  while  the  building  is  in  use,  and,  when 


/inchor 


Secrion 
through 
Jamb 


i>race  T- frame 

Finished  sill 
■formed  after 
sash  are  set 
Line  of  rou^h  yyalhr. 


Grout 

!  Glazing  C//p 


\7a 


Vertical 
Section 


Jamb 


Fig.  111. 


Fig.  112. 


the  need  comes  for  them,  they  are  apt  to  be  overlooked  and  not  closed.  They,  moreover, 
hide  a  fire  and  are  unsightly  for  many  locations.  Frames  and  sash  of  wood  covered  with  metal 
are  sometimes  used — the  wood  furnishing  the  strength  and  the  metal  the  protection.  Note  the 
combination  of  wood,  tin  and  steel  in  the  window  design  shown  in  Fig.  113, 


542 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-45 


Automatic  steel  rolling  fire  shutters,  placed  either  on  the  outside  of  window  openings  or 
in  the  window  reveals  immediately  in  front  of  the  window  frames  and  sash,  form  the  least 
objectionable  appearing  type  of  shutter  protection  for  windows,  and  seem  to  be  entirely  ade- 


J 


Countersunk 
rap  Screyrs  in 
J  "'  /"  Stops 


Fig.  113. 


Fiu.  114. 


Fig.  115. 


Section  through 
Jamb  above 
Transom  Bar 


Section  through 
Box  and  Jamb 


Weight  Box 


rrr 


Fio.  116. 


Section  1-hrough 
Basement  Window 
Fig.  117. 


quate  for  all  ordinary  conditions.  Open  sprinklers,  or  water  curtains  as  they  are  frequently 
called,  are  sometimes  used  in  connection  with  shutters  or  wire  glass  windows,  but  do  not  seem 
to  be  very  efficient  in  themselves  except  in  very  moderate  exposures. 


Sec.  11-46] 


BUILDINGS 


543 


Fig.  114  shows  a  window  construction  with  ordinary  wooden  sash  employed  in  a  large 
hospital  in  the  Middle  West.  Fig.  115  shows  the  window  construction  in  a  shoe  factory  at 
Cambridge,  Mass.  Double-hung  window  details  for  a  building  at  Boston,  Mass.,  are  shown 
in  Fig.  116.  A  detail  of  a  basement  window  opening  is  given  in  Fig.  117.  Fig.  118  shows  a 
common  window  and  wall  construction. 


Tar  ar?cf  ffraye/  Poof" 


/6  oz.  Copper-' 


i"°Pods  4'-0^/or7^  /S^c.foc. 


Wood  Sash  and 

tY/rp  6/ass 


-Cast  Stone  St// 


Bhc/r  Wa/F 
befyreen 

/^"  co/umns 


Floor  Plan 

Fig.  118. — Truck  garage.  Pacific  Mills,  Lawrence,  Mass. 

46.  Door  Openings. — Doors  in  a  reinforced-concrete  building  should  be  fire-resisting,  the 
same  as  windows,  and  may  be  of  either  the  hinged,  sliding,  or  rolling  type.  If  tin-covered  wood 
doors  are  provided  on  openings  in  interior  partition  walls,  they  are  generally  hung  on  inclined 
tracks  so  that  they  will  close  automatically.  Where  it  is  desirable  to  keep  them  open,  an 
automatic  release  operated  by  a  fusible  link  is  provided. 


544 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-46 


Sliding  and  rolling  doors  are  generally  used  only  for  large  openings  such  as  driveway  and 
freight-elevator  entrances  and.  are  usually  arranged  to  close  automatically  in  case  of  fire.  Slid- 
ing doors  should  have  the  rails  on  which  they  operate  protected  by  metal  shields  to  prevent 
obstruction..  Steel  rolling  doors  are  made  in  horizontal,  jointed,  sectional  strips,  which  wind 


Section 
through 
Head 

Hin^e 

Section 
through 
Transom  Bar 


Section 
through 
Head 

Sash 


Section  throu3h 
Trcjngom  Bar 


Section 
through  Jamb 


"Sectfon  through 
Jamb 


Strap  Hinge 

^OQuHle  shecifhing 
battsns  ip  form  panels 
Fig.  120. 


up  on  a  roller  placed  in  a  pocket  above  the  opening,  the  ends  moving  in  metal  grooves  to  hold 
them  in  place  (see  Fig.  118).  There  are  a  number  of  types  of  vertically  operated  doors.  A 
common  type  for  freight  elevators  is  shown  in  Fig.  103. 


Fig.  121, 


Fig.  119  shows  the  details  of  an  ordinary  outside  wooden  door.  Fig.  120  gives  the  details 
of  large  swinging  driveway  doors  used  in  a  building  at  Boston,  Mass.  The  arrangement  around 
the  main-street  entrance  doors  to  the  same  building  is  shown  in  Fig.  121.  Similar  door  details 
in  the  Lang  Building  (Fig.  104)  should  also  be  noted. 


Sec.  11-47] 


BUILDINGS 


545 


47.  Basement  Walls.— Basement  walls  to  sustain  earth  may  be  designed  as  simply  sup- 
ported slabs,  the  earth-pressure  reactions  being  usually  taken  by  the  basement  and  first  floors. 
The  common  construction  is  to  employ  curtain  walls  at  least  8  in.  thick  between  wall  columns, 
and,  in  addition  to  reinforcing  them  vertically  to  take  the  earth  pressure,  to  place  rods  near 
the  bottom  of  the  wall  so  as  to  make  the  wall  carry  itself  as  a  beam  from  footing  to  footing. 
This  type  of  wall  thus  requires  no  foundation  of  its  own  and  may  be  built  in  the  same  way  as 
the  curtain  walls  in  the  upper  stories.  Sometimes  it  becomes  necessary  to  reinforce  hori- 
zontally for  the  earth  pressure.  This  brings  a  lateral  force  on  the  columns,  but  the  resulting 
eccentricity  of  column  loading  may  be  disregarded  for  ordinary  cases  unless  a  very  light  wall 
column  is  used.  It  is  customary  in  the  design  of  basement  walls  to  assume  the  earth  pressure 
as  due  to  a  fluid  weighing  30  lb.  per  cu.  ft. 

Sidewalk  lights  are  formed  of  circular  pieces  of  plate  glass  set  in  reinforced-concrete  slabs, 
and  supported  by  steel  beams.  A  typical  vault-light  construction,  using  concrete  beams  is 
shown  in  Fig.  122.  The  spacing  of  the  beams  should  be  governed  by  the  thickness  of  the  slab — 
the  usual  spacing  being  3  to  4  ft. 


Concrete  beam 


Prisms  " 


Expansion  Joint 
fil/ed  yvit/7 
traterproofin^ 

Fig.  122. 


48.  Partitions. — Solid  concrete  partition  walls  may  be  made  3  or  4  in.  thick  if  reinforced 
in  a  similar  manner  to  exterior  curtain  walls.  Extra  rods  should  be  placed  near  the  edges  of  all 
openings,  and  rods  should  project  into  the  floor  and  ceiling  for  anchorage.  It  is  usually  con- 
venient to  pour  the  concrete  after  the  floors  are  laid,  and,  where  partitions  are  not  located  under 
beams,  this  may  be  done  by  leaving  a  slot  in  the  floor  at  the  proper  place. 

Concrete  blocks  have  been  used  to  some  extent,  but  their  thickness  is  often  objectionable. 
In  a  warehouse  at  Nashville,  Tenn.,  concrete  blocks  were  employed  8  by  8  by  24  in.  in  size 
with  two  hollow  spaces.  The  blocks  around  the  elevators  were  4  by  4  by  6  in.  solid.  Rabbets 
were  formed  in  each  end  and  in  top  ^nd  bottom  surfaces,  and  these  were  filled  with  cement 
mortar  as  the  blocks  were  laid,  in  order  to  secure  as  perfect  a  bond  as  possible. 

A  solid  concrete  wall  4  in.  thick  makes  a  very  efficient  fire-resisting  partition,  but  is  heavy, 
and  difficult  to  install.  For  this  reason  metal  lath  and  plaster,  terra-cotta  tile,  and  plaster- 
block  partitions  are  generally  used  in  preference  to  concrete. 

Metal  lath  and  plaster  partitions  are  extensively  employed  in  concrete  buildings  and 
make  a  fairly  good  (although  not  first-class)  fire-resisting  construction.  Some  tests  of  plaster 
partitions  in  actual  fires  have  shown  such  constructions  to  be  reliable  under  fairly  severe  con- 
ditions, while  other  tests  have  shown  failure,  due  to  the  difficulty  of  obtaining  sufficient  bond 
between  the  plaster  and  the  metal  lath  to  resist  successfully  the  combined  action  of  fire  and 
water. 

The  ordinary  form  of  metal  lath  and  plaster  partition  consists  of  channel-iron  or  other 
steel  studding  set  crosswise  of  the  partition,  and  connected  at  the  top  and  bottom  with  the 
floor.    The  metal  lath  is  then  fastened  to  both  sides  of  the  studding  and  each  side  plastered 
35 


546 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-48 


with  a  mixture  of  lime  and  cement  mortar.  Three  coats  of  plaster  are  generally  applied — the 
first  or  scratch  coat  containing  the  usual  quantity  of  hair  or  fiber.  Openings  are  cased  on  all 
sides  with  a  steel  framework  to  which  the  lath  is  firmly  fastened.  This  type  of  a  partition  is 
usually  made  from  4  to  6  in,  thick,  and  made  either  hollow  or  with  a  central  body  of  cinder 
concrete.  A  2-in.  solid  partition,  however,  is  sometimes  used  and  consists  of  only  one  thickness 
of  metal  lath  wired  to  the  steel  uprights. 

Metal  lath  and  plaster  partitions  made  by  the  Roebling  Construction  Co.  are  shown  in 
Figs.  123,  124  and  125.  The  studs  are  fastened  top  and  bottom  by  means  of  knees.  Where 
flats  are  used  for  uprights,  the  knees  are  formed  by  simply  bending  the  ends  of  the  studs. 
Where  cement-finished  floors  are  used,  wood  plugs  or  expansion  bolts  are  inserted  for  fastening. 
Wood  furrings,  where  required  for  nailing  purposes,  are  attached  to  the  studs  by  means  of 


iC 


Elevation 


/Va  18  Galy.  Wire  Lacing  'Rough  Door 

Frame 

Enlarged  Section  A-B 
Fig.  123. 


staples.  Furrings  are  usually  required  to  receive  the  baseboards,  chair  rail,  and  picture  mold- 
ing. They  are  not  needed,  however,  where  cinder  concrete  is  filled  in  between  the  lath  since 
cinder  concrete  will  receive  nails  readily.  The  vertical  members  at  door  openings  are  made 
to  extend  the  full  height  from  floor  to  ceiling.  Such  members  around  openings  are  punched 
at  intervals  with  holes  to  permit  the  fastening  of  wood  frames  or  other  trim.  Of  course,  from 
a  standpoint  of  fire-resistance,  metal  or  plaster  trim  is  preferable  to  wood. 

Two  types  of  plaster  partitions  erected  by  the  Expanded  Metal  Cos.  are  shown  in  Figs. 
126  and  127.  A  metal  and  plaster  partition  known  as  the  hy-rih  construction  is  shown  in  Fig. 
128.  The  ribs  of  the  hy-rib  take  the  place  of  studs  and  eliminate  the  necessity  of  attaching 
sheets  of  lath  to  studs.    The  manner  of  attaching  a  hy-rib  partition  to  floor  and  ceiling  is  shown. 


Sec.  11-48] 


BUILDINGS 


547 


y/  x8  C/ranrre/ 


No.  18  6a/y,  Wire 


Enlarged  Section  with  Door  Casing 

Fig  124. 


Expanded  Meftr/  or 


Fig.  125. 


Fig.  126, 


548 


CONCRETE  ENGINEERS'  HANDBOOK 


Sec.  11-48] 


Where  hollow  partitions  are  required,  two  thicknesses  of  hy-rib  are  used,  separated  by  means 
of  rib  studs. 

Terra-cotta  tile  partitions  are  very  satisfactory  light-weight  partitions  if  made  of  semi- 
porous  or  porous  material.  Partition  blocks  are  made  in  thicknesses  varying  from  2  to  12  in., 
the  4-in.  block  being  the  most  common.  Plaster  on  both  sides  of  a  terra-cotta  partition  in- 
creases the  thickness  by  13^  in.,  that  is,  in.  to  a  side.  Two-in.  and  3-in.  tile  partitions  are 
not  recommended  for  dependable  efficiency  in  case  of  fire.  The  safe  height  of  a  terra-cotta 
partition  may  be  approximated  by  multiplying  the  thickness  of  the  block  in  inches  by  40. 
This  will  give  the  safe  height  in  inches. 

Full-porous  terra-cotta  blocks  are  slightly  more  expensive  than  semi-porous,  as  they 
weigh  more  per  square  foot,  and  have  heavier  faces  and  webs,  but  they  make  a  partition  which 

is  decidedly  more  dependable  under  fire  test.  At 
least  a  portion  of  a  partition  should  be  built  of 
full-porous  blocks  in  order  to  provide  for  the  nail- 
ing on  of  wood  trim. 

Terra-cotta  partitions  should  be  securely 
braced  with  slate  at  the  ceihng.    The  blocks 
should  be  wet  before  being  laid  and  also  before 
being  plastered,  and  should  be  laid  in  a  mortar 
composed  of  1  part  lime-putty,  2  parts  cement,  and  2  or  3  parts  sand. 

Plaster  blocks  as  used  in  partition  construction  are  made  principally  of  gypsum  or  plaster- 
of-Paris,  with  an  admixture  of  wood  fiber,  reeds,  or  other  suitable  material.  They  are  extremely 
light,  easy  to  handle,  and  can  readily  be  cut  and  sawed,  but  possesses  several  disadvantages 
in  actual  use.    They  also  offer  poor  resistance  to  hose  streams  in  case  of  fire. 

The  following  table  gives  weights  of  various  forms  of  partitions.  The  weights  for  the 
block  partitions  do  not  include  the  plastered  surfaces.  If  a  partition  is  to  be  plastered  on  both 
sides,  add  10  lb.  per  sq.  ft. 


Fig.  127. 


Exparrcfecf 
Me  fa/.. 


Weights  of  Partitions 


Ffoor 


Hy-rib 


My-Rib 

Steel  Channe/  or 
//■ood  strip  may  be 
substitLrted  -tbrang/e 

Expans/'or?  Bo/t  or 
.'  kVoocf  P/u^  and  Screw 


Kind  of  partition 

Thickness 
(inches) 

Weight 
(lb.  per 
sq.  ft.  of 
partition) 

Solid  plaster .... 

/2 

20 

32 

Hollow  plaster.  . 

4 

22 

'  2 

12  to  14 

3 

15  to  17 

Terra-cotta  

4 

16  to  18 

5 

18  to  20 

6 

> 

24  to  26 

2 

7 

Plaster  block. .  .  . 

4 

12 

.8 

22 

Fig.  128. 


Large  buildings  should  be  divided  by  fire  walls  of  either  concrete  or  brick,  so  that  if  fire 
occurs  in  any  part  of  the  structure  it  will  be  kept  from  spreading.  A  fire  wall  to  be  thoroughly 
effective  should  run  from  basement  to  roof  and  be  provided  with  automatic  fireproof  doors. 
Severe  exposures  require  fire  doors  on  each  side  of  such  walls. 


[Sec.  11-49 


BUILDINGS 


549 


Stairs  and  elevator  shafts  should  be  enclosed  in  either  concrete  or  brick  partitions.  Where 
considerations  of  appearance  or  light  prevent  the  use  of  opaque  enclosures,  the  fire  hazard 
should  be  reduced  by  using  wire  glass  in  metal  frames.  Open  grille-work  around  passenger 
elevators  should  be  of  this  construction. 

STAIRS 

49.  General  Design. — The  usual  type 
of  reinforced-concrete  stairway  consists  of 
an  inclined  slab  with  the  steps  formed  upon 
its  upper  surface.  The  design  of  such  stairs 
is  a  simple  problem,  the  slab  being  figured 
as  freely  supported  and  with  a  span  equal 
to  the  horizontal  distance  between  sup- 
ports. Transverse  reinforcement  is  used 
only  for  stiffening  and  to  prevent  shrinkage 
cracks.  A  common  load  used  in  designing 
stairs  in  commercial  and  manufacturing 
buildings  is  100  lb.  per  horizontal  sq.  ft. 

A  simple  method  of  design  is  to  support 
the  ends  of  a  stairway  slab  directly  on  floor 
beams  or  floor  girders,  or  on  some  special 
beam  or  beams  inserted  for  the  purpose. 
This,  however,  cannot  always  be  accomp- 
lished conveniently  and  it  is  common  de- 
sign to  make  the  span  of  a  stairway  slab 
to  include  a  platform  slab  as  well.  Stresses 

in  slabs  of  this  type  are  somewhat  indeterminate  on  account  of  the  angle  which  occurs  at 
the  edge  of  the  platform;  but  many  such  slabs,  however,  have  been  computed  as  simple 
slabs  freely  supported  and  have  given  satisfaction  in  every  case. 

/Vc^foT/t^r)  stairway  design,    some  arrangement  is 

^""^."^^^^  \  usually  made  whereby  short  spans  may  be  em- 
ployed, as  slab  construction  is  not  suitable  for 
long  flights.    When  it  becomes  necessary  to  use 


Fig.  129  a. 


Section  at  A-A 


Fig.  1295. 


stair  spans  of  great  length,  however,  without  any  chance  of  intermediate  support,  a  side 
girder  construction  may  be  employed. 


550 


CONCRETE  ENGINEERS'  HANDBOOK 


Sec.  11-50] 


Stairways  should  be  enclosed  in  fire-resisting  partitions  in  order  to  prevent  the  spread  of 
fire  (see  Art.  48). 


IIP 

rv 

D- 

iiiwi 

\\--  -  -  1 

■•Ion  of  Stairs  under  4^F] 
A 

l.J  

1  

iitit 

Ml 

4d 

Detail  of  Stair  Beam 
ond  Hanger 

Fig.  130. 

50.  Methods  of  Supporting  Stairs. — The  slab  method  of  construction  is  usually  the  cheaper 
and  employed  wherever  possible.    In  long  straight  flights,  a  beam  is  often  used  to  shorten 


[Sec.  11-51 


BUILDINGS 


551 


the  span.  This  beam  may  run  between  the  regular  columns  which  make  up  the  structural 
frame,  or  additional  short  posts  may  be  provided.  Fig.  105,  page  538,  shows  a  stairway  sup- 
ported in  this  way.  The  design  is  that  employed  near  columns  1  and  2  of  the  Lang  Building, 
Fig.  100,  page  533. 


Sars  8  c toe  S'-o' ^ 
'  Stirrups  /B'cYoc 


Fig,  131. 

Where  a  stairway  must  be  broken  into  two  or  more  runs  to  the  story,  it  is  customary  to 
employ  either  rod  hangers  or  beams  intermediate  in  the  story  height.  Figs.  129 A  and  1295 
show  a  stairway  supported  by  rod  hangers  only.  In  Fig.  130  both  intermediate  beams  and 
rod  hangers  are  employed. 

Stairways  are  generally  constructed  at  some  convenient  time  after  the  structural  frame 
is  completed.    Where  stair-runs  start  from  floor  beams  or  floor  girders, 
a  plank  should  be  nailed  to  the  side  of  the  beam  forms  to  cause  rab- 
bets in  the  concrete,  and  dowels  should  also  be  provided. 

The  ends  of  a  stairway  slab  are  usually  fixed  to  more  or  less 
extent  and  the  dowels  provided  in  the  course  of  construction  may 
well  be  made  of  such  length  and  in  such  numbers  as  to  give  a  suffi- 
cient reinforcement  for  negative  moment.  In  short  spans  fixed  in 
this  way,  the  moment  at  the  center  of  slab  may  be  computed  with 


safety  using  the  formula  M  = 


10 


Fig.  132. 


A  stairway  supported  by  brick  walls  is  shown  in  Fig.  131.  The 
same  arrangement  would  be  employed  with  concrete  bearing  walls. 

Steps  are  sometimes  molded  after  the  rough  concrete  stair  slab  is  in  place.  The  steps  may 
then  be  molded  separately  and  set  on  the  slab,  or  they  may  be  poured  in  place.  In  the  former 
case,  rods  should  be  embedded  in  each  step  to  permit  of  handling  without  injury,  while  in  the 
latter  case  the  steps  are  all  poured  at  once  in  a  similar  manner  to  the  way  the  pouring  is  done 
when  they  form  an  integral  part  of  the  slab. 

61,  Stair  Details. — In  factory  construction  stair  treads  are  usually  surfaced  with  a  1  or 


552 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-52 


l)^-in.  ceUient  top  finish.  A  method  of  constructing  the  steps  is  illustrated  in  Fig.  132.  The 
form  board  for  the  riser  is  arranged  as  shown  at  A  and  the  top  of  this  board  is  beveled  so  that 
by  placing  an  upper  form  board  on  the  outside  a  nosing  or  projection  in  the  concrete  work  is 
formed. 

Another  type  of  step  with  cement  finish  is  shown  in  Fig.  130.  This  step  makes  a  good 
appearance,  but  is  a  trifle  more  difficult  to  construct  than  the  step  previously  mentioned. 

The  outer  edge  of  concrete  steps  are  protected  in  many  cases  by  a  light  steel  angle  which 
runs  the  entire  width  of  the  stairs.  When  linoleum  is  used,  this  angle  is  raised  so  as  to  have 
the  upper  leg  flush  with  the  finished  tread.  Metal  non-slipping  treads  embedded  in  the  concrete 
are  sometimes  employed. 

Fig.  1295  shows  the  method  of  connecting  concrete  stairs  with  a  wood-finished  floor.  Fig. 
133  gives  the  details  of  wood-covered  concrete  stairs  employed  in  a  fireproof  residence.  In  the 
best  buildings,  treads  and  risers  are  often  covered  with  marble  slabs  having  plaster  soffits. 

The  rise  of  a  stair  is  the  height  from  the  top  of  one  step  to  the  top  of  the  next.  The  run  is 
the  horizontal  distance  from  the  face  of  one  riser  to  the  face  of  the  next.  The  run  is  usually 
less  than  the  width  of  tread  on  account  of  the  nosing.  To  secure  a  comfortable  stair,  the  run 
must  bear  a  certain  relation  to  the  rise.  One  rule  is  that  the  sum  of  the  rise  and  run  should 
be  equal  to  from  17  to  17>^  in.    For  ordinary  use,  a  rise  of  7  to  7K  in.  is  about  right.  Stairs 


having  a  rise  greater  than  7^^  in.  are  steep.  Properly  designed  stairs  without  nosings  should 
have  at  least  12-in.  treads  to  be  comfortable  and  the  above  rule  does  not  apply  to  this  type 
of  stair. 

The  common  railing  is  of  galvanized-iron  pipe  put  together  with  malleable-iron  fittings 
and  having  the  stanchions  rigidly  secured  in  sockets  in  the  concrete  work.  Fig.  106  gives 
details  of  a  railing  of  this  type  used  in  the  Lang  Building.  The  hand-rail  should  be  placed  at 
a  height  of  about  2  ft.  6  in.  above  the  tread  on  line  with  the  face  of  riser.  Rails  monolithic 
with  the  stairs  are  sometimes  used. 


52.  Elevator-shaft  Pits. — Elevator-shaft  pits  should  not  be  less  than  3  ft.  below  the  base- 
ment floor.  When  oil-cushion  buffers  are  employed,  however,  the  pit  depth  should  vary  accord- 
ing to  the  speed  of  the  elevator  and  the  stroke  of  the  buffer  designed  for  that  particular  speed. 
With  a  car  speed  of  600  ft.  per  min.,  the  pit  should  be  about  11  ft.  deep  at  the  center  where  the 
buffer  is  placed. 

If  the  first  floor  is  made  the  bottom  landing,  a  pit  pan  may  be  suspended  from  the  first 
floor,  and  buffers,  if  used,  may  be  placed  on  the  basement  floor  and  arranged  to  project  up  into 
the  pit  through  special  openings  in  the  pan.  This  method  is  generally  employed  when  it  is 
advantageous  to  gain  headroom  in  the  basement  underneath  the  pit  pans.  All  footings  for 
columns  and  foundations  adjoining  elevator  shafts  should  be  kept  below  the  floor  of  the  elevator- 
shaft  pit,  and  the  pit  itself  should  be  finished  to  plumb-line  dimensions. 

In  localities  where  the  water  level  in  the  soil  is  very  high,  or  where  there  are  underground 


Stcr/r  Land/r?^ 


TbpF/oor, 

,  Sub-  F/oon 
2"S/eeper  and 
,  Cinder  F/// 


Fig.  133. 


ELEVATOR  SHAFTS 


Sec.  11-53] 


BUILDINGS 


553 


springs,  the  pits  should  be  thoroughly  waterproofed.  This  may  be  done  in  the  same  manner 
as  for  basement  floors  (see  Art.  47,  Sect.  11).  If  the  water  pressure  is  very  great,  waterproof 
pans  may  be  employed  as  shown  in  Fig.  134. 

The  sides  of  the  pits  are  usually  made  of  concrete  6  to  8  in.  thick  and  the  bottom  of  the  pit 
is  made  a  slab  of  the  same  thickness  as  the  basement  floor.    The  sides  of  the  pit  are  supported 


Basemenf  Leye/ 


Top  of 
P/f  Ptrn 


/re/nforc/r?^  "-^ 


yvaterproofinj 
Fig.  134. 


at  the  top  and  bottom,  and  may  be  figured  as  a  simple  slab  acted  upon  by  the  earth  pressure 
and  by  a  pressure  due  to  the  live  load  on  the  basement  floor.  The  steel  used  in  the  side  walls 
should  be  run  into  the  basement  floor  in  order  to  take  the  reaction  at  the  upper  end  of  the  slab. 

53.  Pent  Houses. — The  heights  of  pent  houses  over  elevator  shafts  vary  according  to  the 
number  of  sets  of  sheave  beams  and  the  size  of  the  sheaves.    If  the  machine  is  located  in  the 


Terr  and  Grave/  ^oof 


Pe^/et  for 
ff/ashin^ 


8  "Is 


# "  ^Stirrups 
2' /""Bars 


Longitudinaf 


Sect-Ion 

Fig.  135. — Pent-house  details. 


Transverse  Section 


basement  or  on  any  intermediate  floor,  the  height  of  the  pent  house  will  vary  according  to  the 
location  of  the  counterweights  with  respect  to  the  machines.  If  the  machine  is  placed  over 
the  shaft,  the  size  and  height  of  the  pent  house  may  be  affected  by  the  dimensions  of  the 
machine  itself.    Figs.  135  and  136  give  details  of  actual  pent-house  constructions. 

In  all  machine  rooms,  doors  should  be  provided  of  sufficient  size  to  permit  any  part  of  the 


554 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  11-54 


machinery  to  be  removed  in  case  of  repairs.  The  construction  should  also  be  such  as  to  admit 
of  easy  access  for  the  purpose  of  oiling  sheave  bearings,  etc. 

Local  regulations  of  some  localities  require  that  a  grating  be  installed  in  all  elevator  shafts, 
just  below  the  overhead  machinery.  This  grating  should  be  constructed  and  properly  sup- 
ported to  sustain  the  weight  of  a  number  of  men. 


  S^S'   

^-  tVooe/  Skj//ffhi-  Curb 


, 4 "S/ab, .  i  "°/?ods  e'c.toc. 


j  Dowels 
"/d'ctoc 


■3-0 
Door 


2  Pitch 


 4-6 

'I-       I  // 


°-6"  Wa// 


Section  A-A 


Section  B-B 


Fig.  136. — Pent-house  details. 


PROVISION  FOR  CONTRACTION  AND  EXPANSION 

64.  Methods  Employed. — There  is  no  well-established  practice  of  providing  for  contraction 
and  expansion  in  reinforced-concrete  buildings  as  a  whole.    Most  engineers  construct  curtain 


.  Position  of  /ead 
when  p/acec^ 
against  the  form 

6 


Fig.  137. 


walls  into  keyways  leaving  only  the  wall  beams  and  wall  girders  subject  to  contraction,  and  it 
has  been  found  that  these  can  usually  be  reinforced  sufficiently  to  prevent  cracking.  Tempera- 


Sec.  11-54] 


BUILDINGS 


555 


ture  reinforcement  in  wall  beams  should  be  placed  horizontally  near  the  outer  surface  and 
should  be  well  distributed  throughout  the  beam  depth.  This  longitudinal  reinforcement 
should  be  well  lapped  at  the  corners  of  the  building.  Buildings  of  a  length  of  300  ft.  have  been 
constructed  in  this  manner  with  no  expansion  joints  and  have  not  cracked. 

When  used,  expansion  joints  to  be  a  success  should  completely  separate  the  building  from 
bottom  to  top.  They  should  preferably  be  made  by  means  of  a  double  column  supporting  a 
double  girder,  and  the  joints  should  be  waterproofed.  Some  engineers  specify  that  a  complete 
separation  shall  be  made  every  100  ft.  in  length  of  the  building. 

Rather  than  provide  sufficient  steel  to  take  contraction  in  long  walls,  expansion  joints 
are  often  resorted  to.    Fig.  137  shows  different  methods  of  making  such  joints.    In  type  A 


Strip 


.  Sliding  P/af^ 


Center  Line^ 
of  Bu//dincf 

Hoof 


Fig.  138. 


grooves  are  simply  cast  in  the  end  of  one  section  and  coated  with  cold-water  paint  or  pitch. 
In  building  the  next  section  a  tongue  is  formed  fitting  the  groove.  This  type  of  joint  is  generally 
reinforced  with  burlap  when  placed  in  front  of  an  earth  fill.  In  type  Fig.  137,  sheet  lead  is 
used.  The  projecting  portion  of  the  sheet  is  bent  up  against  the  form  while  concrete  is  being 
placed  in  the  first  section.  After  removing  the  forms  it  is  bent  down  parallel  with  the  wall 
surface  so  as  to  extend  into  the  abutting  concrete.  A  U-shaped  bend  is  formed  in  the  lead 
sheet  at  the  concrete  joint.  In  type  C  the  tongue  and  groove  is  formed  as  in  A,  and  in  addition 
a  bent  lead  or  copper  strip  is  inserted. 


Fig.  138  shows  the  manner  of  providing  expansion  joints  in  the  United  Shoe  Machinery 
Co.'s  factory  at  Beverly,  Mass. 

Fig.  139  shows  expansion  joints  in  a  sawmill  at  Waycross,  Ga.  An  expansion  joint  occurs 
directly  on  every  column  line.  This  was  done  by  pouring  columns  and  all  transverse  beams 
on  column  line  monolithic,  and  by  making  all  intermediate  beams  and  girders  distinct  members. 
Recesses  were  made  to  receive  these.  The  slab  was  also  an  after  consideration  and  was  poured 
independently  of  beams  and  girders.  The  walls  were  poured  after  the  columns  had  been  strip- 
ped. The  monolithic  feature  of  concrete  construction  was  entirely  eliminated.  This  was  done 
not  only  for  contraction  and  expansion,  but  to  permit  the  pouring  of  the  concrete  at  convenient 
times.  The  roof  slabs  were  cut  on  all  column  and  ridge  lines  for  movement,  and  afterward 
capped.  No  other  covering  than  concrete  was  used  for  the  roof  and  this  was  waterproofed  by 
introducing  a  foreign  ingredient  into  the  concrete  mixture. 


SECTION  12 


FOUNDATIONS 

1.  Bearing  Capacity  of  Soils. — The  bearing  capacity  of  soils  depends  upon  their  composition, 
the  degree  to  which  they  are  confined,  and  the  amount  of  moisture  which  they  contain.  An 
approximate  idea  of  the  loads  which  may  be  safely  placed  upon  uniform  strata  of  considerable 
thickness  may  be  obtained  from  the  table  on  page  583. 

There  are  many  kinds  and  mixtures  of  soils  and  it  is  not  always  possible  to  judge  the  safe 
bearing  capacity  of  any  given  soil  by  reference  to  a  table  such  as  that  above  mentioned.  When 
there  is  any  doubt,  tests  or  borings  should  be  made.  After  opening  the  trenches,  the  best 
method  is  to  load  known  areas  and  observe  the  settlement,  but  in  interpreting  the  results,  the 
fact  should  not  be  overlooked  that  a  small  area  will  bear  a  larger  load  per  unit  of  area  for  a 
short  time  than  a  larger  area  will  perpetually.  Thus,  the  area  tested  should  be  as  large  as 
practicable  and  the  test  should  continue  for  some  time. 

Ordinary  soils  will  usually  bear  more  weight  the  greater  the  depth,  owing  to  the  fact 
that  they  become  more  condensed  from  the  superimposed  load.  With  clay,  depth  is  especially 
important  as  there  is  less  liability  of  its  being  displaced  laterally  due  to  other  fexcavations  in 
the  immediate  vicinity,  and  also  because  at  greater  depths  the  amount  of  moisture  in  it  is  not 
subject  to  so  much  variation.  In  any  soil,  the  bed  of  the  foundation  should  be  below  the  reach 
of  frost. 

It  is  safe  to  say  that  any  rock  in  its  native  bed  will  bear  the  heaviest  load  that  can  be  brought 
upon  it  by  any  masonry  construction.  It  scarcely  ever  happens  that  rock  is  loaded  with  the 
full  amount  of  weight  which  it  is  capable  of  sustaining.  In  preparing  a  rock  bed,  all  loose  and 
decayed  portions  should  be  cut  away  and  the  bed  dressed  to  a  plane  surface  as  nearly  perpen- 
dicular to  the  direction  of  the  pressure  as  is  practicable.  Any  fissures  or  seams  in  the  rock 
should  be  filled  with  concrete.  A  sloping  surface  should  be  stepped  or  the  foundation  designed 
with  sufficient  toe  to  prevent  sliding. 

Sand  when  dry,  or  wet  sand  when  prevented  from  spreading  laterally,  forms  one  of  the 
best  beds  for  a  foundation.  However,  porous,  sandy  soils  are  easily  removed  by  running  water 
and  require  extreme  care  at  the  hands  of  the  constructor. 

Piles  are  used  in  such  soils  as  are  not  able  to  bear  the  weight  of  structures  without  an  exces- 
sive spread  of  the  footing  base.  If  a  pile  is  driven  so  that  its  lower  end  rests  upon  a  hard  stratum, 
the  loading  is  limited  by  the  strength  of  the  pile  considered  as  a  column.  The  load  on  an  ordi- 
nary bearing  pile  is  carried  by  the  friction  of  the  earth  on  the  sides  of  the  pile.  The  only  for- 
mulas in  anything  like  general  use  for  friction  piles  are  the  following,  known  as  the  Engineering 
News  formulas : 

For  a  pile  driven  with  a  drop  hammer,  P  = 

For  a  pile  driven  with  a  steam  hammer,  P  = 

^  '         s  +  0.1 

in  which  P  is  the  safe  load  in  pounds,  W  the  weight  of  the  hammer  in  pounds,  h  the  fall  of  the 
hammer  in  feet,  and  s  the  penetration  or  sinking  in  inches  under  the  last  blow,  assumed  to  be 
sensible  and  at  an  approximately  uniform  rate.  The  above  formulas  were  deduced  for  wood 
piles,  but  they  are  the  best  there  are  for  concrete  piles.  They  are  also  claimed  to  be  safe,  for 
ordinary  weights  of  hammer  and  the  usual  height  of  fall,  for  a  pile  that  acts  as  a  column. 

557 


558 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  12-2 


In  the  driving  of  pviles,  Joseph  R.  Worcester  of  Boston,  advises  for  piles  which  meet  a  hard 
resistance,  a  penetration  of  1  in.  under  a  2000-lb.  hammer  falHng  10  ft.;  and  for  piles  held  by- 
friction  a  penetration  of  3  in.  under  a  2000-lb.  hammer  falhng  15  ft.  Ordinary  piles  of  spruce 
and  Norway  pine  will  usually  sustain  10  tons  by  friction  and  15  tons  in  bearing.  These  piles 
should  never  be  less  than  6  in.  in  diameter  at  the  small  end  and  never  more  than  18  in.  at  the 
large  end.  They  may  be  driven  2  to  3  ft.  apart  depending  upon  their  length,  the  hardness  of 
the  soil  and  the  size  of  the  butts.  It  has  been  found  that  little  or  no  additional  bearing  power 
is  secured  if  the  spacing  is  much  less  than  2  ft.  on  centers.  Concrete  piles  are  manufactured 
in  different  sizes  and  shapes,  and  their  bearing  capacity  should  be  thoroughly  considered  for 
each  case. 

2.  Pressure  on  the  Soil. — A  footing  must  be  spread  until  the  safe  bearing  capacity  of  the 
soil  is  not  exceeded.  An  effort  need  not  be  made  to  eliminate  all  settlement,  but  rather  to  so 
plan  the  structure  that  whatever  settlement  does  take  place  will  be  uniform.  In  other  words, 
the  center  of  gravity  of  the  loads  from  the  columns  should  coincide  with  the  center  of  gravity 
of  the  upward  reactions,  or  with  the  center  of  gravity  of  the  base  if  the  base  rests  directly  on 
the  soil. 

In  buildings  subject  to  shock  or  constant  live  load,  the  area  of  the  footing  should  be  propor- 
tioned for  the  full  live  and  dead  loads.  In  other  buildings,  that  footing  should  be  chosen  in 
which  the  live  load  bears,  the  highest  percentage  to  dead  load  and  its  area  determined  for  the 
total  load  at  the  allowable  bearing  in  the  soil;  the  pressure  of  the  dead  load  per  unit  area  should 
then  be  determined  and  the  area  of  all  other  footings  should  be  proportioned  for  dead  load  only 
with  this  unit  pressure.  Of  course,  the  preceding  statement  applies  without  change  only  when 
the  soil  is  uniform  throughout. 

The  pressure  on  the  foundation  of  a  tall  building  should  be  considerably  less  than  that  which 
may  be  allowed  on  the  foundation  of  a  low  one-story  structure.  In  the  former  case  a  slight 
inequality  of  bearing  power,  and  consequent  unequal  settling,  might  imperil  the  safety  of  the 
entire  building,  while  in  the  latter  case  no  serious  harm  would  result. 

3.  Plain  Concrete  Footings. — The  depth  of  a  plain  concrete  footing  must  be  sufficient  so 
that  the  allowable  tensile  strength  of  the  concrete  is  not  exceeded.  If  the  area  of  the  base  of 
the  footing  is  considerably  greater  than  the  required  area  for  the  top,  the  footing  may  be  stepped 
or  sloped.  The  top  area  required  depends  upon  the  unit  bearing  pressure  allowed  on  the  con- 
crete (see  recommendation  of  Joint  Committee  in  regard  to  bearing  pressure  in  Appendix  B). 
The  base  area  required  is  governed  by  the  safe  bearing  capacity  of  the  soil. 

In  finding  the  maximum  tensile  stress  in  the  concrete,  the  projection  should  be  treated  as 
a  cantilever  loaded  uniformly  by  the  soil  reaction.  In  stepped  footings,  the  depth  of  the  steps 
should  be  made  such  that  the  tension  in  the  concrete  nowhere  exceeds  the  allowable. 

In  a  series  of  tests  on  unreinforced-concrete  column  footings  made  at  the  University  of 
Illinois,^  the  bending  moment  was  computed  by  the  method  shown  in  Art.  7  for  reinforced 
footings  and  the  moduli  of  rupture  were  calculated  by  using  a  resisting  moment  based  upon  the 
full  width  of  the  footing;  that  is,  by  considering  the  fiber  stress  in  the  concrete  at  the  bottom  of 
the  footing  to  be  uniform  over  the  length  of  a  section  passing  through  the  face  of  the  wall,  in- 
stead of  taking  into  account  the  variation  of  stress  across  the  section.  As  is  usually  the  case 
when  plain  concrete  is  used  in  flexure,  the  unreinforced  footings  showed  considerable  variation 
in  results.  The  variations  were  such  as  not  to  permit  a  method  of  determining  the  effective 
width  of  resisting  section  to  be  established  or  to  obtain  a  formula  for  resisting  moment.  Based 
upon  the  full  section  of  the  footing,  the  moduli  of  rupture  obtained  were  considerably  less  (aver- 
aging about  one-third  less)  than  the  moduli  of  rupture  of  control  beams  made  with  the  same 
concrete. 

4.  Advantages  in  Using  Reinforced  Concrete  for  Foundations. — Reinforced  concrete  is 
well  adapted  to  the  construction  of  foundations.    As  compared  with  plain  concrete,  its  advan- 

1  See  Bull.  67,  University  of  Illinois,  Engineering  Experiment  Station. 


Sec.  12-5] 


FOUNDATIONS 


559 


tages  for  spread  footings  are  a  reduction  in  the  amount  of  excavation  required,  a  saving  in 
material,  and  a  reduction  in  the  weight  of  the  foundation  itself. 

5.  Wall  Footings. — Except  in  residences,  bearing-wall  footings  must  usually  be  reinforced. 
A  cantilever  projection  is  formed  on  each  side  of  the  wall  and  the  amount  of  reinforcement  may 
be  determined  as  for  a  simple  cantilever  beam. 

In  figuring  maximum  bond  stress,  tests  show  that  the  total  external  shear  at  the  wall-face 
section  should  be  used  in  the  formulas  of  Art.  16,  Sect.  7.  For  diagonal  tension,  the  shear 
should  be  computed  at  a  distance  from  the  wall  face  equal  to  the  effective  depth  of  the  footing. 
It  is  good  practice  to  design  small  wall  footings  so  that  no  diagonal  tension  reinforcement  is 
required.  In  stepped  and  sloping  footings  the  depth  to  steel  at  a  distance  (d)  from  the  face 
of  wall  is  less  than  in  footings  of  uniform  depth  so  that  diagonal  tension  is  quite  likely  to  control 
in  such  footings.  In  large  important  footings,  where  diagonal  tension  is  a  critical  element, 
web  reinforcement  should  be  employed  preferably  made  up  in  some  type  of  unit  frame  for  con- 
venience in  construction  and  to  ensure  the  accurate  placing  of  the  steel. 

6.  Types  of  Column  Footings. — Foundations  for  columns  are  of  four  principal  types:  (1) 
single  footings;  (2)  combined  footings,  including  two  or  more  columns;  (3)  cantilever  footings; 
and  (4)  raft  foundations  covering  the  whole  foundation  area. 

7.  Single  Column  Footings. — A  single  symmetrical  slab  either  square  or  rectangular  is 
the  most  common  form  of  spread  footing.  The  reinforcing  bars  are  placed  at  the  bottom  of 
the  footing  and  run  in  either  two  or  four  directions. 

Depth  for  Punching  Shear. — The  punching  shear  on  a  column  footing,  on  an  area  equal  to 
the  perimeter  of  the  column  times  the  depth  to  the  steel  should  not  exceed  the  allowable  value, 
which  for  a  1  :  2  :  4  concrete  is  120  lb.  per  sq.  in.  (see  Report  of  Joint  Committee,  Appendix  B). 
The  load  producing  punching  shear  may  be  found  by  multiplying  the  column  load  by  the  ratio 


footing  area  minus  column  area 
footing  area 


 6  -> 

£ 

c 

Fig.  1. 


Maximum  Bending  Moment. — The  maximum  bending 
moment  occurs  at  the  face  of  the  column.  Referring  to  Fig. 
1,  the  bending  moment  at  BC  is  due  to  the  load  on  the  area 
A  BCD.  The  distance  out  from  BC  to  the  center  of  gravity  of 
the  area  A  BCD — distance  x,  Fig.  2 — may  be  formed  for  a 
square  footing  by  the  following  formula 

A    I  i 


ac 
"2 


a  +  c 


Then,  for  a  square  footing  with  square  or  round  column 

(b  -  a)2(26  +  a) 
2462 

(6  -a)2(26  +  a) 


where  P  is  the  total  column  load 
then 


If  we  let  Ci  = 


2462 


Fig.  2. 


M  =  CiP 


Diagram  1  gives  values  of  Ci  for  various  values  of  a  and  6. 


CONCRETE  ENGINEERS'  HANDBOOK 
Diagram  1 


[Sec.  12-7 


6  8  10  12  W  16  18 

Length  of  footing  side  (b)  in  feet 

Diagram  2 


20  22  24 


Rectangular  footings  for 
square  or  round  colunnns 

M=C2dP 
For  rectangular  columns 

M=C3dP 


.20 


30 


Values  of  f  (or|-) 


AQ 


.5C> 


Sec.  12-7] 


FOUNDATIONS 


561 


For  a  rectangular  footing  with  a  rectangular  column  U....Q.....j^ 
(Fig.  4),  the  moment  at  BC  is  Fig.  3. 

M  =  C^dP  V d  > 


Diagram  2  gives  values  of  Cz  for  various  values  of  v  and  v 


G.  4. 


Width  of  Footing  to  Use  in  Flexure  Computations  for  Two-way  Reinforcement.'^ — With  two- 
way  reinforcement  evenly  spaced  over  the  footing,  it  seems  that  the  tensile  stress  is  approxi- 
mately the  same  in  bars  lying  within  a  space  somewhat  greater  than  the  width  of  the  pier 
and  that  there  is  also  considerable  stress  in  the  bars  which  lie  near  the  edges  of  the  footing. 
For  intermediate  bars  stresses  intermediate  in  amount  will  be  developed.  For  footings  having 
two-way  reinforcement  spaced  uniformly  over  the  footing,  the  method  proposed  for  determining 
the  maximum  tensile  stress  in  the  reinforcing  bars,  is  to  use  in  the  calculation  of  resisting  mo- 
ment at  a  section  at  the  face  of  the  pier  the  area  of  all  the  bars  which  lie  within  a  width  of 
footing  equal  to  the  width  of  pier  plus  twice  the  thickness  of  footing,  plus  half  the  remaining 
distance  on  each  side  to  the  edge  of  the  footing.  This  method  gives  results  in  keeping  with 
the  results  of  tests.  When  the  spacing  through  the  middle  of  the  width  of  the  footing  is  closer, 
or  even  when  the  bars  are  concentrated  in  the  middle  portion,  the  same  method  may  be  applied 
without  serious  error.  Enough  reinforcement  should  be  placed  in  the  outer  portion  to  prevent 
the  concentration  of  tension  cracks  in  the  concrete  and  to  provide  for  other  distribution  of  stress. 

No  failures  of  concrete  have  been  observed  in  tests  and  none  would  be  expected  with  the 
low  percentages  of  reinforcement  used. 

Bond  Stresses.^ — The  method  proposed  for  calculating  maximum  bond  stress  in  column 
footings  having  two-way  reinforcement  evenly  spaced,  or  spaced  as  noted  in  the  preceding 
paragraph,  is  to  use  the  ordinary  bond  stress  formula,  and  to  consider  the  circumference  of  all 
the  bars  which  were  used  in  the  calculation  of  tensile  stress,  and  to  take  for  the  external  shear 
that  amount  of  upward  pressure  or  load  which  was  used  in  the  calculation  of  the  bending 
moment  at  the  given  section. 

Bond  resistance  is  one  of  the  most  important  features  of  strength  of  column  footings,  and 
probably  much  more  important  than  is  appreciated  by  the  average  designer.  The  calculations 
of  bond  stress  in  footings  of  ordinary  dimensions  where  large  reinforcing  bars  are  used  show 
that  the  bond  stress  may  be  the  governing  element  of  strength.  Tests  show  that  in  multiple- 
way  reinforcement  a  special  phenomenon  affects  the  problem  and  that  lower  bond  resistance 
may  be  found  in  footings  than  in  beams.  Longitudinal  cracks  form  under  and  along  the  rein- 
forcing bar  due  to  the  stretch  in  the  reinforcing  bars  which  extend  in  another  direction,  and 
these  cracks  act  to  reduce  the  bond  resistance.  The  development  of  these  cracks  along  the 
reinforcing  bars  must  be  expected  in  service  under  high  tensile  stresses,  and  low  working  bond 

1  From  Bull.  67,  University  of  Illinois,  Engineering  Experiment  Station. 


36 


562 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  12-7 


stresses  should  be  selected.  An  advantage  will  be  found  in  placing  under  the  bars  a  thickness 
of  concrete  of  2  in.,  or  better  3  in.,  for  footings  of  the  size  ordinarily  used  in  buildings. 

Difficulty  may  be  found  in  providing  the  necessary  bond  resistance,  and  this  points  to 
an  advantage  in  the  use  of  bars  of  small  size,  even  if  they  must  be  closely  spaced.  Generally 
speaking,  bars  of  M-in.  size  or  smaller  will  be  found  to  serve  the  purpose  of  footings  of  usual 
dimensions.  The  use  of  large  bars,  because  of  ease  in  placing,  leads  to  the  construction  of 
footings  which  are  insecure  in  bond  resistance.  Column  footings  reinforced  with  deformed 
bars  develop  high  bond  resistance.  Curving  the  bar  upward  and  backward  at  the  end  in- 
creases the  bond  resistance,  but  this  form  is  awkward  in  construction.  Reinforcement  formed 
by  bending  long  bars  in  a  series  of  horizontal  loops  covering  the  whole  footing  gives  a  footing 
with  high  bond  resistance. 

The  use  of  short  bars  placed  with  their  ends  staggered  increases  the  tendency  to  fail  by 
bond  and  cannot  be  considered  as  acceptable  practice  in  footings  of  ordinary  proportions. 
In  footings  in  which  the  projection  is  short  in  comparison  with  the  depth,  the  objection  is  very 
great. 

Diagonal  Tension.^ — As  a  means  of  measuring  resistance  to  diagonal  tension  failure,  the 
vertical  shearing  stress  should  be  calculated  by  using  the  vertical  sections  formed  upon  the 
square  (assuming  square  column)  which  lies  at  a  distance  from  the  face  of  the  pier  equal  to  the 
depth  of  the  footing.  This  calculation  gives  values  of  the  shearing  stress,  for  footings  which 
failed  by  diagonal  tension,  which  agree  fairly  closely  with  the  values  which  have  been  obtained 

V  . 

in  tests  of  simple  beams.    The  formula  used  in  this  calculation  is  v  =tt3'  where  V  is  the  total 

vertical  shear  at  this  section  taken  to  be  equal  to  the  upward  pressure  on  the  area  of  the  foot- 
ing outside  of  the  section  considered,  h  is  the  total  distance  around  the  four  sides  of  the  section, 
and  jfi  is  the  distance  from  the  center  of  reinforcing  bars  to  the  center  of  the  compressive  stresses. 
The  working  stress  now  frequently  specified  for  this  purpose  in  the  design  of  beams,  40  lb. 
per  sq.  in.,  for  1:2:4  concrete,  may  be  applied  to  the  design  of  footings. 

Four-way  Reinforcement.^ — Footings  having  reinforcement  placed  in  the  direction  of  the 
diagonals  as  well  as  parallel  to  the  sides  (four-way  reinforcement)  give  good  tests.  The  sig- 
nificance of  the  results  is  so  obscured  by  the  variety  of  manner  of  failure  (bond,  diagonal  tension, 
and  perhaps  tension)  and  by  variations  in  the  quality  of  the  concrete,  that  a  comparison  with 
two-way  reinforcement  on  the  basis  of  loads  carried  would  not  be  of  value.  This  type  of 
distribution  of  reinforcement  should  be  included  in  further  tests.  Measurements  of  deforma- 
tion in  the  bars  are  needed  to  determine  the  division  of  stress  among  the  four  sets  of  bars. 

Stepped  and  Sloping  Footings.^ — In  stepped  footings,  the  abrupt  change  in  the  value  of  the 
arm  of  the  resisting  moment  at  the  point  where  the  depth  of  footing  changes  may  be  expected  to 
produce  a  correspondingly  abrupt  increase  of  stress  in  the  reinforcing  bars.  Where  the  step  is 
large  in  comparison  with  the  projection,  the  bond  stress  must  become  abnormally  large.  It  is  evi- 
dent that  the  distribution  of  bond  stress  is  quite  different  from  that  in  a  footing  of  uniform  thick- 
ness. The  sloped  footing  also  gives  a  distribution  of  stress  which  is  different  from  that  in  a 
footing  of  uniform  thickness.  However,  for  footings  of  uniform  thickness  the  bond  stress  is  a 
maximum  at  the  section  at  the  face  of  the  pier;  in  a  sloped  footing  the  bond  stress  at  the  sec- 
tion at  the  face  of  the  pier  would  be  less  accordingly  than  in  a  footing  of  uniform  thickness, 
and  a  moderate  slope  may  be  found  to  distribute  the  bond  stress  more  uniformly  throughout 
the  length  of  the  bar.  This  is  not  of  advantage  if  the  full  embedment  of  the  bar  is  effective  in 
resisting  any  pull  due  to  bond. 

Illustrative  Problem. — Design  a  single  square  footing  for  a  round  column  of  24  in.  diameter  carrying 
300,000  lb.,  when  the  safe  bearing  capacity  of  the  soil  is  2  tons  per  sq.  ft.  Use  a  2000-lb.  concrete  with  medium 
steel  reinforcement.  Two  sets  of  bars  are  to  be  used  placed  at  right  angles  to  each  other  and  parallel  with  the 
sides  of  the  footing. 

»  From  Bull.  67,  University  of  Illinois,  Engineering  Experiment  Station. 


Sec.  12-7] 


FOUNDATIONS 


563 


The  required  area  of  footing  is  found  by  dividing  the  load  on  the  column  plus  the  assumed  weight  of  footing 

336,000 


(36,000  lb.)  by  tlie  safe  bearing  capacity  of  the  soil,  or 
(area  84.0  sq.  ft.). 

The  load  producing  punching  shear 


4000 


84  sq.  ft.    A  base  9  ft.  2  in,  square  will  be  selected 


84.0  -  3.1 


84.0 


(300,000)  =  289,000  lb.    (The  weight  of  footing  need  not 

be  considered  except  in  determining  the  area  of  base  of  footing  as  the  upward  reaction  of  the  soil  due  to  weight  of 
footing  is  equal  and  opposite  to  this  weight.)    The  minimum  depth,  then,  for  punching  shear  is 


289,000 


(2)(3.14)(12)(120) 


=  32  in, 


Shear,  as  measuring  diagonal  tension,  is  measured  at  a  distance  from 
face  of  column  equal  to  the  depth  of  the  footing  to  the  steel,  or  32  in.  in 
this  problem.  The  reaction  of  the  soil  on  the  cross-hatched  area.  Fig.  5,  is 
what  causes  shear  on  the  vertical  planes  through  EFGH. 

84.0  -  (7.33)' 


Total  shear  on  EFGH 


84.0 


bjd 


(4)  (88)  (0.875)  (32) 


(300,000)  =  108,000  lb. 

=  11  lb.  per  sq.  in. 


108,000 


Thus  the  footing  needs  no  stirrups  for  a  depth  (d)  of  32  in. 

Whenever  the  unit  shear  is  found  too  great  at  the  given  distance  out 
from  the  face  of  column,  the  plane  where  the  shear  is  just  the  allowable 
"should  be  determined.  Then  the  total  tension  to  be  taken  by  stirrups 
divided  by  the  tensile  value  of  one  stirrup  gives  the  number  of  stirrups 
required. 

In  nearly  all  cases  a  slight  deepening  of  the  footing  is  all  that  is  necessary  to  avoid  using  stirrups.  The  placing 
of  stirrups  is  troublesome  and  footings  should  be  designed  so  that  web  reinforcement  will  not  be  needed,  if  this  can 
be  done  without  greatly  increasing  the  depth. 

The  bending  moment  acting  on  each  set  of  rods  is,  by  means  of  Diagram  1, 


M  =  6.2(300,000) 

.  ,    _  Ji   

fsjd       (16,000)  (0.875)  (32) 


=  1,860,000  in.-lb. 
1,860,000 


4.2  sq.  in. 


Fourteen  56-in.  round  bars  will  be  employed  in  each  band,  of  width  equal  to  diameter  of  column  plus  twice  the  thick- 
ness of  footing,  plus  half  the  remaining  distance  on  each  side  to  the  edge  of  the  footing.    The  effective  width  in 
this  problem  is  8  ft.  3  in.  (see  Fig.  5).    We  will  place  16  bars  throughout  the 
entire  width  of  footing,  as  shown  in  the  complete  design,  Fig.  6.    The  bond 
stress 

 y  289,000(H) 


(1.96) (14) (0.875) (32) 


=  94  lb.  per  sq.  in. 


either  de- 


in 


/!6  deformed  bars  ineachsef 
\l  spaced  7"  c.  to  c 


9-2" 


H?-H+H-l-M+f-H4 


Since  the  allowable  bond  stress  for  plain  bars  is  80  lb.  per  sq.  in. 
formed  bars  must  be  used  or  a  larger  number  of  smaller  plain  bars. 

Illustrative  Problem. — Design  a  single  square  sloping  footing  for  a 
round  building  column  of  30-in.  diameter,  carrying  610,000  lb.  Consider  the 
safe  bearing  capacity  of  the  soil  at  2\'i  tons  per  sq.  ft.  and  use  four-way  rein- 
forcement,   /s  =  16,000.    /c  =  650. 

It  will  be  assumed  that  satisfactory  soil  may  be  found  at  the  required  depth 
below  the  basement  floor.  A  base  plate  will  be  provided  under  the  column 
rods,  and  this  plate  will  be  placed  on  top  of  the  finished  footing.  The  top  of 
the  footing  will  be  made  with  an  area  of  about  twice  that  of  the  column  and  a 
bearing  pressure  of  700  lb.  per  sq.  in.  will  be  permitted  (see  recommendations 
of  the  Joint  Committee,  Appendix  B).  Investigation  shows  that  this  stress  is 
not  exceeded.  '  If  desired,  the  base  plate  may  be  placed  some  distance  down  in 
the  footing,  but  under  such  an  arrangement  the  column  rods  for  the  first  story 
must  be  placed  while  the  footing  is  being  poured,  which  is  troublesome.  Some- 
times, however,  this  is  avoided,  especially  where  the  footing  is  at  considerable 
depth,  by  inserting  only  short  column  rods  of  such  a  length  that  they  may  be 

properly  spliced  immediately  above  the  basement  floor.  If  this  is  done,  the  first  floor  can  be  laid  entire  and  the 
first-story  columns  started  above  it. 

The  top  of  the  footing  will  be  made  square,  42  in.  on  a  side.  This  provides  a  6-in.  ledge  all  around  so  that, 
if  it  is  desired  to  erect  the  first-story  columns  before  pouring  the  basement  floor,  the  column  forms  will  have  some 
place  on  which  to  rest.  The  depth  of  the  footing  at  the  outer  edge  will  be  made  12  in.  The  dead  weight  of  the 
footing  will  be  taken  at  60,000  lb. 


Fig.  6. 


564 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  12-^7 


The  required  area  of  footing  is  found  by  dividing  the  total  load  by  the  safe  bearing  capacity  of  the  soil. 

670,000 
(2.5)  (2000)  = 

We  shall  select  an  area  11  ft.  6  in.  square. 

Four-way  reinforcement  for  single  column  footings  is  shown  in  Fig.  8.  After  deducting  the  area  of  the 
column  base,  the  remainder  of  the  footing  slab  is  considered  as  eight  cantilevers,  four  running  parallel  to  the  sides 
and  four  on  the  diagonals. 

Depth  for  punching  shear, 

/132.2    -  4.9n  610,000  . 

~  {     132.2      /  (3.14)(2.o)(12)(120)  ~ 


Fig.  7.  Fig.  8. 


Referring  to  Fig.  7,  the  reaction  of  the  soil  on  the  cross-hatched  area  is  what  causes  shear  on  the  vertical 
planes  EFGH 

,'  =  52-k  =  52-  =  9.8  in. 

132  2  —  (11  17)2 
Total  shear  on  EFGH  =    ^^^^  ' — -  (610,000)  =  34,200  lb. 

34,200 

'  =  (4)  (134)  (0.875)  (9.8)  =  ^'^ 
The  total  moment  acting  around  the  entire  column  perimeter  is  found  fromDiagram  1  to  be 
M  =  (4)  (7.8)  (610,000)  =  19,030,000  in.-lb. 

_  19,032,000  

~  (16,000)  (0.875)  (52)  ~  26.2  sq.  in. 

This  total  amount  of  steel  will  be  divided  by  eight  in  order  to  determine  the  amount  of  steel  in  each  band.  If 
desired,  more  bars  can  be  placed  parallel  to  the  sides  of  the  footing  than  in  a  diagonal  direction.  In  this  design 
six  1-in.  round  bars  will  compose  each  set. 

In  view  of  tests  made  on  footings  with  two-way  reinforcement  it  would  seem  that  the  bars  need  not  all  pass 
directly  under  the  column.  In  fact,  if  the  width  of  bands  needs  to  be  increased  in  order  to  cover  the  entire  area  of 
the  footing,  it  would  be  conservative  to  say  that  this  may  be  done  provided  that  the  increase  in  the  width  of  each 
band  is  not  great.  Until  more  tests  have  been  made  along  this  line,  it  would  seem  wise  (especially  in  footings  in 
which  the  depth  decreases  toward  the  outer  edge)  not  to  be  too  radical  in  the  design  of  such  important  structures 
as  footings.  Where  a  small  increase  in  the  width  of  bands  does  not  suffice  to  cover  the  entire  area  of  footing,  a 
few  short  cross  rods  may  be  employed  to  span  the  open  spaces.  Increase  in  band  width  should  preferably  be  made 
in  the  bands  parallel  to  the  sides  of  the  footing  as,  in  these  bands,  the  lengths  of  the  rods  do  not  change. 

It  should  be  noticed  that  the  diagonal  rods  have  a  greater  length  subjected  to  cantilever  action  than  the 
rods  parallel  to  the  sides  of  the  footing.  Since  it  is  difficult  to  calculate  accurately  the  stresses  in  a  square  footing, 
it  does  not  seem  proper  to  attempt  any  but  equal  division  of  moment  between  the  rods  in  the  different  directions. 
Some  designers  prefer  an  octagonal  shape  of  footing  so  that  all  rods  will  have  approximately  the  same  length.  The 
rods  should  be  cut  from  2  to  4  in.  shorter  than  the  total  width  of  footing,  but  if  desired,  the  rods  may  be  cut 
considerably  shorter  and  staggered  so  as  to  allow  for  the  decrease  in  bending  moment  from  the  column  toward 
the  edges  of  the  footing. 


Sec.  12-8] 


FOUNDATIONS 


565 


The  bond  stress  along  the  horizontal  twision  bars  must  now  be  investigated. 
/132.2  -  4.9\  610,000 
"  =  {     132.2      )  (48)(3.14)(0.875)(52)  = 

Deformed  bars  will  be  used.    The  complete  design  is  shown  in  Fig.  8. 

Where,  on  account  of  soil  conditions,  a  greater  depth  is  needed  beiow  the  basement  floor  than  that  required 
for  the  footing,  the  pier  or  column  between  the  top  of  the  footing  and  the  basement  floor  should  be  flared  in  a 
similar  manner  (but  inverted)  to  the  flare  in  columns  just  below  flat-slab  floors,  as  by  so  doing  the  bending  moment 
and  shear  on  the  footing  ma'y  be  decreased.    This  should  be  clear  from  the  discussion  on  flat-slab  floors. 

8.  Combined  Column  Footings. — It  is  sometimes  necessary  to  support  a  column  on,  or 
very  near,  the  edge  of  a  property  line  in  order  not  to  encroach  upon  adjacent  property.  In 
such  single  symmetrical  footing  cannot  be  used.    The  nearest  interior  column  is 

usually  selected  and  a  combined  footing  constructed  under  both  columns.  Sometimes  a 
combined. footing  will  include  more  than  two  columns. 

The  design  of  combined  footings  consists  in  constructing  a  base  of  such  shape  that  the 
center  of  gravity  of  the  loads  will  coincide  with  the  center  of  gravity  of  the  upward  reaction. 
In  addition,  the  base  must  have  sufficient  area  so  that  the  allowable  pressure  on  the  soil  will 
not  be  exceeded. 

The  combined  footing  may  be  either  a  slab  of  uniform  thickness  or  an  inverted  T-beam. 
If  the  slab  type  of  combined  footing  is  used  with  two  columns,  the  slab  must  have  a  trape- 
zoidal shape  when  the  columns  are  placed  at  opposite  ends  of  the  footing.  A  rectangular 
shape  may  be  used  where  a  longitudinal  projection  is  possible  beyond  the  heavier  load  of  a 
sufficient  length  to  cause  the  center  of  gravity  of  the  rectangle  to  coincide  with  the  center  of 
gravity  of  the  loads.  Transverse  reinforcement  is  needed  when  the  width  of  footing  is  much 
larger  than  the  width  of  columns. 


Fig.  9. 


Illustrative  Problem. — Design  a  combined  footing  for  columns  1  and  2,  Fig.  9.  Column  1  is  20  in.  square 
and  sustains  a  load  of  280,000  lb.  Column  2  is  24  in.  square  and  sustains  a  load  of  380,000  lb.  Distance 
between  centers  of  columns  is  14  ft.  Allowable  soil  pressure  is  6500  lb.  per  sq.  ft.  Assume  a  2000-lb.  concrete 
with  medium  steel  reinforcement. 

Load  on  column  1  =  280,000  lb. 
Load  on  column  2  =  380,000  lb. 


660,000  lb. 

Assumed  weight  of  footing  =    55,000  lb. 

Total  =  715,000  lb. 


Pressure  on  the  soil  due  to  column  loads  only  is 


715,000 

6500 

660,000 

lio 


■■  110  sq.  ft. 
6000  lb.  per  sq.  ft. 


566 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  12-8 


The  lengths  of  the  parallel  sides  are  unknown  and  two  equations  will  be  needed  to  solve.  First  equation  may 
be  obtained  from  the  formula  that  the  area  of  a  trapezoid  equals  the  average  of  the  sum  of  the  parallel  sides  multi- 
plied by  its  length.  The  second  equation  may  be  found  from  the  principle  stated  above — that  the  center  of  gravity 
of  the  trapezoid  must  coincide  with  the  center  of  gravity  of  the  combined  column  loading.  This  must  be  so  in 
order  that  the  pressure  on  the  soil,  and  the  consequent  settling  (if  any),  may  be  uniform — also  to  prevent  dangerous 
transverse  stresses  in  the  columns. 

Area  of  footing  =  ^L±_^  (16.83)  =  110 
fci  +  62  =  13.07 

'■-■-  =  IS 

or 

h  =  7.44  ft. 

Using  the  common  equation  for  the  center  of  gravity  in  a  trapezoid 

Solving  equations  (1)  and  (2)  for  61  and  62 

61  =  8.82  ft.  and  62  =  4.25  ft. 

The  values  of  61  and  62  may  also  be  found  by  considering  the  footing  1  ft.  wide  and  using  the  formulas  on 
page  582  to  find  intensity  of  pressure  at  each  end.  Thus,  if  we  let  pi  denote  the  intensity  at  the  column  2  end 
and  p2  the  intensity  at  the  column  1  end,  we  have 

0(1^-7.44)-] 

=  52,900  lb. 


660,000 


[. 


.83  '  16.83 

'16.83 


16.83  L  16.83  J 


16.83  '  ^'''^^ 


Then 


8.82  -  4.25  1 
-   (2)(16.83)  '''l""""  -  ^^"■'^ 


To  find  the  necessary  depth  of  footing  and  amount  of  steel  required,  we  must  find  the  section  maximum 
moment  (which  is  the  section  of  zero  shear)  and  then  determine  the  center  of  gravity  of  the  area  to  one  side  of  this 
section  as  an  aid  in  finding  the  value  of  this  maximum  moment. 

8.82  -  4.25 
(2)  (16.83) 
h  -  0.0154^22  =  7.18 
h  --  8.22 

And  by  trial,  61  -  62  =  8.82  -  4.25  =  4.57 

b3  -  b2  ^  16.83  --  8.22 

4.57  16.83 
bs  -  b2  =  2.34 

b3  =  2.34  +  4.25  =  6.59 

^  h   63  +  2bi  _  8^    6.59  +  2(8.82)  _  . 
'  ~  3  '  63  +  61  ~     3    ■     6.59+8.82  ~ 

We  can  now  compute  the  value  of  the  maximum  moment. 

M  =  380,000  (8.22  -  1.5  -  4.31)  =  915,800  ft.-lb. 

or 

M  =  (915,800)  (12)  =  10,989,600  in.-lb. 

The  moment  for  1  in.  of  width  along  the  line  of  maximum  moment,  M  =  ^r  ^nf/fo!^  =  139,000  in.-lb.  The 

(6.59)(12) 

footing  must  be  considered  as  an  inverted  beam  at  this  section,  and  the  required  depth  and  the  area  of  the  steel 
may  be  computed  by  the  usual  methods. 

If  the  moment  had  been  taken  about  a  line  through  the  center  of  gravity  of  the  entire  trapezoid,  the  result 
would  be  133  000  in.-lb.,  or  an  error  of  only  about  2.2  %.  This  approximate  solution  is  often  used  in  practice  as  the 
error  is  small. 

From  Diagram  2,  page  360,  K  =  107.4  and  p  =  0.0077  for  the  stresses  as  recommended  by  the  Joint 
Committee. 


,     ^  139,000 
d  =  V-ToT^  -  36.0  in. 


\  1( 

As  =  (0.0077)  (12)  (6.59)  (36)  =  21.9  sq.  in.  for  the  whole  width. 
Eighteen  IH-in.  round  rods  will  be  needed. 


Sec.  12-8] 


FOUNDATIONS 


567 


The  depth  required  for  punching  shear  at  column  2  is 
,      380,000  -  (6000)  (4) 


and  at  column  1  it  is 


(24)(4)(120) 

280,000  -  (6000)  (1.67) 2 
(20)  (4)  (120) 


31  in. 


28  in. 


In  each  case  the  depth  is  less  than  that  required  for  moment. 

The  depth  required  for  diagonal  tension  must  now  be  determined.  The  shear  at  column  2  equals  380,000 
lb.  minus  the  part  of  this  load  distributed  on  the  soil  over  the  area  mrsn,  Fig.  11,  or 


and 


The  shear  at  column  1  is 


and 


V  = 
d  = 

V  = 
d  = 


380,000  -  (8. 14)  (2.5)  (6000)  =  258,000  1b. 

 258,000  . 

(8.14)(12)(0.875)(120)  ~ 

280,000  -  (4.80)  (2.17)  (6000)  =  217,500  1b. 
217,500 


(4.80)  (12)  (0.875)  (120) 


36  in. 


which  is  just  that  required  for  moment. 

Adopting  a  depth  (d)  of  36  in.  and  assuming  that  deformed  rods  are  used,  then  the  number  of  rods  required 
for  bond  will  be  (assuming  u  =  100) 


or  number  of  rods 


258,000 


21 


Soid'    (3.93)  (0.875)  (36)  (100) 

Thus  the  bond  controls  the  number  of  horizontal  rods  required  and  21  rods  will  be  employed  (see  Fig.  10). 


Stirrups  are  af Cached  b  Uf^r  hngi-hjclinal  rods 


-^J^^T   " 


6-ir^4'-07g\.,^^ 


ie-f^-3fchc  about  ea'c.  foe.  £0-§°^2^'c.foc. 

Fig.  10. 


-31  i. 


Transverse  reinforcement  should  be  provided  to  prevent  bending  of  the  projections  of  the  footing.  Consid- 
ering column  2,  the  width  of  distributing  beam  will  be  taken  at  3  ft.  6  in.    Now  the  loading  for  which  this  cantilever 

should  be  designed  is  equal  to  one-half  of  the  column  loading  multiplied  by  — ^rFK~*    The  moment  arm  equals 

one-half  of  the  length  of  the  projection,  and 

/380,000\  /8.82  -  2n 


8.82 


M  = 
d  = 


K».»z  —  ■z\  /3.4l\  , 
-Sli2-)(—)»2)  -3,010. 


000  in.-lb. 


3,010,000 
(107.4)(3.5)(12) 


=  25. 


The  depth  is  smaller  than  the  depth  of  the  whole  slab  and,  since  a  greater  depth  is  used,  the  amount  of  steel 
found  as  follows: 

_  JW^  3,010,000  

"  ~  fsjd  ~  (16,000) (0.875)  (36)  "  ^  ^ 

Referring  to  table  on  page  357,  fourteen  %-in.  round  rods  will  be  needed. 


568 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  12^9 


In  the  same  manner,  the  distributing  reinforcement  for  column  1  is  determined 
/280,000\  /4.25 

^=  (— 2— )(— 

d 


^  ■^^)(^)(12)  =  658,000  in.-lb. 


\  658,000   ^ 

\(107.4)(3.5)(12)  "^-^^ 


Since  the  depth  of  the  whole  slab  must  be  used,  the  necessary  steel  is  found  as  above. 

658,000 


As  = 


=  1.3  sq.  in. 


(16,000)  (0.875)  (36) 

It  sometimes  happens  that  the  required  depth  of  the  distributing  beam  may  be  larger  than  the  depth  of  the 
whole  slab.  In  such  cases  the  footing  may  have  an  increased  thickness  under  the  column  or  else  steel  may  be 
introduced  at  the  top  and  bottom.  Double  reinforcement,  however,  should  not  be  employed  when  excavation 
can  readily  be  made. 

The  bond  stress  along  the  rods  of  the  distributing  beams  must  now  be  investigated.  Considering  the  beam 
under  column  2,  the  maximum  shear  is 


380,000\  /3.82  -  2.0 


)  =  147,000  lb. 


2      /  \  8.82 

Assuming  that  deformed  rods  are  used,  then  the  number  of  rods  required  for  bond  will  be  (u  =  100) 


or  number  of  rods 


147,000 


(2.36)  (0.875)  (36)  (100) 


20 


In  a  similar 
beam  under 


Thus  the  number  determined  for  bond  controls, 
manner,  12  rods  are  needed  in  the  distributing 
column  1. 

Fig.  10  shows  the  spacing  of  the  transverse  reinforcement. 
Steel  should  be  introduced  between  the  end  distributing  beams 
about  24  in.  c.  to  c.  in  order  to  make  the  footing  more  rigid  and 
more  capable  of  directly  transmitting  the  loads. 

Web  reinforcement  is  not  needed  in  the  distributing  beams, 
as  each  distributing  beam  and  column  has  a  similar  load  to  that 
of  a  single  footing,  and  for  such  footings  we  know  that  the  in- 
tensity of  shearing  stress,  as  measuring  diagonal  tension,  may  be 
computed  on  a  section  at  a  distance  out  from  the  face  of  column 
equal  to  the  depth  of  the  footing  to  the  steel.    In  a  longitudinal 
direction,  however,  shear  should  be  computed  on  a  section  close 
to  the  support,  as  mn,  Fig.  11,  since  in  this  direction  the  tension  steel  is  at  the  top  of  the  footing  and  cracks  may 
open  up  in  the  web  as  in  simple  beams.    The  spacing  of  stirrups  is  given  in  Figs.  10  and  11,  determined  as  in  a 
simple  beam. 

The  loads  beyond  the  centers  of  the  columns  in  a  longitudinal  direction  cause  negative  moment  at  the  sup- 
ports; that  is,  the  load  to  the  left  of  column  1  and  to  the  right  of  column  2  cause  tension  in  the  bottom  of  the 
footing  at  the  sections  AB  and  CD  respectively  (Fig.  9).    This  tension,  however,  does  not  exceed  the  tensile  strength 
of  the  concrete.    At  column  1,  using  the  common  flexure  formula. 
My  _  (8.82)  (1.5)  (6000)  (9)  (18)  (12) 
^  ~    I  ~ 


33  lb.  per  sq.  in. 


(8.41)(12)(36)3 

A  few  rods  4  ft.  long  will  be  placed  at  the  bottom  of  footing  across  the  sections  AB  and  CD  in  order  to  provide 
for  any  possible  defects  in  the  bed  of  the  foundation. 

9.  Cantilever  Footings. — The  cantilever  type  of  construction  may  be  employed  in  place 
of  a  combined  footing  under  the  usual  conditions;  that  is,  when  encroachment  upon  adjacent 
property  must  be  avoided  and  when,  at  the  same  time,  it  becomes  necessary  to  make  use  of 
the  land  close  to  the  property  line.  In  cantilever  construction,  the  wall-column  footing  and 
the  footing  of  the  nearest  interior  column  are  connected  by  a  beam  or  strap,  and  this  strap  is 
extended  so  as  to  support  the  wall  column.  To  save  excavation,  the  top  of  the  strap  is  usually 
placed  at  the  same  level  as  the  tops  of  the  footings. 

Illustrative  Problem. — Let  us  assume  the  size  of  columns  and  column  loading  as  shown  in  Fig.  12.  The 
distance  from  the  center  of  interior  column  to  the  property  line  will  be  made  12  ft.  and  the  outer  edge  of  the  wall 
column  will  be  placed  on  the  property  line.  In  addition  to  the  above,  we  shall  consider  that  piles  are  necessary 
and  that  it  is  not  feasible  to  drive  such  piles  closer  than  2  ft.  apart  in  any  direction.  The  safe  bearing  capacity 
of  each  pile  will  be  taken  at  10  short  tons.  The  working  stresses  as  recommended  by  the  Joint  Committee  for  a 
2000-lb.  concrete  and  medium  steel  will  be  adopted. 

Approximate  figuring  shows  that  about  12  piles  will  be  needed  under  the  wall  footing,  and  18  piles  under  the 


Sec.  12-9] 


FOUNDATIONS 


569 


interior  footing;  that  is,  if  the  center  of  the  wall  footing  is  placed  about  as  shown  in  Fig.  12.  Knowing  the  number 
of  piles  required,  the  shape  of  the  footings  may  be  easily  determined.  The  arrangement  showO  for  the  piles  insures 
a  spacing  of  at  least  2  ft.  in  every  direction. 

On  account  of  cantilever  action,  the  uplift  on  the  interior  column  may  be  due  to  the  combined  live  and  dead 
load  of  the  wall  column,  but,  since  the  live  load  may  not  always  be  present,  the  uplift  from  the  dead  load  only 

should  be  considered.    Disregarding  the  strap  weight  to  the 
right  of  the  center  of  wall  footing,  this  uplift  is 
(130,000)  (2.33)  -  (1200) (9) (4.5) 


9' 
'•■9' 

J'r9. 

/? 

■  ■'e' 

'0''- 

■■> 

/ 



' 

H 

* 

— 0 

,  i' 

1 

tS;' 

K 

\ 

T.   %  _  V 

Plan 

<           s'oo   ' 

<   //  '33  ■— 

<-...,  izloo— 

 4 

Properry.,. 
Line 

9.00 


=  28,000  lb. 


The  strap  will  now  be  designed  for  the  total  live  and 
dead  load  on  the  exterior  column  since  this  loading  gives 
maximum  conditions.     The  total  load  on  the  wall  footing  is 
(175,000)  (11. 33)  +  (1200)  (12)  (6) 


».00 


230,700  lb. 


Stirrups  amched  10 ippernxfs^^iyp  4S00O 
\Dead  130000 

''3 


^■t — tlv  _ 


The  uplift  on  the  interior  column  may  be  found  in  a  similar 
manner  to  that  for  dead  load  only,  or  more  accurately  (tak- 
ing moments  about  the  outer  edge  of  the  wall  column) 
(230,700)  (3.00)  -  (175,000)  (0.67)  -  (1200)  (12) (6) 


12.00 


40,700  lb. 


The  loads  on  the  strap  are  shown  in  Fig.  13.  The  maximum 
moment  occurs  where  the  shear  is  zero,  or  accurately  enough, 


Elevation 


triple- 
looped 

stirrups  6'c.ToOf 


(175,000)  (6^ 
230,700 


4.5  ft. 


IS-i'"*4rc  he 

iPmiiiili^flK 
iTTtiTTTtrrnw..'' 
ittllttiHtitft^:-- 


Total  /TSOOOlb. 
Uniforrp  load  /200  lb.  per  ft  


Plan  of  Steel  in  Footings 


Plan  of  Steel  in  Strap 
Fig.  12. 


Point  of  Max  Momknt. 


■msr 


A    /ora;  230. 700/0 

m\\\\\\\ 

k-  4'S  ■> 


Fig.  13. 


from  the  outside  edge  of  wall  column. 

M  =  (175,000)  (3.83) 

=  3,372,000  in.-lb. 
Then,  assuming  b  =  39  in. 


3,372,000 
'(107.4)  (39) 


(^^^^)  (4.25)  (2.25)  =  281,000  ft.-lb. 


28K2  in. 


The  shear  in  the  strap  at  the  inside  edge  of  wall  column  should  not  exceed  120  lb.  per  sq.  in.  with  an  effective  sys- 
tem of  web  reinforcement.  This  is  due  to  the  fact  that  tension  exists  in  the  upper  portion  of  the  strap;  in  other 
words,  the  inward  spread  of  the  wall-column  load  will  not  aid  to  any  appreciable  extent  in  reducing  the  tendency  to 
fail  through  diagonal  tension.    For  the  dimensions  determined  for  moment 


(175,000) 


'230,700 


)  (1.33) 


(39) (0.875) (28.5) 
123,900 


127  lb.  per  sq.  in. 


(39)  (0.875)  (28.5) 

The  strap  will  be  deepened  so  that  d  =  30  in.  and  total  depth  =  32  in.    Stirrups  will  be  needed  from  the  inner 
edge  of  the  exterior  column  to  a  point  3.5  ft.  from  the  property  line  where  the  shear  becomes  10  lb.  per  sq.  in. 
Triple-looped  y2-in.  round  stirrups  will  be  employed  and  these  will  be  spaced  6  in.  on  centers,  or 
_  3    Asfsjd  _  3    (6) (0.196) (16,000) (0.875)  (30) 
^  ~  2       V      ~  2  123,900 


=  6  in. 


570 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  12-10 


The  unit  shear  at  the  inner  edge  of  wall  footing  is 

(40,700)  +  (1200)  (6) 
(39) (0.875) (30)  = 

Two  triple-looped  }^-in.  round  stirrups  placed  just  to  the  left  of  this  point  will  make  the  design  satisfactory. 
The  number  of  horizontal  rods  will  now  be  determined. 

Jlf  3,372,000 

^  ^  fsjd  ~  (16,000)  (0.875)  (30)  ~ 

Fourteen  Ji-in.  round  deformed  rods  will  be  used. 

123,900 


(14) (2.75) (0.875) (30) 


122  lb.  per  sq.  in. 


This  value  will  be  considered  satisfactory  on  account  of  bending  the  ends  of  the  rods  as  shown. 

The  horizontal  tension  rods  should  have  a  sufficient  length  for  straight  bond  to  the  left  of  the  section  of 
maximum  moment.  Alternate  rods  may  stop  off  at  10  ft.  from  the  property  line,  which  is  about  5  in.  beyond  the 
point  where  they  are  no  longer  needed  in  tension. 

The  interior  footing  may  be  designed  in  the  same  manner  as  explained  in  Art.  8,  except  that  in  this  problem 
we  have  the  moment  from  concentrated  loads  instead  of  from  uniform  loads. 

M  =  (80,000)  (2.37)  (2)  +  (20,000)  (0.62)  (2)  +  (20,000)  (1.87)  (2)  +  (40,000)  (0.87)  (2X 
=  548,400  ft.-lb.,  or  6,581,000  in.-lb. 

The  depth  to  steel  will  be  made  30  in.  in  order  to  provide  properly  for  the  strap.    Web  reinforcement  is  not  needed 

M  6,581,000 


f,jd       (16,000)  (0.875)  (30) 


15.6  sq.  in. 


The  steel  will  be  placed  in  two  directions.  Thus,  for  moment,  3.9  sq.  in.  or  seven  ^^-in.  round  rods  will  be  needed 
in  each  band.  Let  us  now  determine  the  number  of  Ji-in.  round  deformed  rods  in  each  set  that  will  be  required 
for  bond. 

(16)  (20,000) 

^  =  S^'      """^^^^      '•^^^  =  (100)(2.75)V.875)(30) 

This  number  controls. 

The  weight  of  footing,  as  designed,  deducting  the  weight  of  strap  already  considered,  is  approximately  22,000 
lb.  This  gives  a  total  pressure  on  the  piles  of  360,000  +  22,000  -  28,000  =  354,000  lb.  Thus  the  number  of 
piles  was  correctly  chosen.  In  this  design  there  is  no  danger  of  failure  by  direct  shear  above  the  tops  of  the  piles 
as  for  this  kind  of  shear  about  one-half  the  compressive  strength  of  the  concrete  may  be  allowed.  There  i?  also 
no  danger  from  punching  shear  around  the  base  of  the  column. 

The  footing  under  the  wall  column  acts  as  a  simple  cantilever.    The  moment  on  each  edge  of  strap 
M  =  (60,000)  (17)  =  1,020,000  in.-lb. 
As  in  the  interior  footing,  the  depth  to  steel  will  be  made  30  in. 

 1,020,000  

'  ~  (16,000)  (0.875)  (30)  ~  ' 
Twelve  li-in.  round  rods  are  satisfactory  for  moment.    For  bond 

,  ,      ,  60,000   _ 

number  of  deformed  rods  =  (loO)  (1.57)  (0.875)  (30)  = 

A  few  cross  rods  will  also  be  employed  to  better  distribute  the  load. 

The  weight  of  wall  footing  deducting  the  weight  of  strap  is  approximately  10,000  lb.,  giving  a  total  pressure 
on  the  piles  of  230,700  +  10,000  =  240,700  lb.,  or  almost  exactly  10  tons  per  pile,  as  planned. 

It  is  generally  considered  good  practice  to  lay  the  concrete  directly  upon  the  heads  of  the  piles.  The  ground 
is  usually  excavated  around  the  piles,  the  depth  depending  upon  soil  conditions,  and  then  a  layer  of  broken  stone 
is  spread  and  rammed  before  the  concrete  is  laid.  The  supporting  power  of  the  soil  between  the  piles  is  thus 
utilized. 

10.  Raft  Foundations. — The  raft  foundation  in  building  construction  may  be  considered 
as  an  extension  of  the  single  or  combined  footing  until  the  foundation  covers  at  least  a  con- 
siderable, if  not  the  entire,  area  of  the  building.  Its  use  is  limited  to  sites  where  the  allowable 
pressure  on  the  soil  is  very  small  or  where  the  building  is  supported  by  piles  sustained  by 
friction. 

Raft  foundations  may  be  divided  into  the  following  three  general  classes: 

1.  Flat  slabs  of  plain  or  reinforced  concrete. 

2.  Beams  or  girders  with  a  slab  underneath. 

3.  Beams  or  girders  with  a  slab  on  top. 


Sec.  12-11] 


FOUNDATIONS 


571 


A  flat-slab  foundation  may  be  designed  in 
20,  Sect.  11).    The  foundation  is  considered  as 


|T]]jii  ^us'. 


'■•These  t?ars  in  boffvm  of  Lj 
s/at>  -for  a//  Canf-i/et'er  S/abs 

Plan 


the  same  manner  as  a  flat-slab  floor  (see  Art. 
an  inverted  flat  slab  loaded  by  the  reaction  of 
the  ground  and  supported  by  the  columns. 
The  column  base  should  be  made  large 
enough  to  prevent  excessive  moments  and 
shears  in  the  concrete. 


Basement  Floor  Level 
1  


f  /S'-o'^  ^-T'-o'y 

4' Concrete  F/cx>r  S/ab 

J)  \Cinder  [i'^ 

MM 

Section  A-B. 
Fig.  14. 


I  Ml  /// 


<  


•  7'-e'' 


■2'-'f-> 


'•S-p-6'croc, 


Fig.  15. 


Fig.  14  shows  a  design  of  a  raft  foundation  of  the  second  class.  The  action  of  forces  is 
exactly  as  in  an  inverted  floor  and  calls  for  similar  treatment  in  designing.  As  compared  with 
Class  3,  Class  2  permits  a  T-beam  design,  but  on  the  other  hand,  requires  an  extra  fill  and 
separate  floor  surface  in  the  basement. 

11.  Examples  of  Column  Footings. — Fig.  15 
shows  a  design  of  a  single  footing  for  the  typical 
interior  columns  of  a  factory  building  for  the 
Bradley  Knitting  Co.,  Delavan,  Wis.  The  design 
of  the  top  of  footing  should  be  noted. 

Fig.  16  is  an  example  of  a  combined  footing 
employed  in  an  automobile  depot  in  Boston. 

Fig.  17  is  a  special  foundation  of  novel  design 
used  in  the  Garage  Building  of  the  Decanville 
Automobile  Co.,  New  York  City. 


/nf^nor  Co/  m/l  Co/. 

Basemen  f  F/oor  Line_  

 Z4'-o''  

Y-s'-o- 

rods 


Y\4-6>\   >-A 

/  Z /  7\7^/  


\ 


.  ■  -  .       4-1"^ rods  \  \  \  ) 
i  ^' -39- i" 'Prods  8k"c 


6"  ■  /!9'  e' 


L-5-i?'J 


ElevoTiop  erf  Foundation  Beam 
Fig.  16. 


572 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  12-12 


12.  Concrete  Piles,-— Concrete  piles  are  usually  employed  where  wooden  piles  would  be 
subject  to  decay  or-  to  destruction  by  the  action  of  marine  worms.  By  using  one  of  the  types 
of  concrete  piles,  they  may  be  employed  under  almost  any  circumstance  where  wooden  piles 
would  be  suitable.    Wooden  piles,  to  insure  permanency  must  be  cut  off  below  permanent 

water  line,  as,  when  subjected  to  an  atmosphere  which  is  alter- 
nately wet  and  dry,  they  will  decay.  Concrete  piles  are  not 
so  restricted,  as  they  are  permanent  above  water  line  as  well 
as  below  it,  and  the  cutoff  line  can  therefore  be  as  high  as  is 
consistent  with  the  depth  actually  required  in  the  foundations 
which  they  support.  The  cost  of  the  concrete  piles,  them- 
selves, is  somewhat  greater  than  that  of  wooden  piles,  but 
this  cost  is,  in  a  great  many  cases,  more  than  offset  by  the 
fact  that,  due  to  their  size  and  shape,  they  are  capable  of  sus- 
taining greater  loads  than  wooden  piles,  and  by  the  saving  in 
excavation,  pumping,  sheeting  and  masonry  made  possible  by 
their  use. 

Reinforced-concrete  sheet  piling  has  been  used  quite  ex- 
tensively for  permanent  bulk-heads,  piers  and  the  like,  and  is 
designed  to  meet  the  requirements  of  the  particular  situation 
where  it  is  employed.  This  sheet  piling  may  be  designed  with 
an  interlocking  feature,  or  without,  as  may  best  and  most 
economically  meet  the  particular  requirement. 

Concrete  piles  are  of  two  general  types — ^those  molded  in 
place  and  those  molded  before  driving. 

12a.  Piles  Molded  in  Place. — The  Raymond, 
Simplex  and  Pedestal  piles  are  the  forms  of  this  type  which  are 
most  widely  used. 

Raymond  Piles. — Raymond  concrete  piles  are  made  by 
driving  a  tapering  reinforced  steel  shell  to  refusal,  by  means  of 
a  collapsible  steel  core,  withdrawing  the  core  and  thereupon  filling  the  shell  with  concrete. 
There  is  thus  a  shell  or  form  for  every  pile  and  the  concrete  within  the  shell  may  be  reinforced 
or  not,  as  may  be  desired.  Fig.  18  shows  a  partly  and  an  entirely  completed  Raymond  pile. 
Raymond  piles  are  of  8-in.  diameter  at  the  point  and  taper  0.4  in.  per  ft.  up  to  37  ft.  in 
length. 

The  shell  of  a  Raymond  pile  is  made  of  sheet  steel  of  a  thickness  depending  upon  the 
elasticity  and  crushing  tendency  of  the  earth,  and  is  reinforced  by  means  of  steel  wire  spirally 
wound  on  the  interior  of  the  shell  on  a  3-in.  pitch  and  held  in  place  by 
grooving  the  shell  around  the  wire  and  fastening  the  ends  by  electric 
welding.  The  weight  of  both  shell  and  wire  may  be  varied  to  suit  con- 
ditions, but  24-gage  steel  in  the  shell  and  No.  3  wire  are  most  com- 
monly used. 

A  boot  or  point  of  pressed  steel  is  placed  on  the  end  of  the  core  or 
mandrel  and  completely  encloses  the  bottom  of  the  shell. 

After  the  core  is  collapsed  and  withdrawn,  the  shell  is  inspected  to 
insure  its  perfection  and  it  is  then  filled  with  concrete. 

A  mechanical  problem  that  for  several  years  taxed  the  ingenuity 
of  engineers  connected  with  the  Raymond  system,  was  to  provide  a 
shell  of  sufficient  strength  to  withstand  the  back  pressure  of  the  soil 
after  the  driving  core  had  been  withdrawn.  This  difficulty  has  been  successfully  overcome 
by  means  of  the  spirally  reinforced  steel  shell,  which  is  made  on  machines  specially  designed 
for  the  purpose.  This  shell  is  now  universally  used  in  connection  with  this  method  and  is 
illustrated  in  Fig.  19. 


Fig.  18. — Raymond  pile  core 
collapsed  and  partly  withdrawn. 
Completed  Raymond  pile  without 
reinforcement. 


Sec.  12-12a] 


FOUNDATIONS 


573 


Simplex  Piles. — In  the  Simplex  pile  a  hollow  cylindrical  steel  tube  or  form,  16  in.  in  diameter 
and  ^  in.  thick,  is  driven  to  a  suitable  bearing.  When  the  required  depth  is  reached,  the  form 
is  filled  with  concrete  to  a  sufficient  height,  and  then  withdrawn.  The  driving  point,  depend- 
ing on  soil  conditions,  may  be  either  a  conical  cast-iron  point  that  is  left  in  place,  or  a  hinged 
cutting  edge  called  an  alligator  point  which  opens  as  the  tube  is  withdrawn.  Fig.  20  shows  the 
standard  Simplex  pile  which  fills  the  great  majority  of  requirements  and  is  adaptable  in  all 
ordinarily  unreliable  ground.  The  method  shown  is  termed  ''Standard"  as  about  75%  of 
Simplex  piling  stands  on  the  detachable  cast-iron  point.  The  alligator  point  is  limited  in  its 
use  to  a  certain  class  of  soil — ^that  is,  one  that 
stands  well  after  penetration.  As  generally  used, 
no  reinforcement  is  required,  but  the  system  ad- 
mits of  placing  any  desired  reinforcing  members 
within  the  form.  In  very  wet  soil  a  permanent 
casing  of  slightly  less  diameter  than  the  inside  of 
the  cylindrical  form  is  used  to  prevent  washing  or 
displacement  of  the  concrete.  Sometimes  a  pile  is 
molded  on  the  surface  and  lowered  through  the 
form,  which  is  then  withdrawn,  leaving  the  molded 
pile  in  position. 

Pedestal  Piles. — Pedestal  piles  are  made  in  the 
following  manner:  (1)  a  core  and  steel  casing  are 
driven  to  the  required  depth,  (2)  the  core  is  re- 
moved and  a  charge  of  concrete  is  dropped  in,  (3) 
the  core  is  used  as  a  rammer  to  compresg  the  con- 
crete into  the  surrounding  soil,  (4)  this  process  is 


•Pu//ing  Cab/es 
}h~—Po'/Ar?^  C/amp 

i.---Stee/  Dn^in^ 
Form 


Fig.  20. — Method  of  constructing  Simplex  concrete  piles. 


34' Sheet  Pile 


Fig.  21. — Details  of  piles  used  in  ore  dock 
construction  at  Cleveland. 


repeated  until  a  pedestal  base  about  3  ft.  in  diameter  is  formed,  (5)  the  casing  is  withdrawn 
leaving  the  completed  pile  with  an  enlarged  base. 

Composite  Wood  and  Concrete  Piles. — In  order  to  eliminate  the  great  cost  of  placing  extremely 
long  concrete  piles,  a  method  has  been  devised  by  the  Ryamond  Concrete  Pile  Co.  to  install 
what  is  know  as  a  composite  pile.  This  consists  of  a  Raymond  pile  superimposed  upon  a 
wood  pile.  The  length  of  the  concrete  pile  is  determined  by  the  depth  to  which  it  is  necessary 
to  drive  the  wood  pile  in  order  to  insure  its  cutoff  being  below  water.    A  dowelled  connection  is 


574 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  12-12c 


provided  between  the  wood  and  concrete  pile  which  is  strong  enough  to  withstand  any  lateral 
displacement.  By  this  method  long  wood  piles  can  be  used,  where  necessary,  with  short 
concrete  piles  superimposed  upon  them,  thus  avoiding  the  necessit}^  of  excavation,  sheeting 
and  pumping  in  material  which  is  apt  to  be  extremely  difficult  and  costly  to  handle. 

126.  Piles  Molded  Before  Driving. — Cast  piles  must  be  reinforced  to  permit 
handling,  to  withstand  the  shock  due  to  driving,  and  to  withstand  the  lateral  strains,  if  con- 
ditions are  such  as  to  require  it. 

Precast  piles  are  usually  designed  to  meet  the  particular  conditions  under  which  they  are 
to  be  used.  In  some  cases  they  are  provided  with  cast-  or  wrought-iron  or  steel  driving  points 
and  may  also  have  an  iron  pipe  cast  in  the  center  for  jetting.  Usually,  however,  the  iron  or 
steel  point  is  omitted,  and  jetting,  if  found  necessary,  is  done  by  means  of  pipes,  which  are  not 
fastened  to  the  pile. 

To  protect  the  pile  from  shattering  under  the  severe  blows  oi  tne  hammer,  laminated 
wood  blocks  may  be  used,  although  some  contractors  provide  a  special  driving  head  in  which 
a  ciishion  of  sand,  rope,  or  other  material  is  placed  between  a  driving  block  of  wood  and  the 
concrete  to  prevent  crushing  the  head  of  the  pile.  These  piles  can  be  built  in  any  required 
size,  and  have  been  placed  up  to  90  ft.  in  length,  though  considerably  shorter  piles  are  more 
frequently  employed.  On  dock  and  pier  work  premolded  concrete  piles  are  used  both  as 
supporting  piles  and  as  sheet  piles  to  retain  the  ground  behind  them.  Such  piles  must  not 
only  be  reinforced  against  driving  and  handling  stresses,  but  must  be  designed  to  safely  support 
the  soil  load  to  which  they  will  be  subjected.  These  piles  must  ordinarily  be  cured  for  from 
30  to  60  days  after  casting  before  they  can  be  used,  which,  on  rush  work,  is  considerable  detri- 
ment to  their  use.  It  is  also  extremely  difficult  to  predetermine  the  exact  length  which  will  be 
required,  and  if  it  is  necessary  to  qut  off  any  unused  portion  of  the  pile  this  must  be  done  by 
breaking  away  the  concrete  from  the  reinforcement  and  either  bending  this  latter  down  into 
the  superimposed  caps  or  cutting  it  off  with  hack  saws  or  acetylene  torches. 

Fig.  21  shows  the  details  of  the  concrete  piles  employed  in  the  construction  of  ore  docks 
for  the  Pennsylvania  Railroad  Co.  at  Cleveland,  Ohio.  The  piles,  octagonal  in  shape  and 
reinforced  with  eight  1-in.  round  rods,  were  cast  vertically  in  steel  forms,  a  cast-iron  shoe 
being  fitted  into  the  form  and  becoming  a  part  of  the  finished  pile.  A  1:2:4  mixture  of  both 
gravel  and  broken  stone  was  used.  The  forms  were  removed  in  from  12  to  24  hr.  after  pouring, 
depending  upon  the  weather.  No  pile  was  driven  before  it  was  at  least  30  days  old.  Sheet 
piles  were  also  used,  as  shown  in  Fig.  21. 


SECTION  13 


RETAINING  WALLS 

A  retaining  wall  is  a  wall  of  masonry — such  as  stone,  plain  concrete,  or  reinforced  concrete — 
built  to  sustain  the  lateral  pressure  of  earth  or  of  other  material  possessing  more  or  less  frictional 
stability.  In  stone  masonry  and  plain  concrete  walls  the  section  must  be  made  heavy  enough 
so  that  the  weight  of  the  structure  will  prevent  overturning,  whence  the  name  gravity  section. 
In  reinforced-concrete  walls  the  weight  of  a  considerable  part  of  the  sustained  material  is 
utilized  to  maintain  stability  and,  in  addition,  the  sections  may  be  designed  to  more  nearly 
develop  the  full  strength  of  the  concrete. 

The  treatment  of  retaining  walls  here  given  deals  (1)  with  the  earth  thrust  or  pressure  which 
acts  against  the  wall,  (2)  with  the  forces  which  maintain  the  stability  of  the  wall  under  this 
thrust,  and  (3)  with  the  design  of  walls  to  withstand  these  attacking  and  stabilizing  forces. 

1.  Earth  Pressure. — In  Fig.  1  let  AB  represent  the  back  of  a  retaining  wall,  and  AC 
the  surface  of  the  ground.  The  earth  has  a  tendency  to  break  away  and  come  down  some 
line,  as  CB,  thus  producing  pressure  on  the  wall.  The  weight  of  the 
earth  tends  to  cause  this  breaking  away  while  the  resisting  forces  are 
the  friction  on  the  face  AB  and  on  the  plane  BC  (the  latter  called 
internal  friction);  the  cohesion  along  the  line  BC;  and  the  resistance  of 
the  wall  due  to  its  stability  against  overturning  and  sliding.  The 
coefficients  of  these  frictions,  and  of  cohesion,  vary  with  slope  of  the 
surface  AC,  the  fineness  of  the  retained  material,  and  its  moisture 
content.  Cohesion  is  influenced  greatly  by  moisture  and  the  vibration 
of  moving  loads,  and  seldom  obtains  in  a  newly  made  untamped  fill. 
Most  earth  pressure  theories,  therefore,  treat  the  limiting  case  of  an 
ideal  granular  mass  possessing  no  cohesion.^  This  has  the  effect  of  reducmg  the  curve  of 
rupture  BC  to  a  straight  line. 

All  earth  pressure  theories  given  here  assume  (1)  that  the  surface  of  rupture  BC  is  a 
plane,  (2)  that  the  point  of  resultant  pressure  is  at  one-third  the  height  of  the  wall  from  the 
bottom  when  the  surface  of  the  material  meets  the  top  of  the  wall,  and  (3)  that  the  resultant 
pressure  makes  some  definite  angle  with  the  horizontal.  These  theories  result  in  a  triangular 
distribution  of  pressure  against  the  face  of  the  wall  when  the  surface  of  the  material  meets 
the  top  of  the  wall;  and  since  the  resultant  pressure  must  pass  through  the  centroid  of  this 
pressure-distribution  triangle,  it  must  act  at  one-third  the  height  of  the  wall  from  the  bottom. 
Its  inclination  varies  with  different  conditions  and  theories. 


Table  1. — Angles  of  Repose  and  Weights  per  Cubic  Foot  for  Various  Earths^ 


Material 

Slope 

Angle  of 
repose,  degrees 

Weight   in  lb. 
per  cu.  ft. 

Sand,  dry  

2.8 

1  to  1 

4 

1 

20  to  35 

90  to  110 

1.75 

1  to 

1 

1 

30  to  45 

100  t  o  110 

Sand,  wet  

2.8 

1  to  1 

2 

1 

20  to  40 

110  to  120 

2.8 

1  to 

1 

1 

20  to  45 

80  to  100 

2.1 

1  to 

1 

1 

25  to  45 

80  to  100 

Ordinary  earth,  wet  

2.1 

1  to  1 

75 

1 

25  to  30 

100  to  120 

Gravel,  round  to  angular  

1.75 

1  to  0 

9 

1 

30  to  48 

100  to  135 

Gravel,  sand  and  clay  

2.8 

1  to  1 

3 

1 

20  to  37 

100  to  115 

1  For  theory  including  cohesion,  see  Cain's  "Earth  Pressure,  Walls  and  Bins."    It  is  valuable  for  the  investi- 
gation of  stability  of  existing  walls  backed  by  earth  which  has  been  compacted  in  some  manner. 
From  Cain's  "Earth  Pressure,  Walls  and  Bins,"  p.  9. 

575 


576  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  13-la 


Table  2. — Coefficients  of  Internal  Friction^ 


Kind  of  material 

Tangent 
of  angle 
of  internal 
friction 

Appi 
corre 

Angle, 
degrees 

oximate 
sponding 

Slope 

Authority 

Coal,  shingle,  ballast, 

etc  

1 

423 

54 

0. 7  to  1 

B.  Baker 

Bank  sand  

1 

423 

54 

0.7  to  1 

Goodrich 

Riprap  

1 

097 

48 

0 . 9  to  1 

Goodrich 

Earth  

1 

097 

48 

0.9  to  1 

B.  Baker 

Quicksand,  100  up  .  .  . 

0 

895 

42 

1 . 1  to  1 

Goodrich 

Clay  

0 

895 

42 

1 . 1  to  1 

B.  Baker 

Quicksand,  50-100  

0 

750 

37 

1 . 3  to  1 

Goodrich 

Earth  

0 

750 

37 

1 . 3  to  1 

Steel 

Bank  sand  

0 

750 

37 

1 . 3  to  1 

Wilson 

Sand,  50-100  

0 

549 

29 

1 . 8  to  1 

Goodrich 

Bank  sand  

0 

549 

29 

1 . 8  to  1 

Goodrich 

Clay  

0 

474 

25 

2.1  to  1 

Goodrich 

Cinders  

0 

474 

25 

2.1  to  1 

Goodrich 

Gravel,  3'^-in  

0 

474 

25 

2.1  to  1 

Goodrich 

Gravel,  3^-in  

0 

350 

19 

2.9  to  1 

Goodrich 

Bank  sand  

0 

350 

19 

2.9  to  1 

Goodrich 

Sand,  30-50  

0 

258 

14 

3.9  to  1 

Goodrich 

Sand,  20-30  

0 

179 

10 

5.6  to  1 

Goodrich 

la.  Rankine's  Formula  for  Resultant  Active  Earth  Pressure. — Rankine  has 
developed  the  following  formula^  for  the  case  in  which  (1)  the  total  active  thrust  P  acts  uponi 
a  vertical  plane,  (2)  acts  parallel  to  the  surface  of  the  earth  for  all  cases  in  which  e>0,  (3)  actsi 
in  a  material  of  indefinite  extent,  and  (4)  the  earth  carries  no  load  except  its  own  weight  (Fig.  2): 

^  wh^ 


in  which 

P  =  total  active  thrust  of  earth  against  the  vertical  plane  as  described 
above. 

w  =  weight  per  cubic  foot  of  retained  material. 
h  =  height  of  vertical  section  considered,  as  AC. 
cos  d  —  \/ cos^  d  —  cos2  </) 


Fig.  2. 


cos  ^  +  V cos2  d  —  cos2  0 


where 


6  =  angle  of  surcharge. 
0  =  angle  of  internal  friction. 
Diagram  1  gives  the  values  of  Ce  for  various  values  of  9  and  <l>.    It  should  be  noted  that  P  is 

parallel  to  the  surface  AB,  when  6  is  either  positive,  or  zero;  and  that  it  acts  at  a  point  D,  ^ 


(AC\ 


»  E.  P.  Goodrich:  Trans.  Am.  Soc.  of  C.  E.,  vol.  53,  p.  301. 

*  For  derelopment  see  Baker's  "Masonry  Construction,"  10th  Ed.,  p.  493, 


Sec.  13-16] 

When  d  =  <p,  then 
When  6=0 

in  which 


RETAINING  WALLS 


P  =  y^wh^  ■  cos  (f> 


577 


Ce' 


Ce'  =  tan2  (450  _  3^^) 
Diagram  1 


Values  of  Ce  m  P  -  Ce"^' 

The  following  table  gives  values  of  C/  for  varying  values  of  <t>. 


.60  .90 


Ce' 

4> 

Ce' 

4> 

Ce' 

1 

Ce' 

20° 

0.490 

30" 

0.3333 

40° 

0.2174 

50" 

0.1325 

25° 

0.406 

35° 

0.2710 

45*^ 

0.1718 

55° 

0.0994 

16.  Coulomb's  Wedge  of  Maximum 
Pressure. — Coulomb  advanced  the  theory  that  the 
wedge  ACF  (Fig.  3),  lying  between  the  surface  of  the 
earth  AF  and  the  plane  of  rupture  CF  would  move 
down  against  the  vertical  plane  AC  due  to  its  own 
weight,  causing  the  resultant  pressure  P'.  The  prism 
itself  is  in  equilibrium  through  a  force  acting  upward 
against  CF,  and  making  the  angle  <f)  with  CF ;  and  a  force 
opposing  P'  due  to  the  resistance  of  the  wall  BC  and  of 
the  prism  BAC  (if  BC  is  not  vertical).  If  angle  BCA 
is  relatively  large,  there  will  be  found  a  plane  of  rupture 
SC,  in  the  prism  BAC,  tending  to  force  a  portion  of  this 

prism  upward.    This  plane  of  rupture  makes  angle  /S  with  AC,  which  is  dependent  upon 
and  (f).    Its  value  is  given  in  Table  3. 
37 


578  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  13-16 


Table  3 


0 

/3 

Batter 

of  /3 
(inches 
per  foot) 

0 

4> 

Batter 

of  j8 
(inches 
per  foot) 

15° 

15° 

0°  0' 

0 

20° 

20° 

0°  0' 

0 

20 

20°  25' 

25 

15°  30' 

3H 

25 

21°  05' 

30 

18°  25' 

4 

30 

21°  55' 

35 

19°  10' 

4:14 

35 

21°  30' 

40 

18°  55' 

414 

40 

20°  35' 

45 

18°  05' 

Z14 

"/8 

45 

19°  15' 

4M 

50 

16°  45' 

3% 

"/8 

50 

17°  35' 

55 

15°  10' 

55 

15°  45' 

30° 

30 

0°  0' 

0 

25° 

25 

0°  0' 

0 

35 

12°  05' 

214 

30 

13°  35' 

27^ 

40 

14°  25' 

314 

"78 

35 

16°  15' 

^  /  s 

45 

15°  0' 

3Vi 

40 

16°  55' 

"/8 

50 

14°  40' 

314 

45 

16°  40' 

"/8 

55 

13°  40' 

"7a 

50 

15°  45' 

55 

14°  25' 

"/8 

40° 

40 

0°  0' 

0 

45 

9°  45' 

2 

35° 

35 

0°  0' 

0 

50 

11°  30' 

2% 

40 

10°  50' 

2M 

55 

11°  40' 

45 

10°  55' 

50 

10°  15' 

45° 

45 

0°  0' 

0 

55 

12°  45' 

50 

8°  40' 

m 

55 

10°  05' 

2% 

Let  the  point  G  on  BC  be  so  located  that  CG  =  }iBC.  This  will  be  the  point  of  applica- 
tion of  the  resultant  earth  pressure  P.  Its  line  of  action  as  applied  to  the  wall  makes  the 
angle  7J  with  a  normal  to  the  wall  at  G. 


Fig.  4. 


When  the  face  BC  of  the  wall  is  battered  such  that  a  <  ^,  Construction  I  should  be  followed : 
When  a  =     follow  Construction  I  if  Z  >  0;  otherwise  follow  Construction  II. 
When  a  >  /3,  foUow  Construction  II. 

Construction  I. — ^Let  the  wall  BC  (Fig.  4)  retain  material  whose  surface  slope  is  d,  and  whose 
angle  of  internal  friction  is  <j>.    It  will  be  assumed  that  the  resultant  thrust  P  will  be  applied 


Sec.  13-16] 


RETAINING  WALLS 


579 


at  the  third  point  D,  so  that  it  makes  the  angle  </>  with  a  normal  at  D.  [It  may  be  assumed 
to  make  the  angle  of  friction  (Z  of  the  material  against  the  wall)  with  the  normal  when  that 
angle  does  not  exceed  4>.]  Beginning  at  B,  lay  off  on  BG  arbitrary  distances,  equal,  for  con- 
venience, as  Ba,  ab,  etc.,  and  connect  these  points  a,  h,  c,  etc.  with  C.  Compute  the  weight 
of  these  prisms  thus  formed,  with  length  of  1  ft.  normal  to  the  drawing,  and  lay  them  off  to 
some  convenient  scale,  on  CG,  beginning  at  C,  as  Wa,  Wb,  etc.  If  the  distances  on  BG  are 
equal,  those  on  CG  will  likewise  be  equal.  Draw  CS  making  an  angle  k  with  CG,  where  k  is  the 
angle  made  by  P  with  the  vertical.  Draw  a'Wa,  b'Wb,  etc.,  all  parallel  to  CS,  and  through  these 
points  a',  h',  c',  etc.,  thus  obtained,  draw  a  curve.  A  tangent  to  this  curve  parallel  to  CG  is 
tangent  at  m',  through  which  Cm  may  be  drawn.  Thus  the  prism  BCm  is  that  which  causes  the 
maximum  pressure  P  for  the  conditions  assumed;  and  m'n,  drawn  parallel  to  CS,  and  scaled 
off  to  the  scale  of  the  weights  on  CG,  gives  the  maximum  value  of  this  thrust  P. 

When  6=0  the  surface  of  fill  is  level,  and  Cm  then  bisects  angle  BCG,  and  may  thus  be 
drawn  at  once.  The  weight  of  prism  BCm  may  be  laid  off  on  CG  and  m'n  drawn  to  get  the 
corresponding  value  of  P. 

Construction  II  (Fig.  5). — When  it  has  been  found  from  Table  3  that  the  wall  BC  makes 
a  greater  angle  than  /3  with  the  vertical,  it  becomes  necessary  to  determine  the  pressure  P' 


Fig.  5.  Fig.  6. 


acting  parallel  to  AB,  against  a  vertical  plane  AC  through  C.  Lay  off  for  convenience  equal 
distances  Aa,  ab,  etc.,  and  connect  a,  b,  c,  etc.  with  C.  Compute  the  weights  of  the  prisms 
thus  formed,  and  plot  these  weights  to  some  convenient  scale  on  CG  (which  makes  an  angle 
<l>  with  a  horizontal  through  C),  as  CWa,  Wa,  Wb,  etc.  Draw  through  these  points  the  lines 
Waa',  Wbb',  etc.,  making  the  angle  k'  (equal  to  90°  —  d)  with  CG.  A  smooth  curve  may  then 
be  drawn  through  a',  6',  c',  etc.  Point  r'  is  located  by  drawing  a  tangent  to  this  curve  parallel 
to  CG.  The  plane  rC  is  the  plane  of  rupture  for  the  wedge  BCr,  which  might  be  forced  up- 
ward due  to  the  pressure  P'  and  the  resistance  of  the  wall.  The  resultant  pressure  P'  acting  at 
D  in  either  direction  on  the  line  FD  is  equal  to  sr'  scaled  to  that  of  the  plotted  weights  on  CG. 

Let  the  inclination  of  BC  to  the  vertical  be  a.  Extend  CG  beyond  C  and  lay  off  a  counter- 
clockwise; then  lay  off  90  deg.  The  line  thus  obtained  will  make  an  angle  q  with  the  plane  of 
rupture  Cr. 

Now  if  q  is  less  than  Z,  where  Z  is  the  angle  of  friction  of  the  material  on  the  wall,  produce 
P'  to  F,  on  BC.  Through  F  the  resultant  P  on  the  face  BC  will  act,  such  that  its  angle  of  in- 
clination with  the  vertical  (d)  equals  ZrCG,  or  what  is  the  same  thing,  such  that  it  makes  the 
angle  q  with  a  normal  to  BC.    The  magnitude  of  P  is  r'S  scaled  to  that  of  the  weights  on  CG. 

If  q  is  greater  than  Z,  perform  Construction  I  making  P  slope  the  angle  Z  with  the  normal 
to  BC,  Fig.  4. 


580 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  13-lc 


When  6  is  negative  and  not  large,  or  when  oc  is  negative  but  not  to  exceed  10  deg.,  the  con- 
structions I  and  II  may  still  be  used. 

Rebhann's  Construction. — The  value  of  P  by  the  Coulomb  theory  may  be  found  in  the 
following  manner:  Let  BC,  Fig.  6,  be  the  back  face  of  a  retaining  wall  with  the  earth  surface 
on  the  line  BJ.  AC  is  the  vertical  plane  against  which  P  acts,  at  point  D,  y^AC  from  C. 
CJ  makes  the  angle  of  internal  friction  </>  with  the  horizontal.  Draw  AF  so  that  ZCAF  =  6 
+  </).  With  O  as  the  center  and  FJ  as  the  diameter,  describe  the  arc  FMJ.  Draw  CM  tangent 
to  this  arc.  (The  point  of  tangency  M  may  be  located  accurately  by  describing  the  semicircle 
CMO  on  the  diameter  CO.)  Make  CN  =  CM,  and  through  N  draw  QN  \\  AF.  Making  RN 
=  QN  forms  the  triangle  QRN.    The  magnitude  of  P  is 

P  =  (iy)(Area  QRN) 

Its  direction  corresponds  to  Rankine's  thrust,  parallel  to  AJ. 

Point  Q  may  be  located  by  making  a  construction  similar  to  that  for  finding  N.  Draw  TC  \\  AF.  Describe 
arc  A  UJ  on  the  diameter  AJ.  Locate  U  by  drawing  arc  T  US  on  diameter  TS,  whence  TU  is  tangent  to  A  UJ  at  U. 
Make  TQ  =  TU. 

When  6  =  ^,  A  J  and  CJ  do  not  meet;  also,  Z.CAF  =  2^. 
When  6=0,  ZCAF  =  <f>,  and  P  is  horizontal. 

Ic.  Comparison  of  Coulomb  and  Rankine  Results. — Rebhann's  construction, 
also  that  of  Fig.  4,  gives  results  which  check  those  of  the  Rankine  formula,  upon  a  vertical  plane, 
when  the  earth  extends  indefinitely.    The  theories  differ  somewhat  for  other  cases. 

Id.  Useful  Interpretation  of  Results  of  Earth  Pressure  Theories. — Assume  a 
wall  BC,  Fig.  7,  to  retain  a  fluid.  Since  the  pressure  of  fluid  is  dependent  upon  the  depth,  the 
intensity  of  the  pressure  at  any  depth  y  =  wy,  in  which  w  is  the  weight 
per  cubic  foot  of  the  fluid  in  pounds.  Then  the  pressure  at  CD  is  wh. 
Thus  the  variation  in  pressure  intensity  is  as  a  straight  line,  BD.  The  re- 
sultant of  this  triangle  of  pressure  is  F  =  ^if^A^.  It  acts  horizontally,  normal 
to  BC  and  through  the  centroid  of  BCD. 

Suppose  the  top  of  the  wall  to  be  covered  at  a  depth  h'y  Fig.  8, 
with  this  liquid.    The  pressure  at  J5  is       =  wh'.    Similarly,  CD  =  w{h'  +  h). 
The  total  pressure  on  BC  is  equal  to  the  area  of  the  trapezoid  of  pressure 
BPDC ;  and  its  resultant  P  acts  through  the  centroid  of  this  trapezoid  dis- 
tance y  from  CD.    It  acts  normal  to  BC.    The  distance  y  may  be  found 
from  the  formula 


Fig.  7. 


y  = 


h    h  +  3h' 


3   h  +  2h' 


Now  the  precise  difference  between  earth  (granular  mass)  and  fluid 
pressures,  is  that  in  the  case  of  earth  there  is  not  equal  pressure  in  all  di-  yig  8 

rections  at  a  given  point.  If  E„  represents  vertical  pressure  at  a  point  in 
an  earth  mass,  and  Ei  the  lateral  pressure  at  that  point,  then  Ei  =  CeEv.  Since  in  each  of 
the  foregoing  formulas  it  is  obvious  that  the  intensity  of  pressure  varies  with  the  depth,  th 
pressure  areas  caused  by  the  earth  are  similar  to  those  caused  by  a  fluid.  Thus,  from 
Diagram  1  on  page  577,  if  w'  =  CeW,  then  P  would  equal  the  pressure  caused  by  a  fluid  whos 
weight  is  w',  and  whose  direction  of  acting  upon  the  plane  considered  would  be  parallel  to 
the  direction  of  P.  In  like  manner  any  of  the  foregoing  developments  may  be  converted 
into  fluid-like  action. 

2.  Live  Load  on  Top  of  Fill — Equivalent  Surcharge. — When  a  live  load  is  apphed  in  a 
direction  normal  to  the  face  of  the  wall,  as  for  instance  upon  a  track  or  roadway  at  right  angles 
to  a  bridge  abutment.  Fig.  9,  the  earth  thrust  P  is  larger  than  before.  Let  the  weight  of  th 
appUed  live  load  (including  impact)  be  replaced  by  an  equal  weight  represented  by  the  prisE 
AMN,  of  the  same  material  as  that  retained  by  the  wall.  Let  the  depth  of  this  ''equivalen 
surcharge"  be  h\ 


Sec.  13-3] 


RETAINING  WALLS 


581 


The  total  pressure  on  MC  is  given  by  the  trapezoidal  pressure  ACSR,  whose  resultant  is 
P.  It  may  be  obtained  by  determining  an  equivalent  fluid  of  weight  w'  as  described  in  the 
preceding  article;  or  it  may  be  determined  graphically  by  finding  the  thrust  on  M C,  then  on  MA, 


and  taking  their  difference.    In  usual  cases 
being  less  than  5%  on  the  safe  side.    As  before, 

h  h^+Sh 
3  *  h 


P  will  be  nearly  equal  to  +  ^)^>  the  error 


y 


+  2h' 

The  thrust  P  is  finally  prolonged  to  meet  the  face  BC,  where 
it  is  combined  with  the  weight  of  the  prism  BAG,  to  determine 
the  final  thrust  against  the  wall. 

Construction  I,  page  578  could  have  been  employed  to  find 
directly  the  thrust  against  BG  by  placing  the  surcharge  up 
to  B. 

When  roadways,  tracks,  or  other  live  loads  are  placed 
close  to,  and  parallel  to,  the  wall,   the  method  described 

above  will  apply.  If  these  live  loads  are  remote  from  the  wall,  the  method  of  procedure 
described  in  the  following  article  is  recommended.  It  will,  of  course,  apply  to  both  cases, 
but  is  a  saving  for  the  conditions  cited. 

3.  Live  Load  on  Top  of  Fill — Pressure  Distribution. — ^Let  AD,  Fig.  10,  represent  a  track 

parallel  to  the  wall  BG.  Tests ^  show  that  the  pressure  on  AD  is 
practically  all  distributed  between  AF  and  DG,  which  make  30  deg. 
with  the  vertical.  Assuming  uniform  distribution  throughout  this 
region,  the  pressure  per  square  foot  on  the  horizontal  plane  FG  is 
computed,  F  being  the  point  where  AF  strikes  the  wall.  Let  the  in- 
tensity of  pressure  on  ah,  without  the  load  AD,  be  shown  by  the  tri- 
angle abc.  Let  de  (=  c/)  equal  the  unit  pressure  on  FG  due  to  AD 
multiplied  by  some  factor  N  dependent  upon  the  material  in  the  fill. 

The  resultant  of  ahc,  acting  ^  above  G,  and  the  resultant  of  dejc,  act- 
ing y^GF  above  C,  are  then  combined  to  get  the  final  thrust  on  BG. 

The  factor  N  just  referred  to  may  be  determined  from  the  table  on  page  577.  This  fac- 
tor is  the  ratio  of  lateral  unit  pressure  to  vertical  unit  pressure,  and  is  thus  dependent  upon 
the  value  of  the  angle  of  internal  friction.    Thus  N  =  Ge  in  the  table  referred  to. 

4.  Stability  of  a  Retaining  Wall. — Two  motions  of  the  wall  tend  to  result  due  to  the  action 
of  the  earth  thrust  P:  (1)  a  tendency  to  slide  forward;  and  (2)  a  tendency 
to  tip  forward  about  some  point  on  the  base. 

The  tendency  for  the  wall  to  slide  forward  may  be  stated  as  being 
equal  to  the  tangential  component  of  the  resultant  force  R  acting  upon 
the  base,  or  plane  of  bearing.  In  walls  having  a  horizontal  plane  of 
bearing  it  is  equal  to  the  horizontal  component  Rh,  Fig.  11.  The  re- 
sistance to  sliding  may  be  developed  in  three  ways:  (1)  by  the  friction  on 
the  plane  AD,  (2)  by  the  depth  of  A  below  the  surface  of  the  ground  in 
front  of  the  wall,^  and  (3)  by  a  key  wall  projecting  downward  from  the 
plane  AD.    The  frictional  resistance  of  the  base  plane  AD  may  be  taken 

as  the  total  component  normal  to  AD  multiplied  by  the  coefficient  of  friction  of  the  wall  material 
upon  the  supporting  soil  (see  Table  4).  The  key  wall  will  cause  compression  in  the  soil  before 
it,  the  intensity  of  which  should  not  exceed  seven-tenths  of  the  maximum  working  unit  pressure. 

The  resistance  to  overturning  the  wall  is  afforded  by  a  distributed  reaction  of  the  bearing 
soil  upward  against  the  base  of  the  wall.  Since  the  bearing  capacity  of  the  soil  must  not  be 
exceeded,  it  is  necessary  to  study  the  distribution  of  this  reaction,  and  to  determine  simple 
rules  which  may  govern  to  secure  stability. 

1  See  tests  by  Prof.  M.  L.  Enger,  Eng.  Rec,  Jan.  22,  1916,  p.  106-8. 

2  See  Art.  15,  Sect.  17,  page  763. 


582 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  13-4 


Table  4. — Coefficients  and  Angles  of  Friction 
Between  Earth  and  Other  Materials 


Materials 

/  = 

tan  <l> 

4> 

Masonry  upon  masonry  

0.65 

33° 

Masonry  upon  wood,  with  grain  

0.60 

31° 

Masonry  upon  "wood,  across  grain.  .  .  . 

0.50 

26°  40' 

Masonry  on  dry  clay  

0.50 

26°  40' 

Masonry  on  wet  clay  

0.33 

18°  20' 

0.40 

21°  50' 

Masonry  on  gravel  

0.60 

31° 

Fig.  12. 


Consider  the  base  of  a  1-ft.  section  of  wall  to  be  represented  in  projection  by  AB,  Fig.  12. 
When  R  acts  at  the  center  of  gravity  O,  the  intensity  of  pressure  is  uniform  over  the  base 

R  R 

plane  and  is  equal  to  the  vertical  component  of  R  divided  by  the  base  area,  ~  R 

acts  at  any  other  point,  as  Q,  the  force  Rv  is  equivalent  to  an  equal  Rv  at  O  and  a  couple  whose 
moment  is  RvXq.    At  any  point  distant  x  from  O  the  intensity  of  the  pressure  due  to  this  moment 

is  ^"^"^  '  in  which  /  is  the  moment  of  inertia  of  the  base  plane  about  an  axis  through  0  at  right 
angles  to  AB  and  lying  in  the  base  plane.    At  the  edges  A  and  B  this  intensity  =  = 

QRvXo 


^2       The  intensity  of  pressure  at  edge  A  is 

R 

Pi 


QRvXo 


and  at  edge  B  it  is 


P2 


Rvf  6^o\ 

Rvl  _6^o\ 
hV  h) 


(lb.  per  sq.  ft.) 


(lb.  per  sq.  ft.) 


Since  the  base  plane  cannot  resist  tension,  the  second  term  of  ^2  must  not  exceed  the 
first.    As  a  limiting  condition,  if  the  two  terms  are  just  equal,  p2  =  0,  or 

Rv  _  ^RvXq 

in  which  Xo  is  the  distance  to  Q  when  the  eccentricity  Rv  just  causes  this  equality.  Solving 

b 
6 


Xo 


(ft.) 


The  rule  thus  determined  follows:  The  resultant  f orce  acting  upon  the  base  plane  must  strike 
it  back  {toward  B)  of  the  forward  third  point  of  the  base  plane,  if  no  tension  is  to  be  taken  by  that 
plane. 

When  ?>2  =  0, 

Pi  =  (lb.  per  sq.  ft.) 


The  relation  between  the  point  of  application  of  the  resultant  R  upon  the  base  and  the 
unit  stress  in  the  soil  under  the  toe  is  shown  in  Diagram  2.  The  rapid  rise  in  unit  pressure  due 
to  a  small  forward  movement  should  be  noted.  Since  it  has  been  advised  in  this  discussion 
to  limit  the  resultant  to  the  forward  third  point,  the  unit  pressure  under  the  toe  for  that  condi- 
tion is  taken  as  100%.  Its  maximum  value  depends  upon  the  decision  of  the  engineers  re- 
garding the  quality  and  supporting  power  of  the  soil.    If  R  falls  inside  of  the  middle  third,  the 


Sec.  13-4] 


RETAINING  WALLS 


583 


pressure  at  the  toe  will  be  less  than  100  %.    The  difference  between  its  percentage  and  100  %  will 

give  the  unit  pressure  at  the  heel  in  %  of 

Table  5  gives  allowable  unit  pressures  upon  various  soils.  If  high  walls  are  to  be  built, 
tests  should  be  made  at  the  site,  as  described  in  Art.  1,  Sect.  12.  The  tendency  of  the 
pressure  on  the  bearing  soil  to  heave  the  earth  in  front  of  the  wall  should  also  be  investigated. 


Diagram  2 


•£  200 
I 

^  300 

D 


It  400 


O  20  40  60 

Distance  of  K from  toe  in  %oib 


Table  No.  5. — Safe  Bearing  Capacity  of 
Short  Tons  per  Square  Foot 


Soils 


When  the  soil  pressure  under 
the  toe  is  greater  than  the  allow- 
able unit  pressure,  the  base  area 
should  be  increased  by  extending 
the  toe  forward.  On  a  solid  wall 
this  may  be  done  by  projecting  a 
toe  from  the  front  face,  whose 
top  surface  slopes  from  30  to  60 
deg.  with  the  face  of  the  wall, 
and  whose  bottom  surface  is  an 
extension  of  the  base  plane. 
Such  a  projecting  toe  must  be 
designed  for  shear  and  moment, 
the  same  as  the  toe  on  a  rein- 
forced-concrete  wall. 

On  a  reinf orced-concrete  wall 
the  unit  pressure  under  the  toe 
may  be  reduced  by  extending  the 
toe  farther  from  the  face  of  the  wall 
weight  of  fill. 

When  a  base  slab  is  used  under  the  body  of  the  wall  for  capping  piles,  or  for  providing 
suitable  bed,  the  unit  pressure  at  the  front  edge  of  the  wall  at  the  top  surface  of  the  base  slab 
must  not  exceed  the  allowable  compressive  unit  stress  in  the  concrete.  Should  it  exceed  this 
value,  provision  may  be  made  as  above  described.    Care  should  always  be  exercised  in  properly 


Kind  of  material 

Mini- 
mum 

Maxi- 
mum 

Rock,  the  hardest,  in  thick  layers  in 

200.0 

Rock  equal  to  best  ashlar  masonry .... 

25.0 

30 

15.0 

20 

Rock  equal  to  poor  brick  masonry  

5.0 

10 

6.0 

8 

Clay  in  thick  beds,  moderately  dry .... 

4.0 

6 

1.0 

2 

Gravel  and  coarse  sand,  well  cemented. 

8.0 

10 

Sand,  dry,  compact  and  well  cemented. 

4.0 

6 

2.0 

4 

0.5 

1 

Some  designers  extend  the  back  slab  to  obtain  more 


584 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  13-4a 


keying  the  body  of  the  wall  against  sliding  or  overturning  on  the  base  slab.  Keyed  joints  and 
dowel  rods  may  be  used  for  this  purpose. 

4a.  So-called  "  Factor  of  Safety." — In  masonry  walls  it  has  been  customary  to 
define  the  factor  of  safety  against  overturning  by  the  relation 

moment  of  resisting  forces 

factor  of  safety  =   7 — 7^  1  ?  

moment  of  overturnmg  forces 


when  these  moments  are  taken  about  the  toe  of  the  base.  This  would  assume  a  rigid  bed  for 
the  wall.  When  the  bed  is  of  yielding  material,  the  wall  will  not  rock  on  the  toe  because  the 
earth  under  the  forward  third  of  the  base  will  crush,  allowing  the  wall  to  settle  as  it  tips.  This 
factor  of  ''safety"  will  not  be  used  in  this  discussion. 

46.  Factor  of  Limitation. — Two  considerations  resulting  from  the  foregoing 
discussion,  and  from  long  experience,  are  (1)  that  the  resultant  of  pressures  stay  within  the 
middle  third,  and  (2)  that  uniform  settlement  should,  as  far  as  possible,  be  provided  for  by 
bringing  the  resultant  as  near  as  practicable  to  the  center  of  the  base.  These  conditions  make 
it  desirable  that  in  the  usual  condition  of  loading  the  resultant  should  pass  through  the  middle 
third  near  its  center,  and  that  for  the  unexpected  or  unusual  loadings  it  should  never  exceed 
the  forward  limit  of  the  middle  third.  The  "factor  of  limitation"  is  that  factor  by  which  the 
thrust  of  the  earth  may  be  multiplied  to  determine  that  thrust  which  will  cause  the  resultant 
to  pass  through  the  forward  third  point.    In  other  words, 


factor  of  limitation  = 


limiting  thrust 
actual  thrust 


It  is  of  interest  to  note  that  for  a  wall  of  given  height,  supporting  a  level  fill,  the  factor  of 

limitation  may  be  increased  a  certain  percentage  by 
Diagram  3  increasing  the  width  of  base  a  definite  amount,  which 

amount  is  the  same  for  plain  walls  and  for  reinforced- 
concrete  cantilever  or  counterfort  walls.  This  fact  is 
illustrated  in  Diagram  3.  For  example,  suppose  a  given 
wall  with  a  30-ft.  base  to  have  been  designed  with  a 
factor  of  limitation  of  one.  If  12.5  ft.  were  added  to 
the  width  of  base,  the  factor  of  limitation  for  the  wall 
would  be  doubled. 

5.  Types  of  Retaining  Walls. — Retaining  walls  of 
concrete  may  be  of  plain  concrete,  or  of  reinforced  con- 
crete. Plain  concrete  walls  have  proportions  similar  to 
those  of  masonry,  and  their  section  is  usually  the 
gravity  section.  Reinforced-concrete  walls,  however, 
are  not  as  massive.  The  various  types  in  common  use 
are:  (1)  the  T- or  cantilever  wall;  (2)  the  counterforted 
cantilever   or    Wall;  (3)  the  buttressed  wall;  and  (4)  the  cellular  wall. 

Other  special  forms  have  been  developed  for  various 
purposes. 

The  following  discussion  is  intended  to  give  preliminary  proportions  before  the  final  inves- 
tigation is  made  for  stabihty.  For  the  cases  here  given  no  further  designing  need  be  done; 
but  for  irregular  embankments  and  other  unusual  conditions  the  cases  cited  will  aid  in  choosing 
the  preliminary  form  of  wall. 

6.  Design  of  Plain  Concrete  Walls. 

6a.  Formulas  and  Diagrams  for  the  Two  Principal  Types.- 


0  5  10  15 

Additional  width  in  feet 

Level  fill  against  plain  concrete  walls 
and  reinforced  concrete 
counterfort  walls. 


-For  type  (a)  shown 


m  Fig,  13,  let 


Sec.  13-6a] 


RETAINING  WALLS 


5S5 


A  =  area  of  cross-section. 
}Y  =  weight  of  1  ft.  of  wall 

width  at  top  =  g 


150A  for  concrete. 


width  at  base, 
height  of  wall. 

angle  between  P  and  horizontal. 

distance  from  outer  third  point  Q  to  centroid  of  section, 
factor  of  limitation,  or  the  number  of  times  Ph  may  be  in- 
creased before  the  resultant  passes  through  the  third  point  Q. 
Assuming  the  resultant  to  be  passing  through  Q,  then  the  algebraic 
sum  of  the  moments  about  Q  equals  zero,  or  XMq  =  0, 


Wc  + 


2P,b 


When 


and  W  =  150A,  then  c  =  0.3266,  whence,  since  P  = 


28.56^  +  0.333  fw'hh  sin  e  -  0.im7fw'h^  .cos  e 
Diagram  4 


Ratio  of  width  of  base  to  total  height  » 


Many  designers  prefer  to  disregard  the  frictional  component  Pv  It  cannot  well  be  devel- 
oped upon  a  vertical  face.  Walls  should  have  a  slight  batter  on  the  back,  although  presumably 
vertical.    Letting  e  =  0, 

I  =  0.0764  V/u/ 

When  e  =  30  deg. 


28.5      +  0.1667/w;'  t  -  0.1442/w)'  =  0 


Diagram  4  gives  values  of  ^  for  various  values  of     and  /,  when  e  =  0  and  30  deg. 


586 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  13-66 


Type  (b),  {Fig.  14). — For  comparison  with  type  (a),  a  level  filling  will  be  assumed.  It 
may  be  noted  that  a  prism  of  earth  BAC  will  add  to  the  stability  for  this  type.  However, 
the  wall  in  general  is  less  stable  because  its  weight  W  lies  forward  from  Q. 
As  before,  assuming  XMq  =  0,  there  results, 

I  =  0.10\/fw'       when  w  =  100  lb.  per  cu.  ft. 

and 

I  =  0.0915ViV    when  w  =  120  lb.  per  cu.  ft. 

in  which  w  is  the  weight  per  cubic  foot  of  the  material  comprising  the 
material  in  prism  ABC.    Diagram  5  gives  values  of  ^  for  these  two 
cases  when  /  and  w'  have  varied  values  as  well  as  with  e  =  30  deg.  or  zero. 
Diagram  5 


•-> 

\  ^^I 

i 

,  p 

Y 

<  ^  > 

C 

Fig.  14. 


.6  .7  .8,     •  .9 

Ra+io'  of  widfh  Of  base  toto+al  height' -^i 


Ratio  of  width  of  base  to  total  height 


Ratio  of  height 

of  earth  to 
height  of  wall 
above  ground 

Ratio  of  thick- 
ness of  base  to 
total  height  of 

wall  =  r- 

h, 

Ratio  of  height 
of  earth  to 
height  of  wall 
above  ground 

r 

Ratio  of  thick- 
ness of  base  to 
total  height  of 

wall  =  — 

n 

1.0 

0.35 

2.0 

0.58 

1.1 

0.42 

2.5 

0.60 

1.2 

0.46 

3.0 

0.62 

1.3 

0.49 

4.0 

0.63 

1.4 

0.51 

6.0 

0.64 

1.5 

0.52 

9.0 

0.65 

1.6 

0.54 

14.0 

0.66 

1.7 

0.55 

25.0 

0.68 

1.8 

0.56 

or  more 

65.  Trautwine's  Table.— 

Table  on  this  page  taken  from  Traut- 
wine's  ''Civil  Engineer's  Pocketbook" 

gives  values  of  ^  for  various  heights 

of  surcharge,  as  for  instance,  road- 
beds. Values  here  given  are  empirical, 
and  may  be  used  for  average  condi- 
tions. They  are  the  result  of  long 
practice  in  retaining-wall  design. 
The  earth  is  assumed  to  slope  up 
from  the  top  of  wall  till  it  reaches  a 
level  at  the  height  indicated  by  the 
ratio  in  the  first  column. 


Sec.  13-6c] 


RETAINING  WALLS 


587 


Trautwine  recommends  that  when  the  backing  is  somewhat  consoHdated  in  horizontal 
layers,  each  of  these  thicknesses  may  be  reduced,  but  that  no  rule  can  be  given  for  this.  He 
also  states  that  since  sand  and  gravel  have  no  cohesion,  the  full  dimensions  as  above  should 
be  used  with  these  materials,  even  though  the  backing  be  deposited  in  layers.  A  mixture  of 
sand,  or  earth  with  a  large  proportion  of  pebbles,  bowlders,  etc.,  will  exert  a  greater  pressure 
against  the  wall  than  the  materials  ordinarily  used  for  backing ;  and  hence  when  such  backing 
has  to  be  used,  the  above  thicknesses  should  be  increased,  say,  about  }i  to  }i  part. 

6c.  Selection  of  Preliminary  Section. — The  above  methods  of  proportioning 
the  gravity  section  enables  the  selection  of  a  preliminary  wall  against  which  the  earth  pressures 

Diagram  6 


1.0 


(D 
D 


1.5 


e.0 


e.5 


^^slPlain  concrete  walls 
_  5     Gravity  sections 
/a)and(b) 


Reinforced  concrete  walls 
Canti  fever,  counterfort, 
or  buttress  walls_ 


30 


40  50      30  40  50  60 

Distance  of  resultant  from  toe  in  percent  of  b 


may  be  determined,  and  the  actual  resultant  obtained.  The  resulting  soil  pressures  are  then 
determined  and  compared  to  the  allowable  pressures.  Analysis  should  be  made  for  the  lateral 
pressure  /  •  Ph  (the  resultant  for  which  is  to  pass  through  the  forward  third  point)  as  well  as  for 
Ph.  Likewise  resistance  to  sliding  should  be  great  enough  to  prevent  sliding  under  the  action 
of /-P^. 

Since  the  thrust  of  /  •  Ph  will  cause  the  resultant  to  pass  through  the  forward  third  point, 
the  actual  thrust  Ph  will  cause  a  resultant  much  nearer  the  center.  Diagram  6  has  been  drawn 
to  show  the  effect  of  various  values  of/  upon  the  actual  position  of  the  resultant.  For  instance, 
for  type  (a),  by  designing  with  /  =  1.75,  the  actual  resultant  will  pass  through  a  point  0.4756 
from  the  toe.  If  the  actual  thrust,  causing  this  actual  resultant,  should  be  multiplied  by  1.75, 
the  resultant  thus  caused  would  pass  through  the  forward  third  point. 

Having  the  .position  of  the  resultant  (0.4756  from  the  toe), 
the  unit  soil  pressure  under  the  toe  may  be  found,  from  Diagram 

2,  to  be  55  %  of        that  is,  55  %  of  the  allowable  maximum  unit 

pressure  assigned  to  the  case  when  R  passes  through  the  third 
point. 

7.  Design  of  Cantilever  or  T-walls  of  Reinforced  Concrete. — 

A  cantilever  or  T-wall  of  reinforced  concrete  consists  of  a  can- 
tilever stem  AD,  Fig.  15,  rigidly  attached  to  a  base  slab,  BC. 
Since  stability  greatly  depends  upon  the  weight  W2  of  the  earth 
ADNM,  it  is  likewise  affected  by  the  distance  x  of  the  face  of  the 
stem  from  the  toe  B. 

la.  To  Determine  Approximate  Base  Width. — As  an  approximate  determination 
(within  10%),  we  will  assume  the  weight  of  the  wall  and  earth  above  DN  to  be  equal  to  a  block 
of  earth  of  section  A  (6  —  x),  of  the  same  weight,  w,  of  the  earth  in  the  fill.^    Assuming  the 

1  See  article  by  H.  M,  Gibb,  Eng.  News,  July  24,  1913. 


588 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  13-7a 


resultant  to  pass  through  the  forward  third  point,  the  total  moment  about  that  point  must 
equal  zero.    The  weights  of  the  length  x  of  the  base  will  be  neglected.  Thus, 


^  (6  -  x){Sx  +  6)  =  y2fw'h^ 


Whence 


in  which 


Vfi 


Vw(l  ~+  2k  -  3/b2) 


=  CVfi 


C2  = 


1 


lOVl  +  2k 
1 


Sk'- 


for  w  =  100  lb.  per  cu.  ft. 
forw  =  120  lb.  per  cu.  ft. 


'      10-95  Vl  +2k  -  3/c2 
Values  of  Ci  and  C2  (to  be  introduced  in  place  of  C  above)  may  be  taken  from  Diagram  7. 

Diagram  7 

0.14 


20  AO  j60 

Values  oT  k 

Diagram  8 


Proportions  of  cantilever,  counterfort,  or  buttress  retaining  wall. 

It  is  important  to  note  in  Diagram  7  that  for  any  given  value  of  w'  and  /,  the  minimum 

value  of  ^  is  that  for  k  =  }4;  and  that  when  k  =  }i  it  is  very  nearly  the  same.    Since  it  is 

obvious  that  resistance  to  sliding  is  increased  by  increasing  the  weight  on  the  base,  it  is  common 
practice  where  possible  to  place  the  stem  so  that  fc  =  3^. 


Sec.  13-76] 


RETAINING  WALLS 


580 


The  width  of  base  of  a  cantilever  wall  may  be  taken  from  Diagram  8,  by  entering  with  a 
I     value  of  w'  and  moving  to  the  right  to  the  selected  value  of/;  thence  down  to  the  desired  value 

of  k]  thence  to  the  right  margin  where  the  proper  value  of  ^  may  be  read. 

Illustrative  Probsem. — Desired  cantilever  wall,  /t  =  20  ft,;  A;  =  H,  /  =  2,  For  material  to  be  retained, 
w  =  100,  e  =  0,  <t>  =  29  deg.  Determine  width  of  base.  From  the  table  on  page  577  C/  =  0.348.  From  Art.  Id, 
w'  =  Ce'w  or  w'  =  34,8.  Entering  Diagram  8  with  thi.«  value,  thence  horizontally  to  /  =  2.00,  thence  downward 
to  A;  =  H  (for  w  =  100),  thence  horizontally  to  the  right  margin,  ^  =  0.70.    Therefore  6  =  20  X  0.7  =  14  ft. 

From  the  right-hand  side  of  Diagram  6  it  is  found  that  for  /  =  2  and  k  =  H,  the  resultant  will  strike  the  base  at  a 
point  0.50  X  14  =  7.00  ft.  from  the  toe.  The  corresponding  pressure  under  the  toe  for  that  position  is,  from 
Diagram  2,  about  50%  of  the  working  value 

76.  Stem. — The  tendency  of  the  earth  pressures 
is  to  break  the  stem  of  the  wall,  similar  to  a  cantilever  beam. 
This  moment  is  greatest  at  the  junction  of  the  wall  with  the 
base.  Fig.  16  shows  a  cantilever  wall,  with  the  total  earth  pres- 
sure area  divided  into  two  parts — the  pressure  on  the  stem,  and 
the  pressure  on  the  base  slab.  The  thrust  Pi  is  the  same  as  that 
for  a  depth  of  earth  equal  to  the  height  of  the  stem  above  the 
upper  side  of  the  base  slab.  The  bending  moment  per  foot  of 
wall  at  its  junction  with  the  base  surface  is  equal  to  the  moment 
of  Pi  about  that  same  line;  or 

M  =  f  Fi  cos  e  .  ^  =  — g—  •  cos  e 

But  for  balanced  stresses  in  the  reinforced  concrete,  M  =  Kbd'^  (see  Diagram  2  of  Sect.  7, 
page  360).    Whence  for  a  12-in.  width  of  stem, 

d  =  0.408/ii''''^^'-  cos  e  _  (in.) 


Fig.  16. 


(ft.-lb.) 


in  which  d  =  effective  depth  of  stem  slab  in  inches,  hi  =  total  height  of  stem  in  feet,  and 
w'  =  fluid  equivalent  in  pounds  per  cubic  foot. 
When  e  =  0, 

d  =  OAOShi''  yj^-^  (in.) 

When  e  =  30  deg., 

d  =  0.380Ai''^  (in.) 
The  vertical  reinforcing  will  be  on  the  face  next  to  the  backing. 

Diagram  9  gives  the  effective  depth  d  for  various  values  of  fw'  and  K.  The  latter  term 
includes  the  selection  of  working  stresses  and  the  percentage  of  steel.  To  this  effective  depth 
is  added  sufficient  concrete  to  properly  imbed  the  steel.  The  thickness  of  wall  at  the  top  is 
arbitrary,  but  never  less  than  6  in. 

Illustrative  Problem. — The  stem  of  a  wall  is  16  ft.  above  the  top  of  the  base  slab.  Required  its  maximum 
thickness  for  w'  =  40,  /  =  1.50,  n  =  15,  /s  =  16,000,  and  fc  =  650.  Slope  of  surcharge  (hence  e)  is  30  deg.  From 
Diagram  2,  Seet.  7,  K  =  107,  p  =  0.0077. 

Entering  Diagram  9  with  fw'  =  (40) (1.50)  =  60;  thence  to  iv  =  107;  thence  vertically  to  hi  =  16;  thence 
to  right  margin,  where  d  =  19.5  in.  Due  to  the  fact  that  e  =  30  deg.,  from  the  correction  curve  at  the  top  it  is 
found  that  d  for  this  case  should  be  93.2%  of  19.5,  or  18.2  in.    Total  thickness,  therefore,  should  be  21  in. 

It  may  be  necessary  in  some  cases  to  take  into  account  the  weight  of  the  vertical  slab  in 
finding  the  maximum  thickness  required.    The  resultant  of  the  earth  pressure  and  weight  of 


590 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  13-7c 


stem  may  readily  be  found  graphically  and  then  the  eccentricity  of  this  resultant  on  the  section 
at  the  junction  with  the  base  slab  may  be  scaled.  The  required  thickness  and  percentage  of 
reinforcement  may  then  be  found  by  means  of  Diagram  15  or  16  of  Sect.  9,  pages  404  and  405. 

It  is  not  necessary  to  carry  all  the  steel  to  the  top  of  the  stem.  The  moment  diagram 
should  be  plotted  for  the  stem  and  some  of  the  rods  cut  off  a  sufficient  distance  above  the 
point  where  they  are  not  needed  to  secure  anchorage  (see  Arts.  16  and  22,  Sect.  7). 


Diagram  9 

Angle  e  in  degrees 
0      5      to      15      20     g5    .  30    35     4  0  45 


7c.  Base  Slab. — The  greatest  stress  in  the  base  slab  will  be  developed  when  the 
resultant  is  at  the  most  forward  position— that  is,  in  the  present  discussion  at  the  forward 
third  point.  Under  this  condition  the  toe  has  a  maximum  upward  pressure,  while  the  heel 
has  a  maximum  downward  pressure  combined  with  a  minimum  upward  pressure. 

The  toe  slab  MN  (Fig.  17)  must  be  designed  for  the  moment  and  shear  at  caused  by  the 
pressure  area  A .  Investigation  must  also  be  made  for  bond  stress.  Reinforcing  will  be  along  the 
bottom  for  this  portion  of  the  base.  Diagram  14  (see  page  596)  may  be  used  in  the  shear  in- 
vestigation.. Shear  usually  governs  toes  of  length  ^  or  less. 

The  heel  slab  carries  the  upward  pressure  represented  by  the  area  B;  the  downward  com- 
ponent of  Pi  shown  hy  Pz';  and  the  dead  weight  of  all  earth  above  the  slab  RS.    The  thrust 


Sec.  13-7c] 


RETAINING  WALLS 


591 

Plate  I 


/L4'' 


Grade  £/ey  /OO  0 


VAyJ^Rods    \  I  1 


84  c toe 


rrifiifrlnifrif 


Section  A-A 


A- 

 lO'-O"  

Rear  dievarion 


til' 

\'  1  AO 


k--        -»  /-,/^. 
•/fco'  Mark  Fi 

!i"R.--. 
Bend  90  \ 


.  A3 ^14-8"- 


i"°Pod  ;-io''lg.  Mark  A, 
I"'  ••  i2'-io"        ■■  A, 


r 

Steel  Bending  uist 


Concrete  i  i;-4fnjx  8.1  cuyd  per  lOft  lengTti  of  tvalf. 
Steel-  770  Jb  per /Oft.  length  of  wall.  Deformed  oars. 
Use  /Vo.  /6  yVire  f Steel  Wire  Gauge  J  for  ty/ng. 

To  splice  /ong/tudinal  reinforcement  overlap  2  ft  and  wrap  with  wire 


CANTILEVER  TYPE 

RETAINING  WALL 


CORRECT 
«PPROVED 


Plate  II 


r. 


A3- 


t: 


'Rods 

3d 

Tdds 


■Iilihi 


—  lO-O 


Rear  Elevation 
f Footing  rods  not  shown/ 

Concrete  ■/•■     ■  f  mix  /6  4  cuyd.  per  10  ft  of  yrall 
Steel:  1290  la  per  10  ft.  of  wall   Deformed  bars  ' 
Use  No.  16  Wre  f  Steel  Wire  Gauge.]  for  tying 

To  splice  longitudinal  reinforcement  overlap  2' and  wrap  with  wire 


12  R- 


<   8-0  '  >l 

"'/^od  11-2  "fg.  Foofing 


  7^1" 

  I2'-I"...- 

 n^l"-  

I " "  Rod  8  -  8  "Ig.  Mark  Ai 
3"'    "    IJ-8"  "  " 
■l'^    "    l8'-e"  "      "  A3 

Steel  Bending  List 


L- SHAPED 

RETAINING  WALL 

SCALE  DATE 
DRAWN*  BV        TRACCD  ev 
COSRtCT 


592 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  IZ-M 


P2  has  the  distribution  shown  by  area  C,  varying  from  /i  at  S  to  /2  at  R.  Vertical  components 
//  and  fz  of  /i  and  /2  respectively,  designate  the  pressure  area  D.  The  pressure  of  the  weight 
of  earth  above  RS  is  not  shown.  Reinforcing  for  moment  requires  rods  near  the  upper  surface. 
Shear  and  bond  should  be  provided  for. 

Sliding  on  the  base  may  be  figured  from  Rv  and  the  coefficient  of  friction  of  the  base  ma- 
terial on  the  soil  (see  Table  4,  page  582).  If /-P  causes  more  tendency  to  slide  than  resisted  by 
friction,  small  projecting  key  walls  should  be  cast  on  the  under  side  of  the  base  and  anchored 
to  it  by  dowel  rods  (see  page  581). 


Fig.  17.  Fig.  18. 


Diagram  10  7d.  Expansion  Joints. — Expansion 

joints  should  divide  the  structure  into  sections  to 
relieve  continuity  and  to  relieve  temperature  and 
shrinkage  stresses.  These  latter  stresses  should  be 
cared  for  by  the  addition  of  about  0.3  of  1%  of 
steel  placed  horizontally  in  the  stem,  to  confine 
cracking  of  any  extent  to  the  joints.  The  joints 
should  be  lock-joints,  and  in  general  should  be 
waterproofed  to  prevent  unsightly  stains. 

Typical  designs  are  shown  in  Plates  I  and  II. 
8.  Design  of  Counterforted  Walls. — For  walls 
above  about  20  ft.  in  height,  the  cantilever  type  of 
retaining  wall  requires  a  wall  of  great  thickness  to 
be  self-supporting.  A  great  saving  is  effected  in  the 
amount  of  material  used  for  high  walls  by  placing 
ribs,  or  counterforts,  at  intervals  on  the  back  side  of 
the  wall,  tying  it  to  the  back  of  the  base  slab  (see 
Fig.  18).  The  vertical  wall  is  therefore  a  slab  con- 
tinuous over  the  counterforts,  and  loaded  by  hori- 
zontal loads,  thus  saving  much  material  in  the  wall 
itself. 

The  width  b  of  the  base  and  height  of  the 
wall  may  be  found  as  though  the  wall  were  of 
the  cantilever  type,  by  using  Diagrams  1  and  8. 
Minimum  material  is  required  when   the  vertical 

wall  is  from  2     3  from  the  toe,  as  was  shown  for 

cantilever  walls  in  Diagram  7. 
8a.  Thickness  and  Spacing  of  Counterforts. — The  counterforts  should  have  a 
thickness  equal  to  one-twentieth  of  the  height  of  the  wall,  and  perferably  never  less  than  12 
in.    Their  spacing  should  be  such  as  to  give  the  minimum  amount  of  material  required  for  the 
wall.    This  spacing  s,  measured  in  feet  fropa  center  to  center,  should  be 


Spacing  in  feet  (s)  c.io  c. 
of  counterforts 


=  2.46  +  0.216A 


(ft. 


Sec.  13-86] 


kETAlNING  WALLS^ 


593 


and  should  not  be  less  than  7  ft.  for  walls  under  20  ft.  in  height.  The  spacing  may  be  ob- 
tained directly  from  Diagram  10. 

The  reinforcing  of  the  counterfort  will  be  discussed  in  an  illustrative  problem. 

86.  Vertical  or  Face  Wall. — The  face  wall,  as  noted  above,  is  a  slab  supported 
at  its  junction  with  the  counterforts  and  the  base  slab.  Its  thickness  is  commonly  computed 
by  considering  it  to  be  made  up  of  horizontally  loaded  continuous  beams,  as  AB,  Fig.  19. 
At  any  depth       the  load  per  square  foot  would  be  hx  -  w',  and  the 

From  this  the  thickness  at  that 


moment  at  the  center  would  be  hxw' 


10 


depth  could  be  computed.  The  maximum  thickness  would  be  required 
in  a  strip  at  the  bottom  of  the  vertical  wall,  when  hx  would  equal  h', 
if  we  neglect  any  restraint  offered  by  the  base  slab, 

I2fw'h's\ 


Mr 


10 


Then 
=  Khd'' 


Since  6  =  12  in.  for  convenience. 


0.32s 


Ifw'h 
\  K 


(in.) 


tvhich  is  the  effective  depth  of  the  slab  at  the  bottom.  The  total  thickness  is  found  by  adding 
protective  covering  for  the  steel.  The  thickness  of  the  wall  varies  from  this  value  at  the 
bottom  to  a  thickness  not  less  than  3-^o^  at  the  top.  The  equation  given  above  is  the  basis  for 
Diagram  11. 

If  it  is  desired  to  design  for  ""j^^  ,  use  0.9  of  the  effective  depth  given  in  Diagram  11. 


Diagram  11 


Illustrativk  Problem. — Given  f  ^  2,  w'  =  50,  h'  =  36  ft.  To  find  thickness  of  face  wall.  Counterforts 
are  spaced  7  ft.  6  in.  c.  to  c.  Use  fs  =  15,000,  fc  =  650,  whence  K  =  110.  Enter  Diagram  11  with  {fw'h')  =  3600, 
thence  to  right  to  K  =  110;  thence  vertically  to  s  =  7.5  ft. ;  thence  to  right  where  d  is  given  as  13.7  in.  Total  thick- 
ness, say,  15  in. 

Sc.  Back  Floor  Slab. — This  is  the  portion  of  "the  base  slab  to  the  rear  of  the 
vertical  wall.    It  must  be  designed  to  resist  the  upward  reaction  of  the  soil  against  that  por- 
tion of  the  base;  and  the  weight  of  the  earth  immediately  above  it,  together  with  the  vertical 
38 


594 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  13-8c 


component  of  the  inclined  earth  thrust  if  the  surcharge  is  sloped.  Fig.  20  shows  a  counter- 
forted  wall  with  the  earth  sloped  to  the  line  AD.  The  total  pressure  on  the  plane  DC  is  P, 
whose  effect  above  the  base  slab  is  represented  by  the  triangle  of  pressure  Djh.  The  portion 
Ddg  (with  resultant  Pi)  is  transferred  to  Ah,  as  Abe.  The  portion  dghj  (resultant  P2)  is  trans- 
ferred to  hj  as  hcjh.  Vertical  components  of  he  and  jh,  at  h  and  j,  would  determine  the  down- 
ward component  pressure  of  Po.    This  is  the  same  as  was  given  for  the  cantilever  wall,  Fig.  17. 


Fig.  20.  Fig.  21. 


The  various  pressures  acting  are  shown  in  Fig.  21.  Trapezoid  abhg  represents  the  vertical 
component  aedh  of  P2,  plus  the  pressure  eghd  of  the  earth  immediately  above  gh  (ADjb,  Fig. 
20).    The  area  jmn  represents  the  upward  pressure  of  the  soil. 

When  the  surcharge  is  level,  ahdc  =  0. 

The  whole  floor  slab  may  now  be  designed  for  either  shear  at  the  counterforts,  or  moments 
in  the  slab  treated  as  continuous  over  the  counterforts.  In  either  case  the  pressure  on  a  strip 
at  the  back  edge  hm  would  determine  the  depth  of  the  back  slab.    If  the  slab  is  not  reinforced 


Diagram  12 


adequately  against  shear  and  diagonal  tension,  by  the  addition  of  bent-up  bars  or  stirrups, 
then  the  allowable  shearing  unit  stress  will  be  low,  and  shear  will  govern  the  depth  of  the  slab. 
In  this  case,  the  effective  depth  of  slab  in  inches  is  given  by  the  relation  . 

sh" 

d  =        {w  +  fw'  sin  d) 

in  which  h"  is  the  depth  in  feet  oi  the  earth  above  the  slab  at  the  heel.  Diagram  12  is  based 
on  this  formula. 


Sec.  13-8c] 


RETAINING  WALLS 


595 


Illustrative  Problem. — Given:  Stem  of  wall  20  ft.  high,  surcharge  slope,  6  =  30  deg. ;  angle  of  internal 
friction,  <j>  =  40;/  =  1.75;  length  of  base  of  counterfort  =  7.5  ft.;  spacing  of  counterforts,  center  to  center  =  7 
ft.;  weight  of  earth,  w  =>  120  lb.  per  cu.  ft.    Find:  depth  of  back  floor  slab  when  v  =  3Q  lb.  per  sq  in. 

=  20  +  (7.5)  (tan  30  deg.)  =  24.4  ft. 
From  Diagram  1,  Ce  =>  0.316;  hence       =  CgW  =  38  lb.  per  cu.  ft. 

iw  +  fw'sin  e)  =  120  +  (1.75)  (38)  (0.5)  =  153.3  lb.  per  cu.  ft. 

h"{w  -\-  fw'  sin0)  =»  (24.4)  (153.3)  =  3745  lb.  per  sq.  ft.  This  is  the  downward  pressure  per  square  foot 
at  the  top  of  the  back  edge  of  the  slab.  Entering  Diagram  12  from  the  left  margin  with  this  value,  we  move  toward 
the  right  to  v  =  30;  then  vertically  to  s  =  7;  then  out  to  the  right  margin,  where  we  find  d  =  41.9  in.,  say  44  in. 
total  depth,  allowing  proper  covering  for  the  stefel  at  the  lower  face.  This  is  the  total  thickness  required  for  shearing 
forces.    Investigation  must  of  course  be  made  of  this  for  unit  stresses  in  moment  and  bond. 


Diagram  13 


When  stirrups  or  bent-up  bars  are  placed  in  the  slab  to  adequately  resist  the  shearing 
forces,  then  the  bending  moments  will  govern  the  thickness  of  the  slab,  for  walls  up  to  at  least 
40  ft.  high,  since  the  allowable  shearing  unit  stress  will  be  high.  Under  these  conditions,  since 
the  base  slab,  like  the  vertical  wall,  is  continuous  over  supports, 

Khd''  =  1.2{w  +fw'  sin  d)s^ 

Whence 

d  =  0.32s^J^"'+-^^'^ 

in  whieh  d  is  the  effective  depth  in  inches.  The  effective  depth  may  be  taken  directly  from 
Diagram  13,  which  is  based  upon  the  above  formula.  The  use  of  the  diagram  is  essentially  the 
same  as  the  use  of  Diagram  11.  . 

If  it  is  desired  to  design  for  a  moment  of  {w  +  fw'  sin  ^)y2'        ^-^  effective  depth 

given  in  Diagram  13. 

Illustrative  Problem. — Given  same  wall  as  above,  but  with  v  =  120  lb.  per  sq.  in.  In  this  case  the  thick- 
ness will  be  governed  by  the  moment  in  the  slab.  Let  K  =  95.  Entering  Diagram  13  with  (w  +  fw'  sin  6)  = 
153.3,  proceed  to  the  right  to  K  =  95;  then  vertically  to  s  =  7_ft.;  then  to  the  right  margin  where  d  =  9  in.  Use 
11  in.  total  thickness. 

Some  designers  favor  placing  a  beam  along  the  back  edge  of  the  back  floor  slab,  to  stiffen 
it.  The  design  of  this  beam  is  arbitrary  when  a  panel  of  the  back  floor  is  either  square,  or 
as  is  usually  the  case,  has  its  shortest  span  between  counterforts. 


596 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  13-8(/ 


The  methods  of  reinforcing  the  back  slab  are  given  in  Art.  8e  with  a  discussion  of  the  rein- 
forcement of  the  base  slab  as  a  whole, 

M.  Cantilever  Toe  Slab. — When  the  resultant  pressure  R  strikes  the  base  at 
the  forward  third  point,  the  upward  pressure  on  the  base  is  triangular,  and  the  pressure  per 
square  foot  at  the  toe  A,  Fig.  22,  is  equal  to  twice  the  vertical  com- 
ponent of  R  divided  by  the  area  of  the  base  over  which  R  acts,  ex- 
pressed in  square  feet.  Thus  the  total  shear  on  the  section  CD,  neg- 
lecting the  small  downward  weight  of  AD,  is  equal  to  Rv{2  —  k)k, 
for  a  length  of  1  ft.  of  wall  (pierpendicular  to  the  paper).    From  Art. 

13,  Sect.  7,  V  =        whence,  assuming  ji"  = 


hjd 


Fig.  22. 


0.095 


R,\2  -  k)k 


in  which  d  is  the  effective  depth  of  the  toe  slab  in  inches,  at  the  section  CD.  It  may  be  tapered 
toward  A.    Diagram  14  has  been  prepared  to  give  this  depth  from  the  above  formula. 

iLLnsTRATivE  Problem. — Given  i2„  =  18,0001b.;  A;  =  0.3;  v  =  35  lb.  persq.  in.  Find  d.  Enter  Diagram 
14  at  the  left  with  Ry  =  18,000;  then  on  a  horizontal  line  to  k  =  0.3;  then  vertically  to  v  =  35;  and  lastly,  to  the 
right  margin  where  d  =  25  in.     This  must  be  compared  to  the  value  obtained  from  the  moment  requirement. 

Diagram  14 


8e.  Methods  of  Reinforcing  Counterforted  Wall. — In  the  preceding  discussion 
only  the  critical  sections  of  the  main  units  of  the  wall  have  been  dealt  with.  It  should  be 
noted  that  those  same  sections  should  be  investigated  for  diagonal  tension  and  for  bond,  as  in 
the  design  of  continuous  slabs.  Important  considerations  in  the  arrangement  of  the  rein- 
forcement will  be  discussed  for  each  part  of  the  wall. 

Vertical  Slab. — The  reinforcing  bars  in  the  vertical  wall  should  be  at  the  outer  face  at  the 
centei  of  the  span,  and  at  the  back  face  at  the  counterforts.    All  of  the  reinforcement  needed 


Sec.  13-8e] 


RETAINING  WALLS 


597 


at  the  front  in  the  center  of  the  span  is  needed  at  the  back  face  at  the  counterfort,  since  the 
moment  at  the  support  should  be  taken  as  that  at  the  center.  It  is  not  advisable,  however, 
to  bend  all  of  the  rods  to  the  back  face  at  the  supports,  but  to  have  about  one-fourth  of  them 
run  through.  This  amount  of  steel  should  be  supplied  at  the  back  face  by  short  rods  running 
about  }i  s  each  way  from  the  counterfort,  or  further  if  necessary  for  bond. 

About  0.3  of  1%  of  steel  should  be  placed  vertically  in  the  wall,  and  continued  into  the 
base  slab.  This  serves  two  purposes:  it  provides  a  support  for  the  horizontal  steel  before  pour- 
ing; aild  it  resists  the  tendency  to  form  large  horizontal  cracks,  particularly  near  the  bottom 
of  the  face  wall. 

Base  Slab. — The  toe,  after  having  been  proportioned  for  shearing  forces,  must  be  reinforced 
for  bending  moment  at  the  section  CD,  Fig.  22.  Rods  should  be  placed  near  the  bottom  face 
of  the  toe  and  anchored  at  its  outer  end.  Part  of  these  rods  should  extend  the  entire  width 
of  the  base,  near  its  lower  face;  and  part  of  them  may  well  be  bent  up,  with  a  long  radius,  to 
the  back  face  of  the  vertical  wall,  extending  upward  fromt  he  base  a  distance  of  about  ^  s, 
or  more.    About  0.3  of  1  %  of  steel  should  run  parallel  to  the  face  wall,  near  the  bottom  of  the  toe. 

The  principal  reinforcement  at  the  back  slab  runs  parallel  to  the  face  wall.  The  rods 
at  the  center  of  the  span  s  are  at  the  bottom  of  the  slab,  and  at  the  supports  (counterforts)  near 
the  top.  The  points  of  bending  the  rods  should  be  between  the  quarter  and  third  points  of  the 
span,  as  determined  from  Fig.  26,  Sect.  7,  page  298.  Not  all  of  the  rods  should  be  bent  up  at 
these  points,  but  some  should  run  straight  through  near  the  bottom  face.  The  extra  amount 
required  at  the  top  face  at  the  support  may  be  made  up  by  rods  placed  near  the  top  face  and 
extending  3<3  s  either  way  from  the  counterfort,  or  further  if  necessary  for  moment  or  bond. 
Stirrups,  if  placed  near  the  counterforts,  should  be  placed  in  accordance  with  the  shear 
reinforcement  in  continuous  beams  or  slabs. 

When  the  vertical  wall  is  in  front  of  the  center  of  the  base,  longitudinal  steel  is  likely  to 
be  required  in  the  bottom  face  of  the  back  slab  between  the  center  of  the  base  and  the  vertical 
wall,  as  in  this  portion  the  upward  pressures  may  be  greater  than  the  downward  pressures. 
This  is  especially  notable  when  the  face  wall  is  at  the  front  edge  of  the  base  slab  (see  Plate  IV). 

The  Counterfort. — The  reinforcement  of  the  counterfort  must  take  the  tension  developed 
in  the  direction  AC,  Fig.  23;  the  tension  across  BC  due  to  the  overturning 
moment  of  the  stem  AB;  the  tension  across  AB  due  to  the  tendency  of  the 
face  slab  to  move  forward  away  from  the  counterforts;  the  shear  on  BC  due  to 
the  earth  thrust  on  AB;  and  the  shear  on  AB  due  to  the  resultant  downward 
pressure  on  BC. 

The  counterfort  is  designed  as  a  wedge-shaped  cantilever  beam  fixed 
to  the  base  slab.    Such  an  assumption  requires  that  the  base  slab  be  rigidly 
attached  to  the  bottom  of  the  counterfort  over  its  entire  length.    The  principal 
reinforcing  in  the  counterforts  is  the  steel  along  the  inclined  face  tying  the 
upper  end  of  the  face  wall  to  the  back  edge  of  the  base.    Both  ends  of  this  steel  must  be 
thoroughly  anchored.    This  may  be  done  by  hooking,  or  by  hooking  to  cross  rods,  provided 
that  in  the  latter  case  the  bearing  of  the  cross  rods  does  not  exceed  the  compressive  work- 
ing unit  stress  of  the  concrete. 

Illustrative  Problem. — Given  a  counterfort  20  ft.  high,  16  in.  thick,  and  8  ft.  wide  at  the  base  slab;  required 
the  tensile  steel  necessary  to  prevent  exceeding  the  unit  stresses  fc  =  650,  and  fs  =  16,000  lb.  per  sq.  in.  Moment 
on  the  counterfort  =  7,000,000  in.-lb.    Allowing  0.2  ft.  for  steel  covering, 

M  7,000,000 

hd"^  (16)(7.8)2(12)2 

Entering  Diagram  2,  Sect.  7,  page  360,  at  50,  for/s  =  16,000,  p  =  0.0035.  Slope  of  back  face  =  tan  -10.4  =  about 
22  deg.  Entering  Diagram  3,  page  361,  at  the  lower  margin  with  3.5,  trace  vertically  upward  to  =  0,  then 
horizontally  to  /3t  =  22  deg.,  then  vertically  upward  to  values  of  C,  where  3.85  is  found.  Pointing  this  off 
properly,  the  corrected  value  of  p  =  0.00385. 

As  =  (16) (7.8)2  (12)2  (0.00385)  =  5.4  sq.  in. 


;.  13-8e] 


RETAINING  WALLS 


599 


600 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  13-9 


It  will  be  found  by  considering  various  horizontal  sections  of  the  counterfort  that  it  will 
not  be  necessary  to  run  all  of  this  steel  to  the  full  height  of  the  counterfort.  Wherever  any 
steel  is  stopped  because  it  is  no  longer  needed  for  moment,  it  should  be  extended  sufficiently  to 
develop  the  full  strength  by  bonding,  or  should  be  adequately  anchored. 

Horizontal  steel  should  extend  from  the  counterfort  into  the  front  face  to  keep  the  latter 
from  being  torn  fron  the  counterfort.  This  steel  should  be  hooked  to  the  horizontal  rods  in  the 
slab,  or  should  be  bent  either  way  into  the  slab  to  thoroughly  attach  it  to  the  vertical  slab. 

Similar  steel  should  be  extended  and  anchored  into  the  footing  slab. 

If  the  cross-section  of  the  base  of  the  counterfort  is  not  large  enough  to  carry  in  shear  the 
thrust  against  the  wall,  the  thickness  of  the  counterfort  should  be  increased,  or  stirrups  should 
be  extended  from  the  base  slab  into  the  counterfort. 

Typical  designs  are  shown  in  Plates  III  and  IV. 

9.  Special  Types  of  Reinforced-concrete  Walls. — Fig.  24  shows  the  cellular  type  of  re- 
inforced-concrete  retaining  wall.  This  wall  is  formed  of  two  longitudinal  curtain  walls  (A) 
and  (B),  connected  by  transverse  walls  (C).    The  vertical  space  between  the  parallel  longitudi- 


Center  Line  of  Side  Track 


r/3'  To  Center  Line 
cf  Main  Track 


Fig.  24. 


nal  walls  and  the  transverse  walls  is  filled  with  earth.  This  type  of  wall  gives  a  lower  maxi- 
mum soil  pressure  than  either  the  cantilever  or  counterforted  types,  but  under  average  condi- 
tions its  cost  per  linear  foot  is  greater.  Its  use  would  seem  to  be  restricted  to  poor  soil  with 
no  opportunity  to  drive  piles  and  where  the  wall  must  be  built  as  close  as  possible  to  a  given 
property  line — conditions  which  often  occur  in  railway  work. 

Fig.  25  shows  a  design  of  wall  which  gives  a  maximum  soil  pressure  even  less  than  the 
cellular  type  and  which  costs  approximately  the  same  per  linear  foot  of  wall.  This  design 
was  employed  by  the  C.  M.  &  St.  P.  Ry.  in  a  long  retaining  wall  at  Elgin,  111.,  and  was  chosen 
in  preference  to  the  design  shown  in  Fig.  24  on  account  of  the  much  lower  bearing  pressure  on 
the  soil.  The  wall  consists  of  a  footing  (F)  which  supports  a  longitudinal  wall  (T)  and  the 
cross  walls  (t/).  The  cross  walls  at  the  outer  end  support  the  girder  (X),  which  spans  from  one 
cross  wall  to  another.  The  slabs  (F)  are  supported  at  one  end  by  the  girder  and  at  the  other 
end  by  the  longitudinal  wall.  The  great  reduction  in  soil  pressure  is  brought  about  mainly 
by  eliminating  the  weight  of  the  earth  directly  above  the  footings,  the  space  between  the 
cross  walls  (C7)  being  an  open  and  empty  space  in  this  design.  In  this  type  of  wall,  and  in  the 
cellular  type  as  well,  stability  against  sliding  should  be  carefully  investigated. 


Sec.  13-10] 


RETAINING  WALLS 


601 


10.  Construction  of  Retaining  Walls. 

10a.  Backfilling  and  Drainage. — Quite  as  much  attention  should  be  paid  to  the 
earth  filhng  and  to  its  drainage  as  to  the  design  and  construction  of  the  retaining  wall  proper 
or  to  the  matter  of  providing  a  suitable  foundation.  If  the  earth  is  deposited  in  layers  inclined 
from  the  wall,  the  pressure  will  be  small  compared  to  that  resulting  if  the  layers  are  sloped 
toward  the  wall.    It  is  quite  often  the  case  that  by  depositing  the  backfilling  so  as  not  to 


Center  Line  of  S/cfe^  Track 
K— -  11-6"  


i3'  to  Center  Line 
'  of  Main  Track 


Cross  Seci-ion 


Sectional  Elevation 


Fig.  25. 


These  fouf  boards  forming  a 
panel  to  be  set  at  wor/ang  p/ace 
only  to  prevent  spilling  of  concrete 


Runwciy  /or  loacfect  wheel barroiys 

/    Place  boards  -for  crossover 
[opposite  kYorking  place 
\       ....--Punway  "for  empty 

wheelbarroifS 


Bracing  of.  Wall  Forms  .2-6  "C.  to  C 
^IG.  26 

slide  against  the  wall,  a  light  wall  may  be  made  to  stand  where,  under  the  same  conditions,  if 
the  earth  is  dumped  so  as  to  slide  against  the  wall,  even  a  heavy  wall  will  fail. 

When  placing  a  backfill  near  a  steep  undisturbed  slope  of  earth  or  rock,  care  should  be 
taken  that  the  earth  does  not  arch,  or  does  not  form  a  wedge.  If  the  proper  precautions  are 
not  taken,  a  heavy  lateral  thrust  will  occur  near  the  top  of  wall. 

Water  behind  a  wall  is  a  frequent  cause  of  failure.  It  adds  to  the  weight  of  the  backing 
and  softens  the  material  so  that  the  lateral  thrust  is  increased.  Also,  undrained  backfilling 
will  freeze  and  create  lateral  thrust  due  to  the  consequent  expansion.  To  drain  the  backing, 
weepers  or  weep  holes  should  be  left  through  the  wall  just  above  the  footing.    Tile,  3  or  4  in.  in 


602 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  13-106 


diameter  is  generally  used  and,  in  the  North  Central  States,  placed  usually  not  more  than  10 
to  15  ft.  apart.  The  tile  should  be  connected  with  a  longitudinal  drain  in  front  of  the  wall. 
If  the  backing  is  retentive  of  water,  a  vertical  layer  of  broken  stone,  coarse  gravel,  or  cinders 
should  be  placed  next  to  the  wall  to  act  as  a  drain.  The  filling  in  front  of  the  wall  should  also 
be  carefully  drained. 

106.  Forms. — Formwork  as  applied  to  buildings  is  treated  in  detail  in  Sect.  2. 
Since  the  method  of  constructing  forms  and  the  directions  for  their  removal  are  very  much  the 
same  for  different  types  of  structures,  very  little  need  be  said  under  this  heading. 

The  lumber  used  for  forms  should  have  a  nominal  thickness  of  at  least  l}i  in.  before 
surfacing  and  should  be  of  a  good  quality  of  Douglas  fir  or  Southern  long-leaf  yellow  pine. 


Fig.  27. 

The  lumber  for  face  work  should  be  dressed  on  one  side  and  on  both  edges  to  a  uniform  thick- 
ness and  width.  The  lumber  for  backing  and  other  rough  work  may  be  unsurfaced  and  of 
an  inferior  grade  of  the  kinds  above  mentioned. 

Forms  should  be  substantial  and  unyielding,  and  built  so  that  the  concrete  will  conform 
to  the  dimensions  shown  on  the  designer's  plans,  and  they  should  also  be  tight  so  as  to  prevent 
the  leakage  of  mortar.  Forms  may  be  either  continuous  or  sectional,  or  a  combination  of 
both,  depending  upon  the  economy  of  the  work.  The  concrete  in  any  given  section  should  be 
allowed  to  harden  for  36  hr.  before  the  forms  are  removed  and,  in  freezing  weather,  extra  care 
must  be  taken  to  make  sure  that  the  concrete  has  had  sufficient  time  to  become  thoroughly 
set.    Material  once  used  for  forms  should  be  cleaned  before  being  used  again. 

A  design  of  a  form  for  a  reinforced-concrete  cantilever  wall  is  shown  in  Fig.  26. 

Fig.  27  shows  the  method  of  constructing  and  reinforcing  the  counterforts  of  a  retaining 
wall  at  Buffalo,  N.  Y. 


SECTION  14 


SLAB  AND  GIRDER  BRIDGES 

The  methods  of  designing  slabs,  beams,  and  girders  are  explained  at  length  in  Sect.  7,  and  no  attempt  is 
made  in  this  section  to  treat  of  these  methods  in  detail.  Many  things  must  be  considered,  however,  in  designing 
bridges  of  this  class,  aside  from  the  proportioning  of  simple  and  continuous  beams,  and  such  matters  are  given  due 
consideration. 

The  erection  of  forms  and  other  operations  in  slab-and-girder  bridge  construction  are  essentially  the  same  for 
ordinary  conditions  as  the  corresponding  operations  in  the  construction  of  buildings.  On  this  account,  construc- 
tional methods  are  referred  to  only  incidentally  under  this  heading. 

The  loadings  to  use  in  design  are,  of  course,  the  same  as  for  the  floors  in  arch  bridges  of  open-spandrel  con- 
struction (see  Art.  6,  Sect.  16).  In  fact,  it  should  be  noted  that  the  framed  structure  which  is  supported  by  a 
ribbed  arch  is  virtually  a  trestle  form  of  girder  bridge  and  the  loadings  and  general  design  are  identical. 

Impact  may  properly  be  neglected  in  arch-ring  analysis  but  becomes  important  in  bridge-floor  design.  An 
increase  of  25  %  is  usually  made  in  the  live  load  or  live-load  stresses  for  highway  bridges  and  50  %  in  those  for  rail- 
road bridges. 

From  the  standpoint  of  economy,  slab  bridges  should  in  general  be  limited  in  span  length  to  about  25  ft.,  and 
ordinary  girder  bridges  to  about  50  ft. 

SLAB  BRIDGES 


1.  Slabs  Under  Concentrated  Loading. 

la.  Illinois  Tests. — From  tests  made  on  simply  supported  slabs  at  the  Uni- 
versity of  Illinois,  Prof.  W.  A.  Slater  has  recommended  that  where  the  total  width  of  slab  is 
greater  than  twice  the  span,  the  effective  width  e  (Fig.  1)  be  assumed  as 

e  =  Hx  +  d 

where  x  is  the  distance  from  the  concentrated  load  to  the  nearest  support  and  d  is  the  width 
at  right  angles  to  the  span  over  which  the  load  is  applied. 


0:0  0 

1^ 


Fig.  1. 


O.Z   04  0.6  08 
Ratio  of  total  width  to  span 

Fig.  2. 


Tests  showed  the  effective  width  to  be  but  little  influenced  by  the  depth  of  the  slab  or  by 
the  percentage  of  longitudinal  reinforcement.  Prof.  Slater  has  recommended,  however,  that 
the  latter  be  limited  to  1%  "because  of  the  possibility  that  in  a  beam  with  a  large  amount 
of  longitudinal  reinforcement  and  a  relatively  small  depth,  failure  may  be  caused  by  trans- 
verse tension  in  the  concrete  and  not  by  longitudinal  steel  stress." 

The  above  formula  refers  to  a  total  width  of  slab  greater  than  twice  the  span.  For  a 
slab  whose  total  width  is  less  than  this,  the  effective  width  may  be  found  from  Fig.  2  (full  line) 
which  shows  the  ratio  of  the  effective  width  of  the  span  as  determined  from  the  measured 
steel  stresses  in  the  University  of  Illinois  tests. 

603 


604 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14-16 


16.  Ohio  Tests.^ — The  object  of  the  tests  was  to  obtain,  if  possible,  a  sufficient 
knowledge  of  the  distribution  of  loads  through  and  by  concrete  floor  slabs  to  enable  the  de- 
signer to  rationally  proportion  the  joists  of  a  slab  floor,  and  also  the  slab  itself,  to  carry  con- 
centrated loads. 

The  following  conclusions  regarding  the  distribution  of  concentrated  loads  on  a  rein- 
forced concrete  slab,  to  the  floor  joists,  seem  to  be  warranted  by  these  tests: 

1.  The  percentage  of  reinforcement  has  little  or  no  effect  upon  the  load  distribution  to  the  joists,  so  long  as 
safe  loads  on  the  slab  are  not  exceeded. 

2.  The  amount  of  load  distributed  by  the  slab  to  other  joists  than  the  one  immediately  under  the  load, 
increases  with  the  thickness  of  the  slab. 

3.  The  outside  joists  should  be  designed  for  the  same  total  live  load  as  the  intermediate  joists. 

4.  The  axle  load  of  a  truck  may  be  considered  as  distributed  uniformly  over  12  ft.  in  width  of  roadway. 


Fig.  3. — Standard  design  for  slab  bridges  of  12-ft.  span,  Wisconsin  Highway  Commission. 

In  a  slab  of  a  certain  span  and  indefinite  width,  there  is  some  width  symmetrical  with  the 
load,  beyond  which  a  single  concentrated  load  will  have  no  effect.  The  stresses  in  this  slab 
will  be  a  maximum  under  the  load  and  will  decrease  in  each  direction  from  it. 

The  "effective  width"  of  a  slab  is  that  width  used  in  designing  over  which  a  single  con- 
centrated load  may  be  considered  as  uniformly  distributed  on  a  line  down  the  middle  of  the 
slab  parallel  to  the  supports. 

The  tests  of  slabs  seem  to  warrant  the  following  conclusions: 

1.  The  effective  width"  is  affected  very  little  by  the  percentage  of  transverse  reinforcement  (parallel  to 
supports). 

2.  The  "  effective  width"  decreases  somewhat  as  the  load  increases. 

3.  The  "effective  width"  in  percentage  of  the  span,  decreases  as  the  span  increases. 

4.  The  following  formula  will  give  a  safe  value  of  "effective  width"  where  the  total  width  of  slab  is  greater 
than  IW  +  4:  ft. 

e  =  0.61  +  1.7  ft. 
where  e  is  effective  width  in  feet  and  /  is  the  span  in  feet. 

1  From  Bull.  28,  State  of  Ohio,  Highway  Department. 


Sec.  14r-lc] 


SLAB  AND  GIRDER  BRIDGES 


605 


Ic.  Tests  by  Goldbeck. — The  results  of  these  tests  are  shown  by  the  dotted 

curve  in  Fig.  2, 

2.  Slab  Bridges  of  Single  Span. — The  floor  of  a  slab  bridge  may  be  designed  as  any  simply 
supported  slab  except  that  shearing  stresses  may  require  very  careful  attention  where  the  live 


„     ,         / I'^Tyy.  Ifods  'f'c.  foe.  SO ' lonq 

Roadway  <^  ,„aj.^    „    ;2'c./toc  iw^-^'^.  f fnr /Ms-za'cnc.-e' /o> 


5fCfetya//r 


^""Tw.  "  rz'c.foc  Bo'-e'lq.  U' 
(  fnr.    »    3'c.-fDC.  /9'-6'^lq         .  )  I 

o'-o"-  >)<- 


'°Tw.  /fodsii'c  foe.  19^ 


'long 
^'-€'13. 


i    Tw.  \z''ctoc  5io''/ong- 
Transverse  Secrion  on  Centisr  Lin^of  Stream  ^/^>-- 


3 


// -  £" 


Plan  of  Abutmenl- 


C  L  of  Bridge^ 


Fig.  4. — Details  of  Christiana  bridge,  Town  of  Cross  Plains,  Dane  County,  Wis. 


load  is  relatively  large,  as  in  railroad  structures.  The  whole  reinforcing  system  may  be  made 
absolutely  rigid  by  wiring  the  main  reinforcing  rods  to  the  transverse  spacing  rods  at  the  ends 


rmished  Poadway 


^    l"  Ifods  izcfoe. 


ffelnforcement 
Elevation 

■f°'ffods  E"c.ioc.  Wing 

"°ffocls 
l£"cfoc. 


Plan  of 
One  Abutment 





sz'-o' 


rrUe  Drains,  S'ctoC. 
■■.-^"Cyrfods  Bi'-8"long 


^~\---i'"'ffods.iS'l^ 


Section  Exterior 
Elevation 


[""Rods 
is'c.toc.  S^'l 

Cross  Section 


Fig.  5. — Typical  slab  bridge,  Illinois  Highway  Commission.    Abutment  wings  of  the  cantilever  type.    Main  wall 
vertical  slab  supported  at  top  by  superstructure  and  at  base  by  footing. 

of  the  bent-up  steel.  Both  the  straight  longitudinal  rods  and  those  bent  up  to  provide  for 
diagonal  tension  should  be  hooked  at  the  ends. 

Practice  varies  in  regard  to  the  use  of  expansion  joints  between  the  slab  floor  and  the 
abutments.    There  are  none  provided  in  Figs.  3,  4  and  5,  but  such  joints  are  placed  at  both 


606 


CONCRETE  ENGINEERS'  HANDBOOK 


[See.  14-2 


abutments  in  Fig.  6.  In  the  latter  figure,  vertical  end  expansion  joints  are  provided  at  the 
angle  points  between  abutment  wings  and  slab,  making  it  necessary  to  cantilever  the  outer 
portions  of  the  slab  width  on  account  of  insufficient  abutment  support. 

In  Figs.  3,  4  and  5  the  main  wall  or  vertical  slab  of  the  abutment  is  supported  at  the  top 
by  the  floor  and  at  the  bottom  by  the  footing,  and  may  be  figured  for  earth  pressure  as  a  simple 
slab  with  the  main  steel  near  the  outer  or  stream  face.  Of  course,  the  main  wall  should  also 
be  designed  to  act  as  a  column  to  support  the  superstructure.    Since  a  joint  of  low  friction  is 


Half  Plan  View 


A^>7^p.■ 


So  proportion  the  wing 
length  that  A: B  •■C:D  as  l-i^- 
The  point  £  yyhere  the  /y  I  slope 
from  end  of  wing  intersects  the 
elevation  of  stream  bed  may  be 
varied  to  suit  local  conditions. 

In  streams  whose  channels 
are  nearly  the  span  width,  or 
where  there  is  a  possibility  of 
cutting  and  channel  widening,  the 
point  E  Should  be  tairen  at  abutment  face 


<---  18  Clear  Roadway   > 

>     4" Drains  spaced  not  more 
\    /than  IS 'c. toe.  Perforaivd 
Cover 


Expansion  Joints  of  tar  paper 
or  galvanized  iron 

  Z4'-0'l  -  


Cross  Sec-Mon  of  Slab 


Fig.  G.- 


-Typical  slab  superstructure,  Iowa  Highway  Commission. 


not  provided  between  floor  and  abutments,  the  unit  tensile  stress  in  the  steel  of  the  super- 
structure is  usually  kept  low  (12,000  lb.  per  sq.  in.)  so  as  to  provide  properly  for  the  additional 
tension  in  the  steel  caused  by  the  contraction  of  the  bridge  in  cold  weather.  The  wings  may 
be  designed  as  self-supporting  retaining  walls  of  the  cantilever  type,  using  the  methods  ex- 
plained in  Sect.  13.  Theoretically  the  maximum  efficiency  of  the  footing  for  the  wing  walls 
can  be  obtained  by  placing  the  wing  wall  at  about  the  outer  middle-third  point  of  the  base, 
but  in  many  cases  considerable  saving  in  excavation  may  make  it  more  desirable  to  shift  the 
footing  a  little  toward  the  stream  bed.  Counterforted  walls  are  advisable  only  for  abutments 
over  20  ft.  in  height, 


Sec.  14-3] 


SLAB  AND  GIRDER  BRIDGES 


607 


Figs.  6  and  7  show  an  unusual  abutment  design  adopted  by  the  engineers  of  the  Iowa 
Highway  Commission  for  both  slab  and  girder  bridges.  Expansion  joints  being  provided  at 
each  end  of  the  superstructure,  both  the  main  portion  and  the  wings  were  designed  as  self- 
supporting  retaining  walls.  The  main  portion,  however,  was  not  only  analyzed  in  the  ordinary 
manner  for  pressure  on  the  base,  but  was  also  analyzed  taking  into  account  the  stability  due 
to  the  weight  of  the  wings.  The  mean  value  of  the  maximum  pressure  at  the  toe  of  the  foun- 
dation by  the  two  methods  being  found  safe,  and  an  analysis  for  sliding  and  overturning  being 
satisfactory,  the  dimensions  shown  were  adopted.  The  horizontal  rods  designated  as  tension 
bars  were  inserted  in  order  to  utilize  the  weight  above  mentioned.  These  rods  are  placed 
in  the  main  stem  near  the  upper  surface  and  extend  continuously  through  the  wings,  with 
splices  at  the  center  of  the  main  portion.    The  effect  of  considering  the  wings  as  a  part  of  the 


Fig.  7. — Typical  substructure  for  slab  and  girder  bridges,  Iowa  Highway  Commission. 

abutment  body  is  to  shift  the  center  of  gravity  of  the  entire  mass  farther  from  the  stream  face 
and  thus  reduce  the  eccentricity  of  pressure  on  the  foundation.  The  horizontal  reinforcing 
rods  shown  near  the  stream  face  of  the  abutment,  and  which  are  carried  about  5  ft.  into  the 
wings,  were  employed  to  counteract  a  tendency  to  the  formation  of  vertical  cracks  on  the 
outside  at  the  corner  of  wing  and  abutment.  The  vertical  rods  in  the  front  face  serve  as  a 
framework  upon  which  to  build  the  horizontal  rods  and  they  also  prevent  any  tendency  toward 
the  formation  of  horizontal  cracks  in  the  stream  face  due  to  the  clogging  of  an  expansion  joint. 

3.  Slab  Bridges  of  Multiple  Spans. — Slab  bridges  of  multiple  spans  will  be  treated  under 
the  four  following  headings : 

Concrete  pile  trestles.  Trestles  with  framed  bents. 

Pier  trestles.  Cantilever  flat-slab  construction. 

3a.  Concrete  Pile  Trestles. — Figs.  8  and  9  give  the  essential  details  of  design 
of  the  pile  trestles  built  by  the  Illinois  Central  Railroad.  They  can  be  considered  typical  of 
concrete  pile  trestles  in  general.    These  trestles  replace  similar  wooden  structures  over  swamps 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14r-Sa 


I  I 


P'r;    n-n     n^n    r;T;    ht;  r.-n 


Bars  4-0  long  f| 
/'-J  /ong 


~>|/2'|<-  • 


I      J'lBors  /j'-6'/oncf  :.  |  ^     I  | 


SecTion  on 
Cen-ter  Line  of  Track 


10-^' Bars,  B-e'/ory 


Concrete  Piles 


■A'^  3-8 3-8" 3-8 "Xlk 


7- ^  "Bars,  13-6"  lonj  ■ 
-H^  ■ " "  -211  Bars,  13'- 6" long 


■4'-3"-A 


/"Bars 


Section  on 
Center  Line 
of  Track 


Anchor  Pier 

Fig.  8. — Details  of  substructure,  standard  concrete  pile  trestle,  Illinois  Central  R.  R. 


Sec.  14-3a] 


SLAB  AND  GIRDER  BRIDGES 


609 


and  shallow  streams  which  may  not  be  filled  and  where  bridges  on  more  permanent  supports 
would  be  extremely  expensive  because  of  their  great  length.  The  construction  consists  of  pile 
bents  spaced  generally  from  16  to  20  ft.  c.  to  c,  and  with  a  height  above  ground  not  greater 
than  the  span.  The  piles  are  capped  with  reinforced-concrete  girders  which  support  the 
floor  slabs. 

The  piles  and  deck  slabs  are  usually  cast  in  a  convenient  yard,  allowed  to  season  from  60 
to  90  days,  and  are  then  hauled  to  the  bridge  site.  The  lifting  stirrups  shown  permit  of  the 
slabs  being  set  in  place  by  a  wrecking  crane.  The  ballast  and  track  are  laid  directly  on  the 
slabs  after  the  longitudinal  and  transverse  joints  (except  at  anchor  bents)  are  filled  with  cement 


D 

□ 

1  Mu<y  L  ine 

rr 

49 

Cross  Section 
This  concrete  poured 


after  pre  cast  slabs 
are  in  place 


Expansion 
Joint 

\        2 1,   Extending  slab  stei 
/feinforcement        \  S  a    /  to  be  greased 
in  slab  '  '  -  ^/^ 


End  of  fence  slab  iv  be 
greased  to  present  bonding 
to  concrete  in  post 
Fence  Post 


Section  through      Grout  surface 
Typical  Bent     .--before  placing  slab 


/"Sand 
Joint 

I -Iron 


1".  9"  Plate 

"--4  >![<-;■•  ,-J''''5p//fe's 


-n£^--Post 
Expansion  Joint 
at  Railing 


Expansion  Joint 
in  Roadway 


Fic 


(Bent  Cap  50) 

10. — Details  of  pile  trestle  across  the  Miles  River  near  Easton,  Md. 


mortar  and  after  the  floor  surface  is  thoroughly  waterproofed.  The  slabs  are  set  on  a  bed  of 
grout  on  the  pile  caps.  An  anchor  bent  is  used  at  suitable  intervals  to  take  up  longitudinal 
stresses  due  to  tractive  force  and,  by  means  of  an  expansion  joint,  to  prevent  any  great  accumu- 
lation of  movement  of  the  deck  due  to  temperature  changes. 

A  concrete  pile  trestle  for  carrying  a  highway  is  shown  in  Fig.  10 ^  It  was  found  economi- 
cal to  cast  the  piles,  deck  slabs,  and  railing  slabs  at  Baltimore,  60  miles  away,  and  transport 
them  to  the  site  on  scows.  Expansion  joints  were  located  in  the  roadway  slabs,  curb,  and 
railing  slabs  at  every  fifth  bent. 

1  See  also  Eng.  News,  Feb.  5,  1914. 
39 


/ 


610 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14-36 


36.  Pier  Trestles. — Thin  concrete  piers  are  preferable  to  pile  bents  when  the 
height  of  bridge  above  the  ground  line  is  greater  than  about  16  ft.  Fig.  11  shows  a  typical 
trestle  of  the  solid  bench-wall  type  built  by  the  Illinois  Central  Railroad. 


7      6      SB     4      3      e      I  ^^■-^.^ 


^  Base  erf  Rail  ^  _^ 


I  S'hnj  pij 


Top  of  Pier  5B 
li'  Base  of  Bail 

fPgds,  i'-9"!z"c  foe. 


Top  of  Pier 


!<.. s'.o':i^'^^^  V  j7'-o" ■■{■:■ 

fffods.  W'c.  to  c  f/fods.  e'c  fo  C. 

Piers  2.3.4.6,&  7 

Fig.  11. — Pier  details,  Illinois  Central  R.  R.  trestle  over  Kaskaskia  River  near  New  Athens,  111. 


3c.  Trestles  with  Framed  Bents. — Slab  bridges  with  framed  bents  forming 
subways  are  used  on  at  least  fifteen  railroads  in  this  country.    A  design  which  may  be  considered 


\<'  -         'y'-z"  -  X  -  ij'-z"   >j ..  z' 

'%    I     ,°        I     i     !     i  T 


ftAs'-z" 


T 


_LliLil: !  L|l!  I ilili.i_lj.U  III  lij-L  ij  I  !  ili  I 

Half  Elevation-  Curb  Pier       Half  Elevation- Roadway  Pier 


U         6'-6"  --J 

Section  B-B 


Detail  of  Notch 
for  Curb  Piers 


Details  for  Sliding  ^lev. /sse-.. 
Plates ,  Center  Pier  Elevation, 


C  L.  of  Track 


■h  •      — p^y  Batter  S  "        '  ' 


■^.r-  7'-^" >H e'-e"  ^ 

'  r  /?  Alternate  rows 

Batter  S-IZ  of  st,rrvps  ■ 

Parapet  Bars    inverted- .... 


11 


A| 

i— 

Section  A-A 


Plan 


Fig.  12. — Details  of  Mozart  Street  subway,  Bloomingdale  Road  track  elevation,  Chicago,  Milwaukee  &  St.  Paul 

Railway. 


typical  is  shown  in  Fig.  12.  The  deck  slabs  may  either  be  cast  in  place  or  cast  at  some  central 
yard  and  placed  in  a  similar  manner  to  the  slabs  for  pile  or  pier  trestles.  In  Fig.  12  the  design 
is  shown  for  slabs  to  be  cast  in  place.. 


Sec.  14-3c] 


SLAB  AND  GIRDER  BRIDGES 


611 


^...S/idincf  joints  - 


I  "spaces  between  sfdbs 
■fWed  with  grout-. 


Section  Through 
Sidewalk  Girder 


f'Bars./B  c.toc.  \ 
y\    Alternate  bars  bent  • 


Section 
through  Slob 


Inside  Elevation  ond  Section 
showing  Reinforcement  in 
Sidewalk  Girder  and  Bent 


Inside  Elevation 
and  Section  of 
Side  Parapet  a  Bent  ~i~ ''T'  "^'-0'' 

^""Bars  5^6" long  X  'W 


J-L_.  .i-LL  XI. 


Y    ij'  Bar.  s'/ong      Place  bars  in 
'  ^  ■'  position  shown 

before  grouting 
open  space 


  J^'.Q' 


Arrangement  for 
'^ Lifting  Slab 


Detail  of  End  Slab 


!  i"''Bars 


7-^5  ^  -> 


■— ,  //'-//' 
Half  Longitudinal  Section  "I^'picaf  Cross  Section 

oF  Intermediate  .Slab.     for  Tnd  and  Intermediate  Slabs 
Fig.  13. — Details  of  trestle  apErroach  to  Cumberland  River  bridge,  Illinois  Central  R.  R. 


612 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14-3d 


A  framed-bent  trestle  with  continuous  side  girders  to  resist  stresses  due  to  traction  is 
shown  in  Fig.  13.  The  girder  on  one  side  acts  simply  as  a  tie  and  parapet,  while  the  other  with 
a  cantilever  projection  at  the  side  acts  also  as  a  sidewalk.  The  slabs  were  cast  in  a  yard  at  some 
distance  from  the  bridge  site,  loaded  on  flat  cars,  taken  to  the  job,  and  swung  into  place  with 
derricks.  Expansion  is  allowed  for  at  both  ends  by  providing  a  sliding  joint  between  the 
bridge  superstructure  and  the  abutments.  The  shallow  4-in.  curbs  at  the  ends  of  the  slabs 
were  provided  to  prevent  seepage  from  getting  into  the  1-in.  grout  joint  between  slabs.  The 
pier  footings  are  reinforced  longitudinally  in  top  and  bottom,  and  were  figured  as  continuous  T- 


Section  B-5 

Fig.  14. — Cantilever  flat-slab  bridge  on  Mississippi  River  Boulevard,  St.  Paul,  Minn. 

beams  uniformly  loaded  by  the  pressure  on  the  soil.  The  cross  girders  at  the  top  of  the  columns 
support  the  deck  slabs  previously  referred  to,  and  are  made  continuous. 

Sd.  Cantilever  Flat-slab  Construction. — Fig.  14  is  a  flat-slab  structure  of  the 
Turner  Mushroom  type.  The  methods  which  may  be  used  in  the  design  of  the  roadway  slab 
are  treated  in  Sect.  11.    The  hollow  abutments  should  be  noted. 

Many  cantilever  flat-slab  bridges  are  built  in  which  the  abutments  are  of  the  ordinary 
reinforced-concrete  type.  The  abutment  walls  are  considered  as  held  at  the  top  by  the  super- 
structure to  which  they  are  anchored  by  bending  the  vertical  rods  into  the  slab. 

I 


Sec.  14-4] 


SLAB  AND  GIRDER  BRIDGES 


613 


SIMPLE  GIRDER  BRIDGES 

4.  Deck  Girders. — The  deck-girder  type  of  construction  usually  proves  more  economical 
than  the  through-girder  type  wherever  sufficient  headroom  is  available.  The  girders,  of 
course,  should  be  relatively  thin  and  deep  for  the  greatest  economy,  and  a  curtain  wall  should 
be  provided  between  the  girders  at  each  end  of  span  to  retain  the  earth  fill,  thereby  avoiding 
complicated  parapet  walls  on  the  abutments. 

Standard  details  of  deck-girder  bridges  designed  by  the  engineers  of  the  Iowa  Highway 
Commission  are  shown  in  Fig.  15.    The  floor  slab  was  analyzed  both  as  fixed  and  as  continuous, 


•i-9''^  -is"Spacinq  •^^fS'^ Spacing ■><-Z4"$pacinq 

K-  Lonqifudinal  girder  tars  ix>  be  \  I- 
\y'  secure/y  hooked  at  ends  over  ^     \anchor  bars 


StirrdfS 


\<I5>  < 


mil 


£-;^"sVee/  P/ai^s  ■  expansion  Join  f  :  "b  '  < 
a  ..>l<-..b  •->l<-  C  -d  <^rrdereach  ^/rde 

Longitudinal  Section  through  Girder 

Handrail   ( ''"^'Y/ J ''^ '''''' 
)  Hor.  S-f  ears 

ft.    ■>\S  [<■•/  4" mepiro/es  on  each  side  of  roadway 
I    I  not  more  than  /2  ff-  apart.  Perforated 

^^^"^  '^'^^  covers 
f'"^/  .i'"'Bar5.S"c.foc.      \  i" ^P^^ 


1  1 1 1  1 1 

Elevation  and  Section 
of  Post  over  Wing 


z'-i-^'.^isi  '-i" open  ^xp  Joint 
Transverse  Section  through  G/rder       Elevation  of  Spindle  Roi 

Table  of  Dimensions  and  Girder  Reinforcerneni" 


Span 

H 

d 

G 

f 

stirrup  Spaces 

a 

b 

c 

Girder 

Bars 

!2" 

18" 

Z4'> 

Top  Row 

BotlDm  Row 

34' 

2'-Z" 

■}". 

H" 

10 

6 

z 

z'-  3" 

z'-  3" 

2'-  0" 

3  '  1"" 

26' 

2'- 4'' 

H" 

3" 

zi" 

12 

6 

z 

Z'-6" 

2'-l" 

z'-s" 

3-  1'" 

3'- 

Id' 

2-6' 

H' 

3" 

ti" 

12 

C 

3 

2'- 5" 

Z'-Z" 

2'- 11' 

3-1°" 

/'-  /'!' 
B'-  IB" 

30' 

2-9" 

3" 

3i" 

^i" 

10 

C 

5 

Z'-8" 

Z''  6" 

2'-IO' 

3  .  ,"0 

3-ir 

32' 

Z-IO'' 

3" 

H" 

7// 

10 

C 

6 

Z'-7i' 

z'-ei" 

3'-  1" 

3-li"° 

3-ir 

34' 

3-1" 

3" 

4" 

3" 

10 

10 

4 

2'- II" 

z'-io" 

3'- 3" 

1  •li"" 

3-li'"' 

36' 

3'- 3" 

3" 

4" 

3" 

10 

10 

S 

3'-0" 

Z'-ll" 

f-io" 

3  -  li'" 

38' 

3' 5" 

3" 

4" 

3" 

10 

10 

6 

3'- 4" 

Z'-IO" 

3'- 4" 

S'ly" 

40' 

3- a" 

4" 

4" 

4" 

12 

6 

9 

r-6« 

■s'-z" 

3'- 10" 

3-4"" 

3-/r 

Fig.  15. — Standard  details  of  concrete  deck-girder  bridges,  Iowa  Highway  Commission. 


and  was  designed  to  resist  maximum  stresses  caused  by  either  method  of  analysis.  The  method 
of  fastening  the  girder  steel  to  anchor  rods  should  be  noted.  Expansion  joints  are  provided 
under  the  girder  stems  by  means  of  sliding  steel  plates  anchored  into  the  body  of  both  super- 
structure and  substructure. 

Fig.  16  illustrates  the  type  of  deck-girder  bridge  adopted  as  standard  by  the  Illinois 
Highway  Commission.  The  following  description  of  the  methods  employed  in  providing  for 
expansion  in  girder  bridges  is  given  in  the  fourth  report  of  the  Commission: 


614 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14-4 


Two  methods  of  providing  for  expansion  in  girder  bridges  have  been  used  and  both  have  proved  satisfactory. 
In  one  method,  the  wing  walls  of  one  abutment  are  entirely  separated  from  the  abutment  wall  proper,  the  latter 


^^^i  "Felt  Joint 
Section  A-A  Steel  Plate 


Fig.  16. — Details  of  Embarrass  River  bridge,  Cumberland  Co.,  111. 

being  free  to  move  at  the  top  with  the  expansion  or  contraction  of  the  superstructure.  The  wing  walls  are  designed 
to  be  self-supporting.    As  girder  spans  designed  by  the  Commission  have  so  far  been  limited  to  60  ft.,  the  amount 


Sec.  14-4] 


SLAB  AND  GIRDER  BRIDGES 


615 


of  movement  either  way  from  the  normal  is  small  and  is  taken  up  by  deflection  of  the  main  wall  or  a  slight  rocking 
of  the  wall  on  the  footing.  Earth  pressure  against  the  wall  is  of  little  importance  in  this  connection  as  it  but  tends 
to  reduce  the  tension  in  the  girder  steel  during  expansion  and  to  cause  the  abutment  wall  to  follow  the  superstruc- 
ture during  contraction.  It  does  not  increase  the  stress  in  the  compression  area  of  the  girder  as  the  load  is  applied- 
at  the  bottom  of  the  girder,  tending  by  this  eccentricity  of  application  to  reverse  the  dead-  and  live-load  stresses 
in  the  girder. 

This  method  has  been  found  to  be  entirely  successful,  but  is  somewhat  objectionable  as  a  slight  movement  of 
the  wings  due  to  earth  pressure  and  unequal  settlement  sometimes  causes  the  wing  walls  to  move  forward  slightly 
at  the  top,  making  a  somewhat  unsightly  offset  between  the  wing  and  abutment  walls.  This  has  never  been  more 
than  2  or  3  in.  for  the  highest  walls,  but  as  it  is  not  understood  by  the  ordinary  observer,  an  impression  of  weakness 
is  sometimes  caused. 

The  present  method  of  providing  for  expansion  is  to  design  the  abutments  and  wings  in  the  ordinary  way, 
separating  the  superstructure  completely  from  one  of  the  abutments  by  a  thick  paper  joint  and  supporting  each 
girder  at  the  free  end  on  a  single  cast-iron  rocker  of  large  diameter.  The  reaction  is  transmitted  to  the  girder  and 
abutment  from  the  rocker  through  planed  structural-steel  plates  stiffened  with  I-beams  when  necessary.  The 
rocker  surfaces  in  contact  with  the  bearing  plates  are  turned  to  insure  perfect  bearing  on  the  plates.  The  diameter 
of  the  rocker  is  made  proportional  to  the  load  imposed  per  linear  inch,  in  the  same  manner  as  is  commonly  used  in 
proportioning  roller  nests  for  steel  bridges.  The  upper  and  lower  plates  are  bedded  in  the  concrete  of  the  superstruc- 
ture and  abutment.  The  rocker  is  located  in  a  pocket  built  in  the  abutment.  This  pocket  is  filled  with  a  soft 
'  asphalt  to  prevent  the  entrance  of  water  or  dirt  and  to  protect  the  metal  from  corrosion. 

The  rocker  method  of  providing  for  expansion  has  proved  very  satisfactory  and  is  but  little  more  expensive 
than  the  other  method,  especially  when  it  is  considered  that  the  wings  may  be  tied  to  the  main  wall  when  rockers 
are  used  and  advantage  taken  of  the  mutual  support  thus  obtained. 


Crown  of  F/'n/shed  /foadway 


Section  A-A       Half  Rear  Elevation 


I'Bars  l2"c-foc.    '■  ^'Bars /s'c.iuc.  ^"'/\<.-4'-9"-A 
Half  Front  Elevation 


± — 1 

2  End 
of  Wing 


Fig.  17. — Type  of  abutment  used  for  girder  bridges  by  the  Illinois  Highway  Commission.    Wings  of  cantilever 
type.    Main  wall  supported  by  wings  as  counterforts. 


Fig.  17  shows  a  type  of  abutment  adopted  by  the  lUinois  Highway  Commission  in  cases 
where  the  girders  are  supported  on  cast-iron  rockers  and  the  wings  are  nearly  parallel  to  the 
roadway  or  make  an  angle  of  more  than  45  deg.  with  the  face  of  the  abutment.  The  wing 
walls  are  considered  to  act  as  counterforts  and  the  reinforcing  steel  in  the  main  walls  is  hori- 
zontal and  placed  near  the  stream  face  of  the  wall. 

Fig.  18  gives  the  details  of  a  girder  bridge,  the  main  portion  of  the  abutments  and  the 
wings  of  which  were  designed  and  figured  in  the  same  manner  as  the  slab  bridges  of  Figs.  3, 
4  and  5. 

In  the  structure  shown  in  Figs.  19  to  23  inclusive,  cross  girders  and  stringers  were  provided 
in  addition  to  the  longitudinal  girders,  this  type  of  floor  system  being  found  to  be  economical 
for  wide  bridges  of  long  span.  One  end  of  each  span  is  anchored  to  the  pier  and  the  other  end 
is  allowed  to  expand  and  contract  in  a  joint  packed  all  around  with  in.  of  tar  paper  and 
bearing  on  a  pair  of  milled  steel  plates.  Expansion  joints  were  also  made  in  the  roadway 
slab  and  railing.  Cast-iron  scuppers  were  placed  in  each  curb  on  25-ft.  centers.  For  maximum 
stresses  in  the  cross  girders,  the  sidewalks  were  assumed  to  be  unloaded. 


Fig.  19. — North  Samuels  Avenue  viaduct,  Fort  Worth,  Texas. 


Sec.  14-5] 


SLAB  AND  GIRDER  BRIDGES 


617 


Reinforced-concrete  deck-girder  bridges  for  railroad  traffic  are  rather  unusual,  but  a  few 
such  structures  have  been  built.  The  superstructure  in  such  bridges  is  usually  supported  by 
plain-concrete  piers  and  abutments. 

6.  Through  Girders. — From  the  standpoint  of  economy,  the  through-girder  bridge  should 
not  be  built  except  where  insufficient  headroom  or  other  local  conditions  prevent  the  use  of  the 
deck  girder. 


Plan  of  Reinforcement  In  Footing 

Fig.  20. — Details  of  south  abutment,  North  Samuels  Avenue  viaduct,  Fort  Worth,  Texas. 


The  standard  type  of  through-girder  bridge,  adopted  by  the  Iowa  Highway  Commission 
for  locations  where  the  deck  type  is  impracticable,  is  shown  in  Fig.  24.  The  girders  themselves 
were  designed  as  simple  beams  and  the  floor  as  a  slab  partially  fixed,  the  point  of  contraflexure 
being  arbitrarily  assumed  at  about  1  ft.  from  the  edge  of  the  girder.  This  is  approximately  in 
accordance  with  tests  made  by  the  Illinois  Highway  Commission  in  1907. 

In  the  tests  referred  to,  stress  measurements  were  made  on  a  through-girder  span  with  an 
18-ft.  roadway  loaded  with  crushed  stone  and  pig  iron.  The  full  applied  load  was  418  tons, 
which  gave  a  distributed  load  per  square  foot  of  floor  of  1450  lb.    Deformation  measurements 


618 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14r-5 


,    gj/r   -27-04  ■■• 


^/ey.  495-0 


3-^'^- /eh" hops  i/nder 
6" /each  girder  seat 


y  after nafe 


Elevation  of  Stream  Pier 


Section  A-A 


4  Bars  bent  to  form 
one  stirrup 


IT- i"' Bars,  4-0? 


1  il  i[  r  \ 

1  1  1  1 1 

iSiiii 

Detail  of 
Snear  Bars 


*  n-  Section  B-B 

Elevation  of  Pier 

Fig.  21. — Details  of  typical  piers,  North  Samuels  Avenue  viaduct,  Fort  Worth,  Texas. 


Sec.  14-5]  SLAB  AND  GIRDER  BRIDGES  619 


A      Center  Line  of  stringer  and  ra//inq 
^   r         ^/^//    .G    ^  ;  J^,^,A, 


■\-  30-0  face  tv  face  oi^curb 

7'- 6"   H<- 

1  K 


fiecTion  6-6 


Section  FF 


Detail  Cff  Copper 
Expansion  Joint 
(to  be  used  for  side- 
wQlk  slab  and  curb) 


Fig.  22. — Details  of  floor  system,  North  Samuels  Avenue  viaduct,  Fort  "Worth,  Texas. 


620 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14- 


Center  L/ne  of  F/oorbeam  and  pier 


 /£'.$"  >i  ,.C.L.of  F/oorbeam 

C.L.ofF/.beam        \  <^rrc( girder 


.        I^^i  i  i  K  i   i  i 

— >]]<:-->l  ;V/  ^ 


///'•  K>,....-?../£^^^..        ^-^ ''''  c.  to c.  piers 
'  ?  II-" 

^      Elevation  of  girder 


Center  line  of  -Diaphragm 


1 


■>]/-//[<- 
5ect.ion 


VJ-i'^. 

"A 


Stringer  under  Roqdvyaj 


6  ' 


Siope  /-  J 


<?ro^/-       Expansion       ^  ,  ^ 
jQint       Joint  lined  k[ 
witty 


Section  A-A        Section. B-B 


r 


tor  paper  Scuppers 

(to  be  piaced  midway 
between  fioorbeams 
and  25  ft  c.toc.) 


.Chamfer i"  Expansion  Joint-jfc^// 

7//^_/.//     .  ^1!^  tre/^tjt  ofrai/in^ 
'8-'.  B 


I     Li'^'l'*"'    A     J<^/^  V*  ipiufkyuin  z>juu  ■  ^^i"''Conduif,-\^^^^  Tar 

if>7?.  Str/njer  •■'^ 

Typical  Post         Typical  Panel  of  Hand  Railing  Post  carrying  Lamp 

Fig.  23. — Details  of  floor  system  and  railing,  North  Samuels  Avenue  viaduct,  Fort  Worth,  Texas. 


Sec.  14-5] 


SLAB  AND  GIRDER  BRIDGES 


621 


  /S^-O"  Roadway 

I      I   F/oor  may  be  movecf 


. '      Sars,  6  "c.  -foe.  every  S"^  and 
\  S^'^  bar  fo  be  bent  up  as  shown 


Bars 

Bars,  Zbof..4  top 


1^  Theoretical  Half  Span 

fe'-; i5'-6"  ■-. 
■■ir-^-o>^-4^i'-&' 


6/rder 


F/oor 


(  /-/'"Bars 

30- 

5' 

Z-l"" 

36'- 

11" 

3-1"" 

3Z' 

0" 

Z-li"" 

3Z' 

0" 

II' 

3" 

Zl' 

0" 

44-1"° 

7' 

0" 

Zl' 

6" 

Zf-V" 

zs' 

6" 

/3-i"° 

3Z' 

0" 

Fig.  24. — Standard  sections  for  through  girder  bridges  of  30-ft. 


Iowa  Highway  Commission. 


corners  Transverse  Section 


Fig.  25. — Details  of  superstructure  of  Funkelien  bridge,  Town  of  Christiana,  Dane  Co.,  Wis. 


r-'T 
I 


  ^'-o" 


4  -  a" Bars  on  \ 
each  end  ofevery\ 
other  -floor  bar 


^"Tar  paf^r  Joint 


^"Tar paper  K;* 
Joint       \:  o. 


--.  Asphalt 
/ peneiration 

I  PC  mm  ) 


Spacing  for  j"" Stirrups 

t<  -  8"  ••■><•■•-  IZ"  ■■•J>1<   Z4"   >f'' 

\   cfoc    \     c-toc.     I        croc-  I 


-3'Ti/e  Drains 
6'c.toc. 


Fig.  26. — Details  of  through  girder  bridge  of  45-ft.  span,  Illinois  Highway  Commission. 


622 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14-6 


were  made  in  the  reinforcing  steel  of  the  suspended  floor  which  indicated  stress  equivalent  to 
that  theoretically  resulting  from  a  sinple  span  of  15.5  ft.  In  other  words,  since  the  roadway 
was  18  ft.  between  girders,  the  point  of  contraflexure  was  apparently  about  15  in.  from  each 
girder  face. 

Figs.  25,  26  and  27  illustrate  other  design  of  through-girder  superstructures. 


,Bafter 
/  "/fods,  'f'-ol  /e'cfuc. 

\   Batter  ? 


.  j"/fods,s'-3"  IE"ctOC 

.-  2"ffod5,  /8'identj  f4"c  -oc 

I" Pod 5.  yVctoc 


il'tf0ds\        j                                    |\   I     ^"f?ods'         I        \l''ff0d5:3i'ct0c'\  I 
■■.■■3'-ii"-Xi'-^          r'-o' ■ — ->l/-e3<----  e'-o"  —■>^i-6i<         r'-o''  •>i/-'e4f—  j'- //'--: 

Fig.  27. — Cross-section  of  through  girder  bridge,  C.  B.  &  Q.  R.  R. 


Fig.  28  shows  a  rather  unusual  type  of  through  bridge  on  account  of  the  fact  that  the 
girder  reinforcement  is  in  the  form  of  a  truss  of  sufficient  strength  to  carry  the  dead  and  con- 
struction loads.  The  piers  are  simply  columns  braced  between  by  either  a  vertical  slab  or  by 
struts.  As  no  falsework  is  necessary,  this  type  of  construction  is  especially  adapted  for  high- 
way bridges  over  railroads  and  electric  lines,  or  at  locations  where  the  soil  is  very  soft. 


]  D 

n|i — 

—y 

r-/^  1 

1 — 

u-tt 

i  ft 

A 

A 

 f 

J 

i 

Section  A-A 

Fig.  28. — Details  of  bridge  over  Muddy  Creek,  Hamilton  County,  Ohio 

CONTINUOUS-GIRDER  BRIDGES 
Monolithic  Construction 

6.  Expansion  Joints. — In  order  to  prevent  an  accumulation  of  movement  due  to  contrac- 
tion and  expansion,  expansion  joints  should  be  provided  at  least  every  100  ft.  in  length  of  the 
structure.    If  this  is  not  done,  severe  stresses  are  likely  to  occur  in  the  end  columns. 

In  long  bridges  an  expansion  joint  is  usually  provided  between  the  superstructure  and  the 


Sec.  14-7] 


SLAB  AND  GIRDER  BRIDGES 


623 


abutments  for  the  reason  that,  if  an  abutment  witli  a  heavy  pressure  of  earth  against  it  is 
rigidly  connected  with  a  number  of  continuous  spans,  the  expansion  and  contraction  tend  to 
act  in  one  direction  only — that  is,  away  from  the  abutment — the  earth  pressure  back  of  the 
abutment  not  allowing  movement  in  the  opposite  direction.  Such  a  condition  would  lead  to 
difficulties  at  the  center  of  the  bridge,  or  over  the  expansion  piers  next  to  the  abutments,  and 
the  abutments  and  piers  would  also  be  severely  overstressed  due  to  the  continuous  movement 
in  one  direction.  Each  time  an  abutment  would  move  slightly  due  to  contraction,  the  earth 
against  it  by  reason  of  the  heavy  moving  loads  would  fill  in  the  small  space  left  by  the  contrac- 
tive movement,  and  when  expansion  again  took  place,  the  abutment  would  be  restrained  by 
the  earth  so  that  enormous  stresses  might  be  developed. 

7.  Examples  of  Typical  Bridges  of  the  Continuous-girder  Type. — A  rather  simple  highway 
trestle,  applicable  to  comparatively  low  crossings,  is  shown  in  Fig.  29.  The  longitudinal  beams 
are  continuous  over  three  spans,  an  expansion  joint  occurring  over  every  third  pier.  Inter- 
mediate piers  are  made  monolithic  with  the  floor  by  means  of  rods  from  the  columns  and  stir- 
rups from  the  cross  beams.  Because  of  the  indeterminate  degree  of  fixity,  the  lightness  of  the 
structure,  and  unknown  construction  factors,  all  members  affected  were  designed  both  as  fixed 


Half  Transverse  Section  Longitudinal  Section  on  Center  Line 

Fig.  29. — Details  of  standard  trestle  spans,  Engineering  Department,  State  of  Arizona. 

beams  and  as  beams  freely  supported.  The  slabs  were  designed  as  continuous,  with  equal 
positive  and  negative  steel  throughout.  The  center  longitudinal  beam  was  designed  as  a 
T-beam  with  a  36-in.  flange.  The  pier  web,  or  wall  between  supporting  columns  of  bents,  is 
carried  2  ft.  above  high  water. 

A  low  trestle  or  viaduct  type  of  construction  is  shown  in  Fig.  30.  The  slab-beam-and- 
girder  spans  were  selected  since  arches,  it  was  thought,  would  not  appear  to  advantage  for  such 
low  construction.  The  cost  of  the  girder  type  was  also  found  to  be  much  less  than  for  a  series 
of  arches,  due  principally  to  decrease  in  the  dead  weight  of  the  structure  and  to  simplicity  in 
form  work.  Expansion  joints  occur  about  every  200  ft.  and  make  the  viaduct  virtually  a 
number  of  independent  structures,  a  double  row  of  columns  being  provided  at  each  joint.  The 
arched  girders  capping  the  column  bents  were  designed  as  straight  rectangular  beams  and  no 
account  was  taken  of  the  possible  arch  action.  The  entire  top  surface  of  the  roadway  slab  was 
waterproofed  with  a  layer  of  burlap  and  two  layers  of  felt  laid  in  hot  asphalt. 

Fig.  31  gives  the  details  of  a  continuous-girder  bridge  to  span  a  stream  which  is  generally 
dry,  but  which  at  flood  times  reaches  over  a  wide  area  of  bottom  lands.  This  railway  bridge 
is  also  within  the  backward  area  of  the  White  Rock  reservoir  of  the  Dallas  water  supply  so 
that  ample  provision  had  to  be  made  for  high-water  conditions.  The  floor  consists  of  a  double 
T-beam  which  is  monolithic  with  the  bents  and  the  abutments.  There  is  no  expansion  joint  in 
the  structure  since  it  was  considered  of  sufficient  strength  to  take  all  movement  from  end  to 
pnd.    Both  ends  of  the  structure  are  open  between  girder  supports  with  short  trestles  con- 


624 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14-7 


B        Cameqie  Tie  M^S      Ur—  s'-Si" 

Concrete  Ballast '-^jA  ^  \ 


(8-Q  Bars  ,r^-,-gpnnediate 
)     Hoops  6"c. to  c.  Bracket 


'■/"stub,  Id" A 


^oops'^^l^ 


4-l"^T....\ 


•3'm,,-P!.B^''K§''xiZ' 


I — r 


T — I 


Expansion  Joinl" 
in  Rocdway  U    W  U 

SJ-O'  -■:  " 


<i''ivood  Block. 


. -  Z '^""Tyr.  Bars     ^     ^^^^^  Cosh/on  \ 


M''"'{^-/f"Bars 


u..._         — a<   7itf'^  

B-/'"'r^y.  Bars  \ 


^  Section  A-A 

Fig.  30. — Details  of  Gilbert  Avenue  viaduct,  Cincinnati,  Ohio. 


Sec.  14-8] 


SLAB  AND  GIRDER  BRIDGES 


625 


necting  with  the  bridge  which  at  some  future  time  may  be  filled  in  if  high  water  gives  no  trouble 
at  this  point.  The  girders  were  designed  for  Cooper's  E-30  loading  with  an  impact  allowance 
of  100%  of  the  live  load.    The  ribbed  abutments  should  be  noted. 

A  continuous-girder  bridge  or  trestle  with  no  expansion  joints  and  with  abutments  of  the 
ordinary  type  is  shown  in  Fig.  32.  The  structural-steel  core  in  the  column  bents  is  unusual 
but  undoubtedly  adds  greatly  to  the  rigidity. 

Fig.  33  gives  the  details  of  one  of  the  typical  bridges  in  the  Chicago,  Milwaukee  &  St. 
Paul  track  depression  work  at  Minneapolis.  The  girders  are  continuous  from  end  to  end  with 
expansion  joints  at  the  abutments — that  is,  the  girders  were  considered  continuous  over  the 
two  interior  supports  and  simply  supported  at  the  ends.  The  moments  and  shears  were 
calculated  by  influence  lines  in  accordance  with  the  theory  of  continuous  structures  assuming 
constant  /  and  unyielding  supports  (see  Art.  48a,  Sect.  7).    Corrections  were  made  for  >^-in. 


End  Elevotion  Side  Elevation 

Fig.  31. — Details  of  railway  bridge  over  White  Rock  Creek  near  Dallas,  Texas. 

settlement  of  supports  for  variable  /.  An  unusual  feature  of  the  bridges  is  a  curved  shelf  on 
the  outer  face  of  the  outside  girder  which  is  intended  to  act  as  a  smoke  shield  by  diverting  the 
smoke  from  the  parapet  as  engines  pass  under  the  bridge. 

8.  Analysis  of  Stresses  in  Rigid  Viaduct  Structures. — A  viaduct  structure,  composed  of 
one  or  more  cross  frames  or  bents,  and  two  or  more  spans  of  longitudinal  deck  girders,  is  in 
reality  a  rigid  frame  when  girders  and  bents  are  rigidly  attached  to  each  other.  Reinforced- 
concrete  structures  of  this  kind  will  act  as  rigid  frames  between  expansion  joints,  and  should 
be  investigated  as  such.  The  general  problem  may  be  reduced  to  two  problems  for  analysis: 
the  stresses  caused  in  the  frame  as  seen  in  longitudinal  elevation  (hereafter  referred  to  as  the 
viaduct  frame) ;  and  the  stresses  in  the  cross  frame  seen  in  a  transverse  section  of  the  structure 
(hereafter  called  the  cross  frame,  or  bent).  These  problems  will  be  treated  in  the  order  here 
given. 

The  viaduct  frame  should  be  designed  to  withstand:  (1)  the  dead  load  of  the  frame;  (2) 
the  vertical  live  load,  plus  impact;  (3)  the  horizontal  traction  forces,  or  braking  forces,  plus 
40 


626 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14-8 


.   1 

ST 

-J  '"^^ 

Vz'^^  

   3d'' 8"  —  ^  > 

,            fBars  S'c.  foe. 

  /9-4!'   -> 

Side  Girder  ReirrTorcernent 


Interior  Girder  Reinforcennen+ 


AS.&py.  Co's  rr/an^/e  Mesh 
Sty/e  No.  7-50  -  /a  "rndtfr 


/?ound  Corners,  io  /'^/Fad/us 
jSymmefr/ca/  about 
^  Center  L/ne  except 


3-2  ,  of  drain  \    for  S/deyt^affr 


.  2  Bar 


/neacft  side 
of  each  span 


^^Fv?-^  ttC  :_ 


■e-f' 


4,  <V4 


<3-3-h.-/6''--M'-—  6-  7"  J<-  i6"--X  V-/^ 

Transverse  Section 

B 


^.S.&tr.  Cos  Tr/an^/e  Mesir . 
Siy/eAo  7-  i8"yyidttT-  mnd 
spiraiiy  aroc/nd  cg/umn 

Hoies  7^r  ^'^/^ncfror  Boits 


ZPis.6K/8fK^' 


1 

( 

Section  A-A  \ 

Cross  Girder  ^ 
/^n^/es 


Plan 

Section  B-B  th.  B4".B4".f^''  ' 

Fig.  32. — Details  of  Mill  Creek  bridge,  Village  of  Cazenovia,  Richland  Co.,  Wis. 


Sec.  14-8] 


SLAB  AND  GIRDER  BRIDGES 


627 


■M  ,      Bridge  Seat  ^ 


y9" 

8'' Z'^-->'f:-5'-5"-^- 


3/ -6" 


<- 

Bearn  "C 


'>1< 


IS'.S't:  J 


Sectional  Elevation  \<-6-9"-iA 


Baiter4^:/B 


SecTion  B-B 


 «   4.5-0^  ^>|;c  >| 

B    i'^^'^y^^  Paper,  ''^ 


1<  ^'-^//->|         S/770/f6'---l^  J/'-^'''  -J 

Shie/d  ■  _ 

Section  A-A  Elevation  ^Smoke 

Fig.  33. — Details  of  Bryant  Avenue  bridge  over  tracks  of  the  C.  M.  &  St.  P.  Ry.,  Minneapolis,  Minn. 


628 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14-8a 


impact;  (4)  stresses  due  to  changes  in  temperature.  Any  one  of  these  cases  may  develop 
large  moments  in  both  girders  and  columns.  The  reactions  on  the  footings  cannot  be  deter- 
mined in  an  unsymmetrical  frame,  or  in  a  symmetrical  frame  with  unsymmetrical  loading, 
without  consideration  of  the  elastic  distortion  of  the  structure.  The  dead  load  would  consist 
of  the  estimated  weight  of  the  frame.  The  live  load  and  its  impact  would  be  of  the  classes  of 
loading  given  for  arches  (see  Art.  6,  Sect.  16). 

8a.  Viaduct  Frames. — Before  proceeding  with  the  analysis  of  the  viaduct 
frame,  it  is  necessary  to  determine  the  conditions  of  support  of  the  bases  of  the  columns  and 
of  the  outer  ends  of  the  girders.  The  greatest  moments  in  the  columns  due  to  unbalanced- 
loads  on  adjacent  spans  will  occur  when  the  column  bases  are  fixed;  and  the  greatest  column 
stresses  due  to  lateral,  or  tractive,  forces  will  occur  when  the  column  bases  may  be  considered 
as  hinged.  Since  the  tractive  forces  produce  very  large  column  stresses,  and  since  there  is 
usually  great  difficulty  in  securing  a  perfectly  fixed  column  base,  the  discussion  here  given  will 
apply  first  to  viaduct  frames  whose  column  bases  are  hinged,  after  which  certain  modifications 
of  the  development  will  be  suggested  to  care  for  the  case  of  the  perfectly  fixed  column  base. 
End  girders  will  be  assumed  to  have  frictionless  bearings  in  the  expansion  pockets,  thus  allow- 
ing the  maximum  horizontal  deformation  of  the  frame  to  occur. 

The  extent  to  which  the  bent  will  act  as  a  pair  of  columns  in  the  viaduct  frame  should 
also  be  determined.  In  Fig.  34  is  shown  a  two-legged  bent  with  slightly  battered  columns. 
Girders  attached  at  B  and  C  will  deflect  in  vertical  planes;  hence  it  is  convenient  to  replace 

AB  and  CD  with  columns  lying  in  vertical  planes,  as  A'B  and 
CD\  whose  stiffness,  or  ability  to  restrain  the  points  B  and  C,  is 
just  equal  to  that  of  the  legs  AB  and  CD.  The  length  of  these 
equivalent  columns  will  be  h,  and  their  moments  of  inertia  about 
a  horizontal  axis  lying  in  the  plane  of  the  bent  will  be  Ia'b  =  Iab 
cos  d.  When  the  bent  is  composed  of  more  than  two  columns, 
each  column  should  be  replaced  by  a  vertical  one,  as  above;  and 
the  sum  of  the  moments  of  inertia  of  all  equivalent  columns  on 
one  side  of  the  axis  of  symmetry  should  be  considered  as  the 
moment  of  inertia  of  a  single  resultant  column  A'B.  This  resultant  column  will  be  called 
"the  column"  in  the  following  treatment  of  viaduct  frames. 

It  is  immaterial  whether  or  not  the  whole  viaduct  frame  is  split  lengthwise  into  two  parts 
for  analysis.    The  designer  should  arrange  this  matter  to  suit  his  convenience  in  computations. 

Three  cases  of  loading  will  be  applied  to 'the  viaduct  frame:  (1)  a  moving  vertical  con- 
centrated load;  (2)  a  vertical  symmetrical  load,  placed  symmetrically  on  a  single  span;  (3) 
a  horizontal  load  acting  axially  on  the  deck  girder.  It  will  be  possible  from  these  investiga- 
tions to  plot  influence  lines  for  live  load,  and  to  determine  the  effect  of  dead  load  on  the  span. 

The  following  series  of  solutions  will  begin  with  the  general  case  of  the  four-span  frame. 
From  this  case  the  other  cases  may  be  deduced,  since  each  of  the  cases  following  is  a  special 
form  of  the  general  case.  All  solutions  will  be  made  by  the  method  of  slope-deflections  (see 
Art.  2,  Sect.  10).    The  nomenclature  used  is  as  follows: 

M  =  moment.    Subscripts  will  denote  where  this  moment  is  taken — as,  Mab  =  moment 

at  A  in  the  member  AB. 
6  =  change  in  slope  of  the  tangent  to  the  elastic  curve  at  a  given  joint.  Subscripts 

will  denote  the  joint  in  question. 
di  =  lateral  movement  of  the  top  of  any  first-tier  column  due  to  eccentric  vertical,  or 

lateral,  loads. 

di  =  lateral  movement  of  the  top  of  any  second-tier  column. 
h  =  column  height.    Subscript  designates  the  column  in  question. 
I  =  girder  length.    Subscript  designates  the  girder  in  question. 

n  =  T-    Subscript  designates  the  column  in  question. 


Sec.  14-86] 


SLAB  AND  GIRDER  BRIDGES 


620 


K 
F  _ 
I 

X  = 


for  girder;  or  ^  for  column 


Subscript  indicates  member  in  question. 

constant  for  symmetrical  loading.  See  page  413  for  values  for  different  types  of 
loading. 

moment  effect  at  left  end  of  girder  due  to  load  P  on  that  girder,  and  in  general 

equals  — ^  ,  in  which  a  is  the  distance  from  the  left  end  of  the  girder  to  P,  and 

a  -\-  h  =  I.    Subscripts  will  denote  the  girder  in  question, 
y  =  moment  effect  at  right  end  of  girder  due  to  load  P  on  that  girder,  and  in  general 
Pa% 

equals  — jj-.    Subscripts  will  denote  the  girder  in  question. 

Sb.  Four-span  Viaduct  Frame  with  Rigidly-connected  Column  Tie  (Type  I). — 
The  general  case  of  the  unsymmetrical  frame  shown  in  Fig.  35  will 
be  analyzed  for  the  loads  Pi  and  P2  and  Q  occurring  separately. 

Since  the  structure  and  its  loads  are  for  the  general  case  un- 
symmetrical, there  will  be  a  horizontal  movement  of  the  members 
AB,  and  of  the  members  FL,  besides  rotation  at  all  of  the  joints. 
Vertical  components  of  this  nearly  horizontal  motion  will  be  neg- 
lected in  this  analysis. 

Referring  to  Arts.  2  and  3,  Sect.  10,  the  equations  for  the 
moment  at  the  end  of  each  may  be  written  as  follows: 


N 


K, 

K2 

K3 

K4 

Kg  6 

H 

Kj  J 

K,  L 

0 

\ 

k 

s 


Fig.  35. 


Mfn 

SEKi^idF  -  niM 

Mle 

2EKi3{2dL  +  Be  - 

3ni3(i2) 

Mpg 

2EK^{2dF  +  Og) 

Mlt 

SEKisidL  -  nisdi) 

Ufa 

2EIU{2dF  +  dA  -  3/19^2) 

Mlj 

2EKs(2dL  +  dj) 

Map 

2EK^{2dA      Of  -  ?>n^d2) 

Mjl 

2EK^{2dj  +  Ol) 

Mab 

2EKi{2dA  +  ds)  -  Xab 

Mjs 

dEKn(dj  -  ni7di) 

Mba 

2EKi{2dB  +  0^)  +  Yba 

Mjd 

2EKi2(2ej  +  60- 

3ni2C?2) 

Mbg 

2EKio(2eB  +  dG-  Sniod2) 

Mjh 

2EK7{2dj  +  Bh) 

Mbc 

2EK 2(268  +  dc)  -  Xbc 

Mhj 

2EK'ji2dH  +  ej) 

McB 

2EK2(2dc  +  Ob)  +  Ycb 

Mhr 

SEKuidH  -  nidi) 

McH 

2EKii(2ec  +  dH  -  Snud2) 

Mhc 

2EKni2dH  +  dc  - 

3nii(i2) 

McD 

2EKz{2dc  +  Od) 

Mhg 

2EK,{2dH  +  Og) 

Mdc 

2EKz{2dD  +  dc) 

Mgh 

2EK6(2dG  +  Oh) 

Mdj 

2EKi2{2dD  +  dj  -  3ni2d2) 

Mgo 

SEKi5(dG  -  niM 

Mde 

2EK4.{2dD  +  Be) 

Mgb 

2EKio{2dG  +  eB  - 

3nioc^2) 

Med 

2EK4{2dE  +  do) 

Mgf 

2EKr,[2dG  +  Of) 

Mel 

2EKiz{2dE  +  dL-  3ni3fi2) 

Mob 


Ma 


Since  from  statics,  any  joint  in  a  structure  is  in  equilibrium,  the  sum  of  the  moments  about 
that  joint  must  equal  zero.  Thus, 

Mfn  +  Mfg  +  Mfa  =  0 

The  values  of  each  moment  (from  above)  may  be  substituted  into  this  equation. 

In  liice  manner  the  equations  above  for  the  members  concurring 
at  any  joint  may  be  summed  up  and  this  sum  set  to  zero.  This  will 
result  in  ten  equations,  one  for  each  of  the  joints  A  to  L,  inclusive, 
which  will  involve  twelve  unknowns;  that  is,  a  6  for  each  of  these 
joints,  and  in  addition,  c?2  and  di.  For  solution  it  is  necessary  to  write 
as  many  equations  as  there  are  unknowns.  One  of  the  two  additional 
equations  may  be  supplied  from  the  following  condition: 
The  sum  of  the  moments  at  the  top  and  bottom  of  all  columns  of  one  tier,  plus  the  product 
of  the  shear  (Q),  and  the  height  of  the  tier  (/ig),  equals  zero.    Thus,  referring  to  Fig.  36, 


Fig.  36. 


630 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14-86 


Maf  +  Mbo  +  McH  +  Mdj  +  Mel  +  Mfa  +  Mgb  +  Mhc  +  ATjz)  +  ATle  +  Qh^  =  Q 

The  second  of  the  two  equations  may  be  written  from  the  requirement  that  the  sum  of  all  hori- 
zontal components  of  reactions  at  the  bases     to  T,  inclusive,  must  equal  Q.  Thus, 

MpNnii  +  MGoni5  +  MuRTiie  +  MjsUn  +  MltUu  -  Q  =  0 

These  two  equations,  and  the  ten  equations  mentioned  above,  have  been  tabulated  in  Table 
I,  after  having  first  been  divided  through  by  E.  All  terms  having  no  variables  have  been  put  on 
the  right-hand  side  of  the  equations,  and  have  been  tabulated  as  three  cases:  (1)  with  the  load 
Pi  on  AB;  (2)  with  the  load  P2  on  BC;  (3)  with  the  horizontal  load  Q  at  E.  Vertical  loads 
on  other  spans  may  be  treated  as  in  Cases  (1)  and  (2).  This  arrangement  allows  any  case 
to  be  analyzed  entirely  separately.  In  either  Case  (1)  or  (2),  the  position  of  the  load  may 
be  altered  by  changing  the  distances  a  and  b,  hence  changing  the  values  of  X  and  Y  (see 
page  629,  Fig.  35).  It  was  found  convenient  to  divide  the  last  two  equations  by  a  common 
constant  term. 

After  a  table  similar  to  Table  I  has  been  prepared,  the  known  terms  may  be  evaluated, 
and  the  resulting  simultaneous  equations  solved  as  in  the  illustrative  problem  under  Type 
VII.,  Art.  8h. 

Table  1. 


Variable  Terms 
CLeft  hand  side  of  equations) 


Constant  Terms 
(Right  hand  side  of  equations) 


ec 

Go 

Or 

e„ 

ej 

d^ 

d, 

Case  I 

Casen 

Casein 

1 

-6  Kan  9 

2 

2  Kg 

3 

eK. 

4K,MKj+4Ka 

2K,o 

-SKionio 

-\\ 

1 

4 

-6K„n,i 

£D 

6 

5 

-6Kjn,2 

C 

1  1  1  1 

load -Span  BC 

MM 

Horizontal  load  ^ 

M  M  1 

6 

4Kit4K,3 

-6K|3n,3 

CO 

7 

4K^4Ko+3Kia 

-3K„,n,6 

8 

+4^:^+3^,7 

-3Knn,7 

— £  — ^ 

9 

-6K,in,i 

"3K,6n|6 

— L^y  — 

10 

^Ks 

-6K|onio 

-3K,5n,5 

— s_ 

If 

K|4ni4 

-(|<«?i!4+l(itn,s+IC4ri|6 
•fKiinS+KiiTiis') 

Hi 

-1- 

?{^[ 

IE 

K„ 

K,3 

K9 

K„ 

K,3 

6 

It  sliould  be  noted  both  in  the  moment  equations,  and  in  Table  I,  that  when  the  load  is  on 
AB^  Xbc  and  Ycb  both  equal  zero. 

F 

When  the  load  is  symmetrically  placed  on  a  member,  X  =  F  =         Thus,  if  a  load  is 


symmetrically  placed  on  AB,  Mas  =  2EKi(2eA  +  Ob)  -  y    Equation  (2),  Table  I,  equals 

^^^for  Case  I.    Equation  (3),  Table  I,  equals^  —        for  Case  I.    The  same  scheme  holds 

F 

for  other  members.    For  values  of  y  for  various  symmetrical  loadings,  see  page  413. 

Case  a  {Fig.  37). — The  solution  for  this  case  may  be  obtained  from  the  general  equations 
of  Table  I,  by  substituting  Ki  =  K13  =  Kis  =  0. 

C  D        E  A  B        C         D  E 


2 

10 

6  6 


15 


3 

II 

H  7 


Fig.  37. 


/ 

2 

9 

10 

5  G 

6  H 

14 

15 

h 

C 

Fig. 

3     \     ^  ^ 

II 


It  is  important  to  note  the  variation  if  hn  =  0,  and  a  hinge  is  placed  at  J.  Then  JD 
and  JH  would  be  hinged  at  J.    In  this  special  case  Kn  =  0;  Mjd  =  Mjh  =0;  di  =  0; 


Sec.  14-8c]  SLAB  AND  GIRDER  BRIDGES 


631 


Mdj  =  SEK12  {Od  -  niid^)',  Mhj  =  SEKjdn.  With  these  modifications  a  table  Hke  Table  I 
may  then  be  constructed. 

Case  h  (Fig.  38).— In  this  case  =  Ks  =  Kiz  =  Ku  =  =  0;  Mjd  =  0;  Mdj  =  SEK^ 
{Od  —  riiM.  These  variations  from  the  general  moment  equations,  pages  629  and  630,  will 
allow  a  new  table,  similar  to  Table  I,  to  be  made  up. 

Case  c  {Fig.  39). — The  equations  of  Table  I  apply  to  this  frame  when  =  =  Kg  = 
Kiz  =  Kii  =  K18  =  0. 


2 

J 

10 

11 

G  6 

H  7 

15 

16 

1 

7 

; 

?  ~ 

Fig 

39. 

I 

2 

3 

9 

10 

II 

12 

S  6 

6 

H 

7 

J 

14 

1 

15 

16 

.  : 

17 

Fig.  40. 


8c.  Three-span  Viaduct  Frame  with  Rigidly-connected  Column  Tie  (Type  II). — 

Equatiojis  of  moment  at  the  ends  of  each  member  (Fig.  40)  in  the  frame  may  be  written  as  in 


Type  1. 

Mfn 

=  SEKnidF  -  nidi) 

Mdj 

=  2EKi2{2dD  +  dj  - 

3ni2C?2) 

Mfg 

=  2EK,{2dF  +  Bg) 

Mjd 

=  2EKi2{2dj  +  do  - 

3ni2C?2) 

Mfa 

=  2EK,{2dF  +  eA'-  SnM 

Mjs 

=  SEKuidj  -  nudi) 

Maf 

=  2EK,{2dA  +  dp  -  Sn,d2) 

MjH 

=  2EK^{2dj  +  Oh) 

Mab 

=  2EK,{2dA  +  Ob)  -  Xab 

Mhj 

=  2EK,{2dH  +  ej) 

Mba 

=  2EKi(2dB  +  Oa)  +  Yba 

Mhr 

=  SEKuidH  -  niM 

Mbo 

=  2EKtoi2dB  +  do  -  Sniod2) 

Mhc 

=  2EKni2dH  +  do  - 

37211(^2) 

Mbc 

=  2EK2(2dB  +  do)  -  Xbc 

Mhg 

=  2EK,{2dH  +  Og) 

Mcb 

=  2EK2{2dc  +  Ob)  +  Ycb 

Mgh 

=  2EK^{2dG  +  en) 

McH 

=  2EKii{2dc  +  Oh  -  ^niM 

Mgo 

=  SEKi,{dG  -  nM 

McD 

=  2EKsi2dc  +  Od) 

Mgb 

=  2EKioi2dG  +  9b  - 

3nioc?2) 

Mdc 

=  2EK,{2dD  +  ec) 

Mgf 

=  2EK,{2dG  +  dp) 

The  general  equations  set  up  from  these  moment  equations  are  the  first  eight  of  the  follow- 
ing.   The  ninth  and  tenth  are  found  in  the  same  manner  as  the  eleventh  and  twelfth  of  the  pre- 
ceding type  (see  page  630). 
(1)  2K,dA  +  (3Ki4  +  4^5  +  ^K,)dF  +  2K,dG  -  ^K^ndi  -  3Kunidi  =  0 

Xab 


E 


(2)  (4Xi  +  4:Kg)dA  +  2KidB  +  2KgdF  -  QK^n, 

(3)  2KidA  +  (4Ki  +        +  4:K:o)dB  +  2X260  +  2KiodG  -  ^K,,n,od2  =  -  -|- 

(4)  2K2eB  +  (4^2  +  4Z3  +  4:Kn)ec  +  2X^60  +  2KixdH  -  QKiinnd2  =  0 

(5)  2K,dc  +  (4^3  +  4X12) +  2Ki2dj  -  QKufindi  =  0 

(6)  2Ki2dD  +  2K7eH  +  (3Xi7  +  4K7  +  4Xi2)^j  -  6Ki2ni2C^2  -  SK^nndi  =  0 

(7)  2Kiidc  +  2^6%  +  (3Zi6  +  4^6  +  4K7  +  4Kii)0ff  +  2K7dj  -  QKnnnd2  -  3Kuni^di=0 

(8)  2Ki,dB  +  2K,dF  +  (3Ki5  +  4X5  +  4^6  +  4Kio)0g  +  2KedH  -  6XionW2  -  SKuUndi  =  0 

(9)  KuUudF  +  Ki^ni^dG  +  Ki^niedH  +  KnUndj  -  {KuUu^  -f-  Xunis^  -h  Kunie^  +  Knni-j'^)di 

=  0 

(10)  KgdA  +  Kio05  +  Kxidc  +  Ki25z>  +  -^90/^  +  KioOg  +  i^ii^//  +  Kx2ej  -  2d2{Kgng  + 

i^ionio  +  KiiMii  +^^i2ni2)  =  0 
The  right-hand  side  of  the  above  equations  is  given  for  a  vertical  load  Pi  in  span  AB.  For 
a  vertical  load  P2  on  span  BC,  replace  (—  Yba/E)  in  equation  (3)  with  (X^c/^) ;  set  equation 
(4)  equal  to  (—  Ycb/E)  instead  of  zero,  and  set  equation  (2)  to  zero.  For  a  horizontal  load  at 
D,  set  equation  (9)  equal  to  (Q/3E);  set  equation  (10)  equal  to  (  —  Qh^/QE);  and  all  other  equa- 
tions to  zero.  It  will  be  noted  that  the  modifications  are  in  accordance  with  Cases  I,  II  and  III 
of  Table  I. 


632 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14r-Sd 


When  any  horizontal  member  is  loaded  symmetrically,  then  for  that  member,  X  =  Y  =  j- 

F 

Thus,  if  a  load  is  placed  symmetrically  on  AB,  Mab   =  2EKi{2dA   +63)  -  j',  Mba  = 
F 

2EKi(2dB  +  ^a)  +7'  equation  (2),  page  631,  would  equal  (F/ZE) ;  and  equation  (3),  page  631, 

would  equal  ( —F/IE).  Values  oiF/l  for  various  symmetrical  loadings  are  given  in  the  table  on 
page  413. 

These  ten  equations  may  now  be  tabulated  as  in  Table  I,  and  may  be  solved  by  the  same 
method  as  that  employed  in  a  problem  under  Type  VII  (see  Art.  Sh). 

Case  a  {Fig.  41). — This  frame  may  be  analyzed  by  letting  K12  =  Kt  =  Kn  =  0,  in  the  gen- 
eral equations  of  Type  II,  page  631. 


/5 
0 

Fig.  41 


D 

I 

1     3  2L 

3  22. 

F 

9 

5  6 

10 

r 

H 

14 

i 

C 

15 
1 

Fig.  4fi. 


Suppose  /ii6  =  0,  and  a  hinge  is  placed  at  so  that  HC  and  HG  are  hinged.  Then  Kie  = 
0  =  Mhc  =  Mhg  =  0;  Mgh  -  SEKgOg]  Mch  =  SEKuidc  -  UiM^di  =  0.  These  modifica- 
tions would  be  made  in  the  moment  equations  on  page  631,  and  a  new  set  of  general  equations 
would  be  written. 

Case  b  (Fig.  42).— For  this  case,  Ke  =  K7  =  K12  =  Ki^  =  Kn  =  0]  Mhc  =  0;  Mch  = 
SEKniOc  —  ^11^2).  These  values  would  be  set  into  the  moment  equations  on  page  631  and  the 
resulting  modifications  would  be  made  in  the  ten  general  equations. 


00  / 

c 

2 

10 

6 

3  .22 

II 
H 

1 

/■ 

15 

16 

< 

Fig.  43. 


Fig.  44. 


Case  c  {Fig.  43). — Equations  (1)  to  (10),  on  page  631,  may  be  used  for  this  case  by  placing 
in  them  K^  =  Kt  =  K,  =  K12  =  Ku  =  Kn  =  0. 

Sd.  Two-span  Viaduct  Frame  with  Rigidly -connected  Column  Tie  (Type  III). — 

The  method  of  analysis  does  not  differ  from  that  of  the  preceding  cases.  The  moment  equations 
are  as  follows  (see  Fig.  44) : 


Mfn 

SEKu{dF 

—  niidi) 

Mfg 

2EK,{2dF 

+  Og) 

Mfa 

2EK,{2dF 

+  - 

2>n^d2) 

Map 

2EK,{2dA 

+  Bf  - 

2n^d'i) 

Mab 

2EKi{2dA 

+  dB)  - 

-  Xab 

Mba 

2EKi{2dB 

+  Oa)  +  Yba 

Mbg 

2EKio{2dB  +  do  - 

3/110^2 

Mbc 

2EK2{2dB 

+  ec) 

McB 

2EK'i{2dc 

+  Bb) 

Mch 

=  2EKn{2ec  +  Oh  - 

3^11^2) 

Mhc 

=  2EKn{2dH  +  dc  - 

3nii(i2) 

Mhr 

=  SEK,e{dH  -  niM 

Mhg 

=  2EK,{2dH  +  Og) 

Mgh 

=  2EKe{2dG  +  Oh) 

Mgb 

=  2EKio{2dG  +  Ob  - 

37110^^2) 

Mgo 

=  SEKi,{eG  -  niM 

Mgf 

=  2EK^{2dG  +  dp) 

Sec.  14-86] 


SLAB  AND  GIRDER  BRIDGES 


633 


General  equations: 

(1)  (4i^9  +  4:Ki)dA  +  2K,eB  +  2K,eF  -  QK^n^dz  =  Xab/E 

(2)  2KidA  +  (4/^1  +  4K^o  +  ^K,)dB  +  2K,ec  +  2KicdG  -  QK,oniod2  =  -Yab IE. 

(3)  2^:205  +  (4^2  +  4ivu)^c  +  2K^xQh  -  QKuUudi  =  0 

(4)  2K9dA  +  (3i^i4  +  4^5  +  4:K,)dF  +  2K50(?  -  SKi^nudi  -  QK,n,d2  =  0 

(5)  2KiodB  +  2/^:6^^^  +  (4^5  +  4Xio  +  4^6  +  SKis)^  +  2^60^/  -  8X15^15(^1  -  C)Kum,,d,  =  0 

(6)  2Kudc  +  2K6^G  +  (4Kii  +  4:K,  +  SKie)^//  +  ZK,,n,di  -  QK,,n,,d2  =  0 

(7)  K.miAdF  +  Ki5ni5^G  +  Ky.m^dH  -  {K,mx^  +  X^nu^  +  K,,n,^)d^  =  0 

(8)  Xg^A  +  i^io^5  +  Kiidc  +  K,dF  +  i^io^G  +  KiiOh  -  {K^n9  +  KwUio  +  Knnn)2d2  =  0 

For  a  horizontal  load  at  C,  equation  (7)  would  equal        equation  (8)  would  equal 

and  all  others  would  equal  zero. 

See  preceding  case  for  directions  for  analysis  with  symmetrical  loading  on  a  horizontal 
member. 

Case  a  {Fig.  45). — Solution  of  this  frame  is  accomplished  by  the  above  set  of  eight  general 
equations,  by  letting  K 6  =  ^ii  =  Kie  =  0. 

Be.  One-span  Viaduct  Frame  with  Rigidly-connected  Column  Tie  (Type  IV). — 

The  general  moment  equations  for  this  case  (Fig.  46)  are  as  follows: 


Mfn 

=  SEKiiidF 

—  niidi) 

Mba 

=  2EK,{2dB 

+  dA)  +  Yab 

Mfg 

=  2EK,{2eF 

+  Og) 

Mbg 

=  2EF,,{2dB 

+  60—  8n  10(^2) 

Mfa 

=  2EK,{2eF 

+  Oa  - 

8719(^2) 

Mgb 

=  2EKi,{2dG 

+  Ob  —  Sriiodi.) 

Maf 

=  2EK,(2dA 

+  Of  - 

8719(^2) 

Mgf 

=  2EK,{2dG 

+  Of) 

Mab 

=  2EKi{2dA 

+  Ob)  - 

Xab 

Mgo 

=  3EKi5{dG 

-  nidi) 

0 

Fig.  45. 


A 

B  C 

D  E 

2 

n 

6 

n 

Y\ 

7  / 

1  L 

Fig.  46. 


Fig. 


General  equations: 

(1)  (4X9  +  4X1)0^  +  2KieB  +  2K,dF  -  QK,n,d2  =  Xab/E 

(2)  2KidA  +  (4Xi  +  4Kic)05  +  2Kio^G  -  6KionW2  =  -Yba/E 

(3)  2K,dA  +  (3i^i4  +  4K5  +  4:K,)dF  +  2K,dG  -  ^Kimxdi  -  ^K,n,d2  =  0 

(4)  2KiodB  +  2K,dF  +  (4^5  +  4i^io  +  8X15)^0  -  ^Ki.mdi  -  QKion,od^  =  0 

(5)  KiiTiiidF  +  Ki^nudG  -  {Kunii^  +  Kunis-)^!  =  0 

(6)  K,dA  +  KioOb  +  KsdF  +  KiodG  -  (K,n,  +  Kionio)2d2  =  0 

For  a  horizontal  load  at  B  equation  (7)  would  equal  {Q/3E);  equation  (8)  would  equal 
i—Qhg/QE);  and  all  others  would  equal  zero. 

For  a  load  placed  symmetrically  on  AB,  replace  the  terms  Xab  and  Yab  by  F/l  in  above 
equations,  without  altering  the  present  signs.  Values  of  F/l  for  various  symmetrical  loads  are 
given  on  page  418. 

8/.  Four-span  Viaduct  Frame  (Type  V). — The  general  case  here  given  (Fig.  47) 
deals  with  a  frame  that  is  either  symmetrical  or  unsymmetrical.  A  load  on  a  single  span  will 
cause  a  sidewise  movement  of  the  deck.  The  vertical  component  of  this  movement  is  insig- 
nificant here,  and  will  be  neglected. 

The  following  moment  equations  and  general  conditional  equations  will  treat  of  a  vertical 
load  Fi  on  AB;  a  vertical  load  P2  on  BC]  and  a  horizontal  load  Q  at  E. 


634 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14-^ 


Map  =  SEK,(dA  -  n,d) 

Mab  =  2EK,{2dA  +  ds)  -  Xab 
Mb  A  =  2EKi{2dB  +  Oa)  +  Yba 
Msg  =  SEK.idB  -  n,d) 

Mbc  =  2EK2{2dB  +  ec)  -  Xbc 

McB  =  2EK2{2dc  +  Ob)  +  Ycb 
McH  =  SEK^idc  -  n-jd) 

General  equations  {E  is  constant)  for  loads  Pi  and  Q'. 

(1)  (3i^5  +  4.Ki)dA  +  2K,dB  -  SK.nd  =  Xxb/E 

(2)  2KrdA  +  (3^6  +  4Ki  +  4X2)^5  +  2K2dc  -  SK.nd  = 

(3)  2K2dB  +  (3^7  +  4^2  +  4K3)^c  +  2X3^  -  SK^n7d  = 

(4)  +  (37^8  +  4^3  +  4:Ki)dD  +  2X4^^  -  ^Ksnd  = 

(5)  2K4dD  +  (4^4  +  SK,)dE  -  3A%n9(Z  =  0 
K^UidA  +  K^nedB  +  i^yny^c  +  K^n^do  +  K^^n-^dE 


McD  =  2EKs{2dc  +  0d) 
ikfi>c  =  2EK^{2dD  +  M 
Mzj^  =  SEKsidD  -  nsd) 
Mde  =  2EK4{2dD  +  0^) 
M^D  =  2EK4{2dE  +  ^i)) 
ilf^^L  =  SEK^idE  -  ngd) 


(6) 

K,n,^)d  =  Q/3^; 

When  only  Pi  is  acting,  Q  =  0.  When  only  Q  acts,  Xab  Yab  =  0.  When  only  P2 
acts  on  BC,  =  Yba  =  0;  Q  =  0]  equation  (2)  equals  {Xbc/E)]  equation  (3)  equals 

( —  Yqb/E).    When  a  symmetrical  load  is  placed  on  a  member,  X  and  Y  for  that  member  are  re- 

F  F  .  . 

placed  by  y  of  the  load.    Values  of  j  for  various  symmetrical  loads  may  be  found  on  page  413. 


4  £0 


Fig.  48. 


Fig.  49. 


G  " 

Fig.  50. 


Fig.  51. 


Case  a  {Fig.  48). — A  special  case  arises  when  =  0,  or  joint  E  rests  on  rollers.  A  solution 
of  this  case  may  be  reached  by  making  Kg  =  0  in  the  general  equations  of  Type  V. 

Case  b  {Fig.  49). — This  case  is  very  common.  It  may  be  analyzed  by  placing  Ks  = 
Kg  =  0  in  the  general  equations  for  Type  V. 

8^.  Three-span  Viaduct  Frame  (Type  VI). — A  solution  of  this  frame  (Fig.  50) 
may  be  made  from  the  equations  given  on  page  633,  by  substituting  into  those  equations 
Ki  =  Kg  =  0.  It  will  be  noted  that  Be  drops  out,  and  in  accordance,  equation  (5)  disap- 
pears.   In  all  other  respects  the  solution  is  identical. 

Sh.  Two-span  Viaduct  Frame  (Type  VII). — General  equations  for  this  frame 
(Fig.  51)  may  be  set  up  by  placing  Kz  =  Ki  =  Ks  =  Kg  =  0  in  the  general  equations  for 
Type  V.    Hence,  for  the  loads  Pi  and  Q: 

(1)  (3^6  +  4:K,)dA  +  2KidB  -  SK.nd  =  Xab/E 

(2)  2KidA  +  (3^6  +  4Ki  +  4:K2)dB  +  2i^2^c  -  SK.nd  =  -Yba/E 

(3)  2K2dB  +  (3X7  +  4:K,)dc  -  SK^nyd  =  0 

(4)  K^n.dA  +  Ken.dB  +  K-.mdc  -  {K,n,^  +  K^n,^  +  K7m^)d  =  Q/SE 

In  these  equations,  when  Pi  acts  alone,  Q  =  0.    When  Q  acts  alone,  Pi  =  0.    When  a 

F 

load  is  placed  symmetrically  on  AB,  Xab  and  Yba  are  replaced  by  j  for  that  load  (see  page  413). 

Illustrative  Problem. — 'A  viaduct  frame  of  Type  VII  has  two  spans  of  17.0  ft.  each,  with  columns  of 
length  42.5  ft.,  34.0  ft.,  and  29.75  ft.  The  moments  of  inertia  are: /i  =  I2  =  80,000  in. /s  =  100,000  in.*;  Je  =  Ii 
=  10,000  in.*.  Determine  horizontal  reactions  at  F,  G,  and  H,  when  a  tractive  force  of  12,000  lb.  acts  along  the 
deck  (as  at  C).    From  these  data  the  following  table  of  constants  is  made  up: 


Sec.  U-Sh] 


SLAB  AND  GIRDER  BRIDGES 


635 


Member 

Length 
(in.) 

I  (in.4) 

T 

1 

3Kn 

3Kn2 

1 

204 

80,000 

392 . 50 

2 

204 

80,000 

392 . 50 

5 

510 

100,000 

196.20 

0.00196 

1.154 

0.002263 

6 

408 
357 

10,000 

24.50 

0.00245 

0.180 

0.004410 

7 

10,000 

28.05 

0.00281 

0.236 

0 . 000664 

From  this  table  of  constants  the  four  general  equations  were  reduced  to  the  following  equations,  in  which 
E  =  3,000,000  lb.  per  sq.-  in.  The  fourth  equation  has  been  multiplied  by  3,  which  permits  values  to  be  drawn 
directly  from  the  above  table.    All  equations  were  finally  divided  by  10. 


Left-hand  side  of  equations 

Right-hand 
side 

Equation  No. 

OA 

OB 

oc 

d 

Constant 
terms 

1 

2 
3 
4 

215.86 
78.50 

0. 1154 

78.50 
321.35 
78.50 
0.0180 

78.50 
165.42 
0.0236 

-0.1154 
-0.0180 
-0.0236 
-0.0003368 

0 
0 
0 

0 .0004 

1' 
2' 
4' 

1.0 
1.0 
1.0 

0.364 

4.08 

0.156 

1.0 

0.2045 

-0.000534 
-0.000229 
-0.00292 

0 
0 

0.00347 

2'  -  1'  =  5 
-  4'  =  6 

3.716 
3.924 

1.0 

0 . 7955 

0.000305 
0.002691 

0 

-0.00347 

5' 
6' 
3' 

1.0 
1  .0 
1.0 

0.2693 
0.2027 
2.106 

0.0000822 
0.000685 
-0.0003008 

0 

-0.000884 
0 

3'  -  5'  =  7 
-  6'  =  8 

1.8367 
1.9033 

-0.0003830 
-0.0009858 

0 

0 . 000884 

7' 
8' 

1.0 
1.0 

-0.0002085 
-0.0005170 

0 

0 . 000464 

8'  -  7'  =  9 

-0.0003085 

0.000464 

Solving  equation  (9)  gives  d  =  —  1.503  (inches  lateral  shifting). 

ec  =  -  0.0003135  (rotation  of  C  in  radians). 

Ob  =  +  0.0002078  (rotation  of  B  in  radians). 

Oa  =  -  0.000876  (rotation  of  A  in  radians). 

Map  ^  E  =  SKsdA  -  SKsn^d  =  -  (588.6)  (0.0008786)  +  (1.154)  (1.503)  =  1.223 
Mbg  -i-  E  =  SKedB  -  SKened  =  (73.5) (0.0002078)  +  (0.18) (1.503)  =  0.2863 
McH  ^  E  =  SKjdc  -  ZKimd  =  -  (84.15)  (0.0003135)  +  (9.236)  (1.503)  =  0.3286 

Map  =  3,669,000  in.-lb.  Hp  =    7,190  lb. 

Mbg  =     858,900  in.-lb.  Hg  =    2,110  1b. 

McH  =    985,000  in.-lb.  Hh  =   2,760  lb. 


Total  to  check  =  12,060  lb.  (error  0.5%) 


636 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14-8^ 


Case  a  (Fig.  52).— The  solution  may  be  made  by  using  the  general  equations  of  Type  VII, 
making  Kr  =  0. 

Case  b  (Fig.  53) —In  this  case  =  Kt  =  0.  Substituting  these  into  the  general  equations 
of  Type  VII,  the  solution  is  found  at  once. 

Bi.  One-span  Frame,  Unequal  Columns  (Type  VIII). — The  solution  for  this 
frame  (Fig.  54)  may  be  obtained  from  the  equations  of  Type  VII,  by  making  K2  =  Kt  =  0. 
This  will  eliminate  equation  (3),  and  modify  the  other  equations. 


B 


I  2  £2 

'  \ 

G 

Fig.  52. 


4  

£S  T 


E  00 


G 

Fig.  53. 


Fig.  54. 


8;.  Temperature  Stresses. — Stresses  caused  by  changes  in  temperature  may 
become  very  large,  and  require  thorough  irivestigation.  They  come  about  from  the  fact  that 
the  members  tend  to  change  length,  whence  each  causes  a  lateral  displacement  of  a  member  at 
right  angles  to  it. 

The  following  analysis  will  be  made  for  a  frame  of  Type  I,  in  which  the  lower  tier  of  columns 
increase  in  length  toward  the  left  (see  Fig.  55).  We  will  note  later  that  this  was  to  cause  all 
values  of  A  to  be  positive;  and  will  then  give  the  effect  upon  the  resulting  equations  when  A 

is  negative.  The  change  of  temperature  is  as- 
sumed in  the  development  to  be  positive. 
Later,  corrections  will  be  noted  for  cases  when 
the  change  is  negative. 

If  the  rise  in  temperature  is  then  for  a 
material  having  a  coefficient  of  expansion  of  C  t, 
the  increase  in  a  length  Z  is  +  Cttl.  Its  value 
is  negative  for  a  drop  in  temperature.  This 
increase  in  length  should  be  computed  and 
tabulated  for  each  member. 

Suppose  for  the  present  that  the  column 
LT  is  held  vertically  during  a  rise  in  tempera- 
ture. Then  the  horizontal  movement  of  any 
joint  to  the  left  of  L,  will  equal  the  elongation  occurring  between  L  and  that  joint.  LT  does 
not  really  remain  vertical,  however,  since  L  will  move  to  the  right  an  amount  dependent 
upon  the  elastic  rigidity  of  the  frame.  Hence  the  horizontal  movement  of  any  joint  to  the 
left  of  L,  will  be  equal  to  di  minus  the  elongation  occurring  between  L  and  that  joint.  The 
shifting  of  the  frame  causes  flexure  in  the  columns,  which  in  turn  develops  horizontal  reac- 
tions at  the  bases.  The  sum  of  these  horizontal  reactions  must  equal  zero. 
The  moment  equations  for  the  frame  are  as  follows: 


Maf 

2EK,{2eA 

+  dp  - 

Mde 

=  2EKi{2dD  +  Be  - 

3n4A8) 

Mab 

2EK,{2dA 

+  6b  - 

3niA5) 

Med 

=  2EK^{2Be  +  Bd  - 

3n4A8) 

Mba 

2EKi{2dB 

+  eA  - 

3niA5) 

Mel 

=  2EKu{2Be  +  Bl  - 

3^13C^2) 

Mbo 

2EKioi2dB 

+  60  +  ^niodi) 

Mle 

=  2EKiz{2Bl  +  Be  - 

37113^2) 

Mbc 

2EK2{2dB 

+  ec  - 

3n2A6) 

Mlj 

=  2EKs{20l  +  Bj  - 

3n8A8) 

McB 

2EK2{2dc 

+  dB  - 

3n2A6) 

Mlt 

=  SEKisiBL  -  nisdi) 

Mch 

2EKn(.2dc 

+  Bii  - 

-  3niid2) 

MjL 

=  2EKs{2Bj  +  Bl  - 

3n8A8) 

McD 

2EKz(2dc 

-\-dD  - 

3M3A7) 

MjD 

=  2EKu(2Bj  +  Bd  - 

-  3ni2(i2) 

Mdc 

2EK3{2dD 

^Bc  - 

Mjs 

=  SEKn[Bj  -  nxi{di 

-es)] 

Mdj 

2EKu{2eD  +  dj  - 

-  3^126^2) 

Mjii 

=  2EK^{2Bj  +  Bh  - 

-  3n7A7) 

Sec.  14-8i] 


SLAB  AND  GIRDER  BRIDGES 


637 


Mhj 

=  2EK^{2dH 

■\-ej  - 

Mgf  =  2EK,{2eG  +  dp  -  BnsAs) 

Mhc 

=  2EKn{2dH  +  dc  - 

-  3niic?2) 

MiPG  =  2EK,{2eF  +  dG  -  B^sAs) 

Mhr 

=  SEKieidn 

—  nu{di 

-  68  — 

67)] 

Mfa  =  2EK,{2dF  +  0a  -  Snad,) 

Mhg 

=  2EKe(2dH 

+  dG  - 

Mf,v  =  3£'i^i4[0f  —  nii{di  —  es  —  67  —  66  — 

Mgh 

=  2EKe{2dG 

-\-  Oh  - 

Mfmu 

14  +  MgoUx^  +  MhrUig  +  MjsUn  -\-MLTrii8  ■ 

Mgb 

=  2EKio{2dG 

+  eB  - 

■  3^10^2) 

Map  +  Mfa  +  Mbg  +  Mgb  +  Mch  +  M//c  + 

Mdj  +  Mjz)  +  Mel  +  Ml£ 

Mgo 

=  ^EKi,[dG  ■ 

—  68  - 

ei  -  66)] 

General  equations: 


(1)  (4i^i  +  4i^9)0A  +  2KxeB  +  2K,dF-  QK,n,d2  =  GZiniAg 

(2)  2Ki0A  +  (4Ki  +  4^2  +  4Zio)0B  +  2K2  dc+  2KiodG  -  QKi^nxod^  =  GXanaAe  +  GKiniAs 

(3)  2K2dB  +  (4^2  +  4^3  +  Kxi)ec  +  2X3^  +  2KiieH  -  6Knnud2  =  6K2n2A6  +  QK^n^Aj 

(4)  2K30C  +  (4^3  +  4K4  +  42^12)^0  +  2KidE  +  2Ki2dj  -  QKi^nizdz  =  QKm^^A^  +  GKsnaA? 

(5)  2X4^  +  (4^4  +  4.Kx^)dE  +  2KxzdL  -  QKun,zd2  =  6K4n4A8 

(6)  2KueE  +  (3i^i8  +  4^8  +  4:Kis)dL  +  2^8^/  -  SKi.nisdi  -  QKizUizd^  =  GXsWsAs 

(7)  2Ki20z)  +  (3Ki7  '+  4^7  +  4Ks  +  4Ki2)0j  +  2^70//  +  2K,dL  -  2>K,,nudi  - 

6Ki2ni2d2  =  QK^nrA^  +  Gi^s^^sAg  —  3Ki7ni768 

(8)  2Kndc  +  (3Zi6  +  4^6  +  4^7  +  4:Ku)dH  +  2K,dG  +  2K7dj  -  ZK^mxdi  - 

6KiiniiC?2  =  GKeneAe  +  6K7n7A7  —  BKieWieCe?  +  63) 

(9)  2i^io0fi  +  (3Ki5  +  4^5  +  4^6  +  4Xio)0G  +  2^5^^  +  2K,eH  -  SK,,ni,d,  - 

QKioniod2  =  GKsnsAs  +  GKeneAe  —  3X15^15(66  +  67  +  eg) 
(10;  2Kc>dA  +  (3J^i4  +  4^5  +  4:K,)dF  +  2X5^0  -  2>Ki^ni4i  -  QK,n^d2  =  6K5n5A5  - 

3i?i4ni4  (65  +  66  +  67  +  es) 

(11)  KiiniiOF  +  KuUi^dG  +  KiGTiiedH  +  KnUnOj  +  KisTIisOl  -  d{KuniA'^  +  i^is^is^  +  Ki6ni62 
+  Ki7ni72  +  Kisnis^)  =  -  [^68  2)14  -K^'  +  e7  Xn^  +  ee         Kn^  +  65(Ki4ni42)] 

(12)  QK^Oa  +  6Kio0B  +  QKudc  +  6i^i20z)  +  Gi^is^F  +  QK^dp  +  6i^io%  +  QKudn  + 

6i^i20j  +  6Ki30L  -  2d(K,n,  +  i^ionio  +  Kunn  +  ^12^12  +  Xis^u)  =  0 

The  left-hand  side  of  the  above  equations  is  identical  to  that  of  the  equations  in  Table 
I.  All  values  on  the  right-hand  side  are  known  as  soon  as  one  assumes  a  given  change  in  tem- 
perature and  computes  the  corresponding  changes  in  length.  They  may  be  put  into  a  separate 
column,  similar  to  Case  I,  Table  I,  for  instance.  Solution  of  this  column  may  be  made  after 
some  one  other  case  has  been  solved.  Thus,  in  the  problem  on  page  635,  if  a  column  for  tempera- 
ture change  is  added  to  the  right-hand  side,  its  solution  could  be  made  by  following  the  pro- 
cedure noted  in  the  column  headed    Equation  No."  at  the  extreme  left  of  the  table. 

In  the  foregoing  equations,  it  was  assumed  that  all  values  of  A  were  positive.  For  instance, 
before  the  rise  in  temperature,  F  and  G  were  on  the  same  level.  After  the  temperature  change 
the  final  position  of  G  is  helow  the  final  position  F  by  an  amount  equal  to  +  A5,  since  to  attain 
this  sloped  position  the  member  FG  would  have  to  rotate  in  a  positive  direction  about  either  F 
or  G.  Suppose,  however,  that  GO  for  a  given  case  is  longer  than  FN.  Then  the  final  position 
of  G  would  be  above  the  final  position  of  F  by  an  amount  equal  to  —  A5.  Hence,  for  such  a 
case,  all  terms  involving  A5  in  equations  (1)  to  (11),  above,  would  become  negative.  The 
following  rule  may  therefore  be  stated:  Beginning  at  the  left  end  of  the  frame  after  distortion 
from  temperature  change  has  taken  place,  if  a  normally  horizontal  member  slopes  downward 
to  the  right,  A  for  that  member  is  positive,  and  its  value  is  equal  to  the  vertical  displacement 
of  its  right  end.  If  the  member  slopes  upward  to  the  right,  A  for  that  member  is  negative, 
and  its  value  is  equal  to  the  vertical  displacement  of  its  right  end.  This  relation  between 
the  final  positions  of  points  holds  for  either  a  rise  or  fall  of  temperature.  If  all  columns  of  the 
structure  have  the  same  length,  then  all  values  of  A  are  zero. 

The  value  of  e  in  the  foregoing  equations  would  become  negative  for  a  fall  of  temperature. 


638 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14-8/c 


8k.  Effect  of  Fixed  Bases. — Certain  modifications  made  in  the  foregoing  equa- 
tions will  permit  them  to  be  used  for  the  analysis  of  frames  of  the  type  which  they  affect,  but 
with  fixed,  instead  of  hinged  bases.  Take,  for  instance,  a  portion  of  the  frame  of  Type  I 
(see  page  629).    There  is  no  rotation  at      (Fig.  56)  when  N  is  perfectly  fixed,  hence 

Mfn  =  2EKi4  (2dF  -  3ni4i) 

This  would  replace  that  for  Mfn  given  on  page  629.  Equations  precisely  similar,  except  for 
subscripts,  may  be  written  for  the  moment  in  the  top  of  all  other  lower  columns  of  the  frame. 

These  values  of  moment  would  replace  corresponding  ones  in  the  equations  on 
pages  629  and  630.  Having  made  these  changes  in  the  moment  equations,  the 
general  conditional  equations  will  be  affected  thereby,  and  must  be  revised  ac- 
cordingly. 

After  the  conditional  equations  have  been  solved,  the  moments  at  the  ends  of 
■  each  member  may  then  be  found.    The  moment  at  the  base  of  the  fixed  column 

N  FN  above,  is 

Fig.  56.  Mnf  =  2EKu{dA  -  ^riidi) 

=  y2{MFN  +  QEKunudr) 

Having  found  the  moment  at  the  ends  of  each  column,  the  point  of  inflection  may  readily 
be  obtained;  and,  supposing  a  hinge  to  be  introduced  at  the  point  of  inflection,  the  horizontal 
reaction  at  this  ''hinge" — or  shear  on  the  column — may  be  found  as  for  a  frame  with  hinged 
bases.    The  vertical  reactions  may  likewise  be  found  as  for  hinged  bases. 

The  same  modification  to  take  into  account  fixity  of  the  base  of  supporting  columns  may 
be  applied  to  any  other  of  the  foregoing  types  of  viaduct  frame. 

Bl.  Viaduct  Bent. — The  cross-frame  or  bent,  provides  the  lateral  stiffness  for 
the  viaduct  structure,  in  addition  to  being  the  supporting  unit.  It  should  be  designed  to  with- 
stand: (1)  the  dead  load  of  the  entire  structure;  (2)  the  direct  and  flexural  stresses  set  up  in 
the  "columns"  of  the  viaduct  frame,  due  to  live  load,  as  determined  in  the  foregoing  discussion; 
(3)  lateral  forces  of  wind,  and  centrifugal  forces  on  curves;  (4)  lateral  expansion;  (5)  moments 
due  to  loads  on  floor  girder;  (6)  moments  due  to  overhanging  floor  beams  carrying  walks,  etc. 

For  bents  having  a  batter  steeper  than  1  to  6,  the  procedure  of  analysis  for  the  first  five 
cases  of  loading  given  above  is  identical  with  that  for  the  viaduct  frame  of  similar  dimensions. 
Frames  with  excessive  batter,  however,  require  consideration  of  the  vertical  component  of 
lateral  displacement  due  to  lateral  forces  or  to  underbalanced  loads  (see  assumptions,  page 
628).  The  relation  is,  of  course,  purely  trigonometrical,  so  that  the 
method  of  attack  is  as  already  outlined,  save  for  the  adding  of  this 
component  of  lateral  movement  to  the  lateral  displacement  of  the  ends 
of  horizontal  members. 

When  the  bent  is  symmetrical  and  carries  lateral  loads  at  the 
joints,  there  is  a  point  of  inflection  of  moment  in  each  horizontal  mem- 
ber at  the  point  where  it  is  intersected  by  the  axis  of  symmetry.  For 
the  analysis  of  such  a  frame  see  "Modern  Framed  Structures"  by 
Johnson,  Bryan  and  Turneaure,  Part  II,  Arts.  283-4. 

The  sixth  case  of  loading — that  of  a  known  moment  applied  at  a  joint  may  be  treated  by 
a  slight  modification  to  the  foregoing  equations.  Fig.  57  shows  a  bent  or  cross-frame  of  Type 
III,  of  viaduct  frames,  with  a  cantilever  at  A  applying  a  known  moment  M'.  Referring  now 
to  page  632,  the  equations  there  given  for  Mab  and  Maf  are  equally  true  for  this  case.  It  will 
be  noted,  however,  in  forming  equation  (1)  on  page  633,  where  no  load  is  acting  on  AB,  that  the 
sum  of  the  moments  in  the  A-ends  of  members  meeting  at  A  is  zero.  In  this  case  where  M'  is 
acting,  equation  (1)  would  now  equal  M',  since  the  moments  in  the  members  must  offset  the 
external  moment  at  any  joint.  M'  as  shown  in  the  figure  is  negative  on  the  right-hand  side  of 
the  equation,  since  the  moment  required  to  resist  it  is  clockwise. 


/ 

2 

9 

10 

F  5 

G  6 

14 

i 

IS 

A 

N 

0 

Fig. 

57. 

Sec.  14-9] 


SLAB  AND  GIRDER  BRIDGES 


639 


CANTILEVER  BRIDGES 


A  type  of  bridge  which  in  appearance  is  a  concrete  arch,  but  which  in  reaHty  is  composed 
of  balanced  cantilevers,  is  shown  in  Figs.  58  to  61  inclusive.  A  structure  cf  this  type  can  be 
made  with  longer  spans  than  the  ordinary  girder  and  is  suited  to  locations  where  the  real  arch 
would  be  exceedingly  costly  on  account  of  unsatisfactory  foundation  conditions. 

9.  Theory  of  Design. — A  pier  and  the  cantilever  arms  on  each  side  compose  a  unit,  the 
arms  being  balanced  for  dead  load  and  for  full  live  load.    The  piers  are  designed  for  bending 


F/n/shed  sc/rface 

of  Roadway  ,  "'^ 


Typical  Elevation  of 
Inside  35ft.  Cantilever  Beam 


Short  strc!i^t7t  bars  in 
top  and  bottom  at Jo/nt,  ;s'^c  toe 
->![<■•       ,//        /^/ternate  bars  bent. 


Section 

Fig.  58. — Details  of  Hopple  Street  viaduct,  Cincinnati,  Ohio. 

due  to  the  maximum  eccentric  load  that  can  be  applied,  and  considering  the  load  on  only  one 
of  the  cantilever  arms  at  a  time.  The  pier  footings  are  designed  so  that  the  pressure  on  the 
base  of  a  pier  due  to  this  same  eccentric  loading  will  not  cause  an  intensity  greater  than  the 
unit  bearing  value  of  the  soil. 

10.  Examples  of  Cantilever  Bridges. — The  viaduct  shown  in  Fig.  58  consists  of  twenty- 
five  skewed  spans,  each  span  comprising  two  curved  cantilever  arms  supported  on  reinforced- 


Cxpansion  Joint 


Detail  of  Expansion  Joint 


I  Line  of 
V-  Bridge 


Fig.  59. 


-Half-elevation  and  detail  of  expansion  joint  of  arch-shaped  cantilever  bridge  over  Rouge  River,  Wayne 

County.  Mich. 


concrete  piers.  A  single  cantilever  arm  occurs  at  each  end  of  the  viaduct.  Each  cantilever 
arm  comprises  four  curved  ribs  which  were  designed  as  cantilevers  from  the  skewed  piers. 
The  joint  at  the  center  of  each  span  is  shown  in  detail.  In  designing,  this  joint  was  considered 
as  transmitting  only  shear  from  one  cantilever  arm  to  another  and  not  any  bending  or  arch 
action.  Since  each  pier  and  its  cantilever  arms  are  symmetrical  about  the  center  line  of  the 
pier,  no  bending  exists  in  the  pier  due  to  dead  load  or  to  full  live  load  on  both  cantilevers. 
Piers,  footings,  and  piling  were  designed  to  withstand  the  overturning  effect  produced  by  the 
loading  of  a  single  cantilever  with  the  full  live  load. 

The  expansion  joint  at  the  center  of  the  structure,  shown  in  Fig.  59  is  entirely  different 
from  that  employed  in  the  bridge  just  described.    It  should  be  noted,  however,  that  the  same 


640 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  14- 


U  //'■o^''  ••••>1 

Section  B-B 


Section  A-A 


-^1    A  k£4"->^^S^. 
->^^j"°Bars  e"c.toC 
both  vrays 

SJ"  6'o"c.foc. 


One  Layer 
Tar  Paper 

£'-o"c.t>c. 


-/"''rl.  Bars- Bent  at i  po/nt  ^-f'Tir.ffa/^ 


J-0' 


.AM 


Cross  Section  D-D  Post 

Fig.  60, — Details  of  Runnymede  Avenue  bridge  over  West  Fork  Creisk,  Cincinnati,  Ohio. 


Sec.  14-10] 


SLAB  AND  GIRDER  BRIDGES 


641 


result  is  accomplished — that  is,  that  the  two  abutting  arms  are  permitted  to  move  longitudin- 
ally, but  not  laterally  or  vertically.  The  joint  consists  of  two  3-ft.  piers  of  2^-in.  steel  shafting 
each  inserted  in  two  13-^-ft.  pieces  of  3-in.  gas  pipe  embedded  in  the  concrete.  End  joints 
were  made  by  placing  sheets  of  three-ply  tar  paper  on  top  of  the  abutments  before  the  end  can- 
tilevers were  poured,  thus  permitting  a  slight  movement  of  the  ends  of  the  structure  under 
changes  of  load  and  temperature.  There  was  no  apparent  deflection  at  any  of  the  expansion 
joints  due  to  live  load. 

The  joints  at  the  ends  of  the  bridge  shown  in  Fig.  60  are  of  the  same  type  as  employed  in 
the  viaduct  spans  of  Fig.  58.  The  absence  of  such  a  joint  at  the  center  of  the  middle  span  is, 
however,  the  principal  feature.  In  spite  of  this  continuity  between  piers,  no  account  was 
taken  of  continuous  action  upon  supports  and  the  bridge  was  designed  in  the  same  manner  as 
the  cantilever  viaduct  previously  referred  to.  In  fact,  it  has  been  found  that  a  joint  at  the 
center  of  span  is  an  unnecessary  refinement  in  cantilever-bridge  design,  and  might  be  omitted. 


Perspective  View 


Field  Splices 


Field  Splices 


Fig.  G1.- 


Th/s  crossbeam 

occurs  at  the  ^^^^^  ^^.^^^ 

Quarter  and  Half  Points  ^ 

Half  Section  at  Quarter  and  Half  Points  of  Span 
-Details  of  Washington  Street  bridge,  Norwalk,  Conn. 


The  bridge  was  designed  and  constructed  so  as  not  to  rest  on  the  abutments  at  all,  the  abut- 
ments being  used  merely  to  hold  back  the  earthfill  at  each  end  and  to  serve  as  anchorage  for  the 
end  cantilevers.  A  structure  of  this  type  with  end  openings  closed  by  earthfill  has  all  the  ap- 
pearances of  a  real  arch.    In  such  a  case  abutments  are  not  needed. 

If  a  number  of  bridges  similar  to  the  bridge  of  Fig.  60  were  placed  end  to  end,  the  result 
would  be  essentially  a  structure  such  as  shown  in  Fig.  61.  It  should  be  noted  that  the  Nor- 
walk bridge  is  continuous  in  sections  of  maximum  length  of  100  ft.  The  structural-steel  work 
was  designed  to  be  self-supporting  during  erection  and  to  carry  the  erection  stresses  of  the 
forms  and  the  fluid  concrete  in  the  ribs,  cross-girders,  and  sidewalk  brackets.  Although  a 
deflection  of  3^  in.  at  the  free  ends  of  the  cantilevers  was  anticipated,  a  deflection  of  only 
to  ^8  in.  actually  resulted  due  principally  to  the  rigidity  of  the  forms  and  to  the  fact  that  the 
concrete  was  continuously  setting  during  the  process  of  placing.  The  combined  steel  and 
concrete  in  the  ribs  was  proportioned  to  carry  the  roadway  slab,  paving,  and  all  live  loads. 
The  trusses  were  proportioned  to  carry  all  shear  not  safely  taken  by  the  concrete  but  were  not 
proportioned  to  carry  all  the  tension  developed  by  the  bending  moment  since  extra  horizontal 
rods  were  embedded  in  the  concrete  adjacent  to  the  top  chords  of  the  trasses, 
41 


SECTION  15 


CONCRETE  FLOORS  AND  ABUTMENTS  FOR  STEEL  BRIDGES^ 

1.  Concrete  Floors  on  Steel  Bridges. — Within  recent  years  it  has  become  the  general 
opinion  among  railroad  engineers  that  a  ballasted  solid  floor  is  the  most  satisfactory  form  of 
floor  for  steel  bridges.  Perhaps  the  best  type  of  such  a  floor  is  the  reinforced-concrete  slab 
resting  directly  on  the  steel-floor  members. 

Figs.  1  and  2  show  details  of  reinforced-concrete  deck  slabs  for  plate-girder  spans.  The 
slab  floors  are  seen  to  rest  directly  upon  the  top  flange  of  the  steel  girders.  Comparison  of  the 
two  designs  is  of  value  since  they  show  a  wide  difference  in  the  concrete  details  and  in  the  ar- 
rangement of  the  reinforcement.  The  slabs  are  usually  made  at  some  convenient  location  and 
hoisted  into  place  when  suflficiently  cured.  Before  adding  the  ballast,  the  upper  surface  of  the 
slabs  is  thoroughly  waterproofed  by  painting  with  tar  paint.  Drain  holes  are  placed  in  such 
a  position  as  to  keep  the  drip  clear  of  the  steel  members. 


Fig.  1. — Reinforced-concrete  deck  for  steel-girder  spans  on  D.  M.  &  N.  Ry. 


A  reinforced-concrete  floor  for  a  through  plate-girder  bridge  is  shown  in  Fig.  3.  The  con- 
crete of  the  floor  slab  is  seen  to  extend  up  on  the  sides  to  form  curbs,  and  these  curbs  extend 
entirely  around  the  gusset  plates.  Steel  trough  floors  filled  with  concrete  are  also  used  in 
through  plate-girder  bridges. 

Steel  I-beams  encased  in  concrete  and  supporting  a  reinforced-concrete  floor  slab  is  the 
most  common  type  of  highway  bridge  with  steel-floor  members.  On  account  of  the  ease  with 
which  forms  may  be  constructed  to  hold  the  concrete,  this  bridge  for  short  spans  is  sometimes 

*  For  treatment  of  concrete  piers  for  steel  bridges  see  "Foundations  of  Bridges  and  Buildings,"  by  Jacoby 
and  Davis,  or  "Structural  Engineers'  Handbook,"  by  Ketchum. 

643 


644 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  15-1 


Half  Section  Single  Track  Slab  Half  Section  •  inside  Slab 


End  View 


Fig.  2. — Standard  reinforced-concrete  slab  for  deck  girders  of  C.  M.  &  St.  P.  Ry. 


j" Pods,  iz'c  foe 


::T^f^yj:T4:ir-r4:t:^h ' 

.1-4-1-  \-\-\-..-  Z' Drain  Ho/es ■■.   4-  j- 


Sectional  Plan 


-  /4-8"  

Section  A-A 


Sheet  Zinc 


Part  Longitudinal 
Section  of  Floor 


Fig.  3. — Reinforced-concrete  floor  for  through  plate-girder  bridge,  C.  B.  &  Q.  R.  R. 


'^"°Bar  over  each  floor  beam 
j  "°  Bars  •  3  per  panel 

/  i"''Bars,9''civc.- 


^^^"°Bars.9"cioc 


8-9' 


_     ,  Lonqitudinal  Section  of  Floor 

18  Roadway  •  ^ 


■  Weephole  yyith 
perforated  cover 


'■55*1 


19'- O"—  

Section 

Fig.  4, — Concrete  slab  floor  for  highway  steel  truss  span,  Iowa  Highway  Commission, 


Sec.  16-2] 


CONCRETE  FLOORS  AND  ABUTMENTS 


645 


used  in  preference  to  slab  bridges  of  all  concrete.  The  only  disadvantage  of  this  bridge  is  in 
point  of  economy. 

Timber  floors  for  highway  bridges  are  not  in  great  favor  at  the  present  time.  Since  the 
expense  of  maintaining  wood  floors  is  considerable,  the  engineers  of  a  number  of  highway  com- 
missions design  practically  all-steel  bridges  with  concrete  floors  covered  by  a  wearing  surface 
of  gravel  or  macadam.    For  exceedingly  light  traffic  on  country  bridges,  driving  is  sometimes 

allowed  directly  on  top  of  the  floor  slab,  mak- 
ing an  allowance  of  at  least  1  in.  in  the  thick- 
ness of  the  slab  for  wear  and  cutting  trans- 
verse grooves  to  prevent  slipping.  Figs.  4 
and  5  show  typical  designs  of  reinforced- 
concrete  floors  for  steel-truss  spans. 

2.  Abutments  for  Steel  Bridges. — An 
abutment  in  its  simplest  form  is  a  retaining 
wall  terminating  the  approach  embankment 
to  a  bridge,  and  provided  with  a  bridge  seat 
for  the  end  of  the  first  span  to  bear  upon. 
The  discussion  here  given  is  limited  to  those 


Fig.  5. 


fVeep  fro/e  yy/th  perforafecf  cover 


,-3  nif 


-Concrete  slab  floor  for  highway  steel-truss  span, 
Iowa  Highway  Commission. 


abutments  of  plain  or  reinforced  concrete  which  receive  a  vertical  downward  bearing  from 
the  bridge.    Abutments  for  arches  are  treated  in  Arts.  4  and  39,  Sect.  16. 

3.  Types  of  Abutments. — Bridge  abutments  of  concrete  may  be  classified  according  to 
general  form  as  follows: 


1.  Pier  abutments. 

2.  Wing  abutments. 

3.  Cellular  abutments. 

4.  U-abutments. 


5.  T-abutments. 

6.  Buried  pier  abutments. 

7.  Skeleton  and  arched  abutments. 


Base  of  rail 


The  design  and  advantages  of  each  form  will  be  discussed  separately. 

4.  Pier  Abutments  of  Plain  Concrete.— This  is  the  simplest  form  of  abutment  (Fig.  6). 
Since  many  of  the  other  forms  are  elaborations  of  this  one,  its  stability  will  be  studied  in  detail. 

The  thrust  P  of  the  earth  against  the  back  is  found  from  the  method  of  equivalent  surcharge 
h!^  as  described  on  page  581.  The  force  F 
is  due  to  frost  expansion,  and  depends 
upon  the  depth  to  which  the  ground  or 
ballast  may  freeze.  It  can  at  best  only  be 
estimated,  on  the  basis  of  ice  pressures. 

The  vertical  load  of  the  trusses  or 
girders  with  their  live  load,  cause  two 
forces  B  bearing  on  the  bridge  seat.  The 
dimensions  s,  c?,  and  n  depend  upon  the 
structure  supported.    The  intensity  of  B 
depends  upon  the  span  and  loading,  and 
is  taken  from  the  design  of  the  super-  L 
structure.    The  force  T  may  either  be  ^ 
caused  by  the  tractive  effort  of  the  train 
on  the  bridge;  by  braking  of  the  train; 
or  by  temperature  changes  not  wholly 
adjusted  by  poorly  operating  expansion  joints 
design  of  the  superstructure. 

The  best  form  of  abutment  is  that  which  puts  the  resultant  pressure  very  close  to  the  center 
of  the  base.  This  requirement  is  particularly  desirable  in  yielding  soil,  since  the  vibratory 
loads  will  nearly  always  cause  settlement.    Many  abutments  have  tipped  forward  notice- 


FiG.  6. — Plain  concrete-pier  abutment. 


All  of  these  forces  are  determined  from  the 


646 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  15-5 


ably  because  the  pressure  caused  a  non-uniform  pressure  on  the  soil,  and  hence  a  non-uniform 
settlement. 

The  back  wall  should  have  a  thickness  a  at  its  top  of  at  least  12  in.,  and  more  for  railway 
bridges.  Owing  to  the  uncertainty  of  actual  freezing  forces,  the  thickness  c  at  the  bottom  of 
the  back  wall  may  be  taken  as  0.4/  to  0.45/,  the  larger  value  for  railway  structures.  These 
thicknesses  have  given  good  results  in  practice  for  back  walls  not  reinforced. 

The  length  of  the  back  wall  should  be  such  that  when  material  spills  around  its  ends  at  a 
slope  of  1}^'2  to  1,  it  should  not  strike  the  pedestal  of  the  bearing  shoe.  The  batter  of  the  back 
face  of  the  back  wall  should  be  about  2  in  12.  The  height  /  is  of  course  set  by  the  superstruc- 
ture. The  length  w  of  the  bridge  seat  is  governed  by  the  overall  dimensions  of  the  structure 
being  supported.  J.  E.  Grenier^  specifies  a  minimum  thickness  of  the  coping  as  18  in.  for 
railway,  and  12  in.  for  other  bridges.  He  also  specifies  the  distance  d  to  be  "at  least  12  in. 
greater  than  required  for  the  bedplates  of  steel  superstructures." 

It  is  a  general  rule  that,  below  the  coping,  the  plain  concrete  abutment  shall  have  a  thick- 
ness at  any  point  of  from  0.4  to  0.5  of  the  depth  of  the  point  below  the  base  of  rail.  The  thick- 
ness m  should  be  such  that  the  compressive  unit  stress  at  the  forward  edge  is  within  that  allowed 
for  plain  concrete.  This  stress  is  determined  precisely  as  though  the  wall  rested  on  the  soil 
at  that  plane. 

The  base  slab  should  have  a  forward  projection  o  sufficient  to  keep  the  forward  soil  pressure 
within  the  allowable  range.  The  thickness  of  such  a  projection  will  determine  the  thickness  t 
of  the  slab.  It  is  found  the  same  as  that  for  the  toe  of  a  reinforced  retaining  wall.  The  whole 
slab  should  preferably  be  reinforced. 

The  body  of  the  wall  should  be  well  bonded  by  dowel  rods  to  the  base  slab,  so  that  it  can 
neither  rock  nor  slide  upon  it. 

5.  Pier  Abutments  of  Reinforced  Concrete. — Pier  abutments  of  reinforced  concrete  are 
divided  into  two  general  groups:  (1)  buttressed,  and  (2)  counterforted.    Fig.  7a  shows  the 

general  form  of  a  buttressed  abutment.  The  back  wall  is  designed 
as  a  cantilever  wall,  while  below  the  bridge  seat,  the  back  slab  is 
designed  as  a  continuous  slab  spanning  horizontally  the  space 
between  buttresses.  The  back  slab  must  be  well  anchored  to  the 
base  slab  to  prevent  rocking  forward  on  the  base;  and  ample  steel 
should  be  pr9vided  at  the  junction  of  the  upper  portion  of  the 
wall  with  the  base  slab  to  prevent  failure  in  shear  (sliding)  on  the 
plane  of  the  top  face  of  the  base  slab.  Reinforcing  in  the  body  of 
the  buttress  is  very  light,  and  is  necessary  only  to  prevent  cracks. 

Fig.  7b  shows  a  counterforted  pier  abutment.    The  back 
wall,  as  before,  is  designed  as  a  cantilever  wall.    The  whole 
structure  below  the  bridge  seat  is  designed  as  a  counterfort  retain- 
ing wall,  and  the  discussion  of  the  design  of  that  wall  will  apply  directly  here. 

It  is  of  course  the  best  arrangement  to  place  the  counterfort  or  buttress  immediately 
beneath  the  bridge  seat,  and  at  such  other  points  as  is  necessary  to  provide  against  the  thrust 
of  the  earth. 

6.  Wing  Abutments. — If  wing  walls  are  extended  out  beyond  the  ends  of  the  bridge  seat 
of  a  pier  abutment,  the  structure  is  called  a  wing  abutment.  The  wings  may  either  be  on  a 
line  with  the  face  of  the  abutment,  or  deflected  backward  from  the  face  (Fig.  8).  The  straight 
wing  is  used  where  dry  crossings  are  made,  as  for  instance,  street  or  railroad  crossings.  They 
usually  extend  to  the  foot  of  the  supported  embankment,  and  are  caped  about  2  ft.  above  the 
surface  of  the  slope.  When  the  toe  of  the  slope  at  the  end  of  the  wing  wall  requires  protection 
from  stream  flow,  deflected  wings  are  usually  built.  They  are  usually  put  at  30  deg.  with  the 
face  wall. 

The  wing  walls  are  designed  for  earth  thrust,  as  in  a  retaining  wall. 


Fig. 


7. — Reinforced-concrete 
pier  abutments. 


The  best  design  is 


1  Gbenier's,  "General  Specifications  for  Bridges." 


Sec  16-7] 


CONCRETE  FLOORS  AND  ABUTMENTS 


647 


one  which  gives  the  same  intensity  of  pressure  over  the  base  as  is  developed  under  the  body  of 
the  abutment;  and  it  is  particularly  desirable  that  the  resultant  pressure  on  the  base  of  the  wing 
wall  cuts  at  relatively  the  same  point  as  that  of  the  body  of  the  wall.  Expansion  joints  are 
often  placed  at  the  junction  of  the  wing  with  the  body.  Such  joints  should  be  lock-joints  so 
that  uneven  tipping  or  settling  will  not  cause  unsightly  offsets  to  develop  between  the  wings 
and  the  body.  Where  no  joints  are  provided,  especial  attention  should  be  paid  to  the  similarity 
of  pressure  on  the  entire  foundation,  as  noted  above. 

Because  of  the  desire  not  to  obstruct  stream  flow,  reinforced-concrete  wing  abutments  are 
usually  of  the  counterfort  type  rather  than  the  buttress  type.  Such  a  wall  is  shown  in  Fig.  9. 
The  body  of  the  wall  is  designed  like  the  same  form  of  pier  abutment.  The  counterforts  of 
the  wing  walls  may  either  be  parallel  to  the  track,  or  normal  to  the  wings. 


Fig.  8. — Plain  concrete  wing  abutment. 


7.  Cellular  Abutments. — The  cellular  abutment,  like  the  cellular  retaining  wall,  consists 
of  a  box-shaped  pocket  buried  in  the  fill,  to  increase  stability  against  overturning.  A  modified 
form  consists  of  a  pier  abutment,  with  wings  running  normal  to  the  face  of  the  abutment,  and 
a  tie  wall  across  the  outstanding  ends  of  these  wings.  Such  an  abutment  is  more  costly  than 
the  pier  form,  and  has  not  been  in  common  use. 

8.  U-abutments. — A  very  common  form  of  abutment,  called  the  U-abutment  because  of 
its  shape,  is  shown  in  Fig.  10.  It  consists  of  the  face  wall  with  bridge  seat,  and  two  wings  at 
right  angles  to  the  face  wall.  The  pocket  thus  formed  has  a  floor  formed  by  the  footing  slab. 
Such  a  type  of  abutment  is  very  useful  at  the  end  of  a  moderately  high  fill  which  has  a  long 
slope  in  the  direction  of  the  track.  This  form  of  abutment  is  usually  of  plain  concrete  and  is 
cast  in  one  piece.    Its  total  length  is  generally  about  13-^  times  its  height. 

The  constituent  parts  of  the  U-abutment  are  designed  like  a  pier  abutment  or  retaining 
walls.  The  outside  faces  are  either  vertical  or  slightly  battered.  The  inside  faces  are  either 
heavily  battered  or  stepped,  the  latter  being  the  more  common.  The  fill  is  allowed  to  slope 
from  the  top  of  the  outer  ends  of  the  wing  walls  in  all  directions  away  from  the  track  at  about 
IK  to  1.  The  inner  faces  should  be  battered  2  in  12  for  the  upper  3  ft.,  to  provide  for  frost 
expansion.    The  whole  abutment  should  be  thoroughly  drained. 

9.  T-abutments. — This  form  of  abiitment  is  shown  in  Fig.  11.  It  is  of  practically  the 
same  cost  as  the  U-abutment.  The  front  face  and  stem  are  usually  of  plain  concrete  and  the 
floor  over  the  stem  of  reinforced  concrete.    The  wall  is  secure  against  tipping  forward. 


648 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  15-10 


10.  Buried-pier  Abutments. — Usually  when  extremely  high  abutments  are  required,  or 
when  the  abutment  extends  to  considerable  depth  for  suitable  foundation,  the  earth  slope  may 
be  allowed  to  spill  freely  around  the  abutment.  For  this  purpose  a  tall  pier  may  be  used,  with 
short  wing  walls  to  protect  the  bridge  seat  from  the  earth  slope.  An  abutment  of  this  type  is 
called  a  buried-pier  abutment.    It  should  be  designed  for  the  vertical  reaction  of  the  span, 


40-7'  -  -  »l<  - -   40-7"- 

Elevation 


Section  L-Z 
near  4  of  track 

Fig.  9. — Reinforced-concrete  counterfort  wing  abutment. 

and  the  lateral  earth  and  traction  forces.  It  is  especially  desirable  that  the  resultant  pressure 
on  the  base  should  pass  through  its  center,  particularly  when  the  subsoil  is  yielding.  The 
economy  of  this  abutment  makes  it  more  desirable  than  the  wing  abutment  for  high  embank- 
ments. 

11.  Skeleton  and  Arched  Abutments. — A  large  number  of  special  forms  of  abutments 
have  been  developed  recently,  the  most  notable  from  an  economic  standpoint  being  the  skeleton 


Sec.  15-12] 


CONCRETE  FLOORS  AND  ABUTMENTS 


649 


and  arched  abutments.  The  skeleton  abutment  consists  of  a  very  heavy  viaduct  frame  of  two 
or  more  spans,  upon  the  outer  end  of  which  is  placed  the  bridge  seat.  The  arched  abutment 
differs  only  in  that  it  is  a  series  of  small  arches  on  high  walls.  The  proper  length  of  these 
abutments  is  governed  by  the  cost  per  additional  foot  of  abutment  and  of  superstructure. 

The  analysis  of  the  skeleton  abutment  does  not  differ  from  that  of  a  viaduct  frame  (see 
Art.  8,  Sect.  14).  The  arched  abutment  may  be  analyzed  as  a  system  of  arches;  or  more  easily 
by  an  approximate  solution  of  a  rigid  viaduct  frame  of  similar  proportions,  having  girders  of  a 
section  equal  to  that  at  the  crown  of  the  arches.  This  is  of  course  approximate;  but  limiting 
conditions  may  be  assumed,  remembering  that  if  the  girder  section  is  assumed  too  small  the 


■43-6" 

Side  Elevation 


j<-.7£5T-I_7<.6'!.j 


Half  |<-y(7-5'-->l 

,,_if-n  1  r-r7^»       Section  |  Half 

'-^'^■:^..eL3fl^.^a'-3k''\^^-  ■  A-A    front  Elevation 

Plan 

Fig.  10. — U-abutment. 


■40-0" 


■5-^-^ 


Side  Elevation 


K  le-o"  >j 

Gas  pipe  dram-^ 


End  ml! 


B 


Cross  section 
/\-B 


Fig.  11, — T-abutment. 


stresses  in  the  columns  or  bents  will  be  too  large,  and  vice  versa.  The  deck  girders  may  be  ana- 
lyzed as  though  continuous,  and  then  their  under  sides  arched,  for  rigidity  and  for  appearance. 
Two  very  important  considerations  should  be  borne  in  mind,  namely,  tractive  or  braking 
forces,  and  temperature  variation. 

12.  Care  in  Constructing  Abutments. — In  abutments,  as  in  retaining  walls,  special  care 
should  be  taken  to  obtain  a  structure  that  is  impervious  to  water.  Fills  and  embankments 
accumulate  water,  which  will  seek  outlet  through  the  abutment.  Unless  the  wall  is  of  proper 
density  throughout,  without  reliance  on  a  smooth  face,  disintegration  along  percolating  planes 
and  later  partial  or  total  destruction  is  sure  to  take  place. 

For  valuable  material  on  the  economic  selection  and  design  of  abutments  see  J.  H.  Prior, 
Proc.  A.  R.  E.  A.,  vol.  13  (1912),  page  1085. 


SECTION  16 


ARCHES 
GENERAL  DATA 

1.  Definitions. — The  following  are  some  of  the  common  technical  terms  applied  to  the 
various  parts  of  an  arch  (see  Figs.  lA  and  IB). 

Soffit. — The  under  or  concave  surface  of  an  arch. 
Back. — The  upper  or  convex  surface  of  an  arch. 

Skewback. — The  surface  upon  which  the  end  of  the  arch  rests.  This  definition  applies  particularly  to  the 
stone  or  brick  arch  since  the  surface  mentioned  is  purely  imaginary  in  the  case  of  the  concrete  arch.  The  term, 
however,  is  useful  in  concrete-arch  analysis. 

Springing  Line. — The  line  in  which  the  soffit  meets  pier  or  abutment — that  is,  the  inner  edge  of  the  skewback. 

Span. — The  horizontal  distance  between  springing  lines  measured  parallel  to  the  center  line  of  roadway. 

Intrados. — The  line  of  intersection  of  the  soffit  with  a  vertical  plane  taken  parallel  to  the  center  line  of  roadway. 

Extrados. — The  line  of  intersection  of  the  hack  with  a  vertical  plane  taken  parallel  to  the  center  line  of  roadway. 

Crown. — The  highest  part  of  the  arch  ring. 

Rise. — The  height  of  intrados  at  crown  above  level  of  springing  lines. 

Haunch. — The  portion  of  the  arch  ring  about  midway  between  the  springing  line  and  crown. 
Spandrel. — The  space  between  the  back  of  arch  and  the  roadway. 

£xfrarcfo$ 


Fig.  IB. 

Arches  are  divided  into  right  arches  and  skew  arches,  depending  upon  the  angle  made  by 
the  springing  lines  with  the  center  line  of  roadway.  A  right  arch  is  one  that  makes  this  angle 
exactly  90  deg. 

2.  Curve  of  the  Intrados. — The  form  or  general  outline  of  an  arch  is  the  first  consideration 
in  its  design.  According  to  the  curve  of  the  intrados,  arches  are  usually  divided  into  circular, 
multi-centered,  elliptical,  and  parabolic.  If  the  intrados  is  a  semicircle,  the  arch  is  a  semi- 
circular arch;  and,  if  the  intrados  is  less  than  a  semicircle,  it  is  a  segmental  arch.  A  multi- 
centered  arch  is  one  in  which  the  intrados  is  composed  of  several  arcs  of  circles  tangent  to  each 
other.  Semicircular  and  semi-elliptical  arches  are  full  centered — that  is,  they  spring  from 
horizontal  beds — while  segmental  and  parabolic  arches  spring  from  inclined  beds  called  skew- 
backs  (see  Fig.  IB).    Multi-centered  arches  may  have  beds  either  inclined  or  horizontal. 

651 


652 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-2a 


The  parabola  may  be  modified  for  the  sake  of  appearance  by  short  circular  curves  at  its  ends, 
made  tangent  to  the  parabola  and  to  the  vertical  side  of  the  pier  or  abutment.  Minor  curves 
joining  the  arch  soffit  to  the  pier  are  not  effective,  however,  and  should  not  be  considered  as 
part  of  the  arch  rise. 

2a.  Three-centered  Curve. — A  segmental  arch  cannot  often  be  used  to  advan- 
tage, for  it  seldom  can  be  made  to  fit  the  line  of  pressure.  The  three-centered  arch  is  perhaps 
the  most  common  for  solid-spandrel  construction  and  gives  a  pleasing  and  generally  an  econom- 
ical design.  The  formula  for  the  radius  of  a  circular  segment  when  the  chord  distance 
(span)  and  mid-ordinate  (rise)  of  the  segment  are  known  is  as  follows: 

m  chord) 2  +  (mid-ordinate)  2 


Radius 


2  X  mid-ordinate 


P'ollowing  are  the  formulas  for  the  radii  of  a  three-centered  curve  (see  Fig.  2). 

+  y' 


R 


2y 


2  FE  cos  d  -  AF  sin 


Fig.  2. 


Fig.  3. 


26.  Semi-ellipse. — The  multi-centered  curve  can  be  made  to  approximate  an 
ellipse.  Entirely  graphical  methods  of  obtaining  the  semi-ellipse  and  corresponding  approxi- 
mate multi-centered  curves  are  as  follows: 

Let  AD  and  CD  (Fig.  3)  be  the  semi-major  and  semi-minor  axes,  respectively,  of  the 

ellipse.    With  D  as  a  center,  draw  circular  arcs  with  radii  AD  and     c    n 

CD.  From  points  where  a  common  radius  intersects  the  two  circu- 
lar arcs,  draw  vertical  and  horizontal  ordinates. 
The  intersection  of  these  ordinates  gives  one  point 
on  the  ellipse.  Other  points  may  be  found  in  a 
similar  manner. 

Suppose  now  that  a  three-centered  intrados  is 
required  which  approximates  a  true  ellipse.  The 
form  of  the  true  ellipse  is  first  drawn  by  the 
method  given  above  and  is  shown  in  Fig.  4  by  the 
full  line.  The  approximate  form,  shown  dotted,  is 
what  is  required.  Assume  any  two  equal  distances 
CB  and  AE  more  than  one-half  of  the  semi-minor 
axis.  Join  BE  and  bisect  the  line  BE  at  F.  Through  F  draw  a  perpendicular  to  BE,  inter- 
secting the  line  CD  at  0.  The  two  points  O  and  E  will  be  centers  of  two  circular  arcs  which 
will  form  an  approximate  ellipse.  By  first  selecting  the  position  of  the  point  E  so  that  the 
circular  arc  described  from  E  as  center  will  conform  as  closely  as  possible  with  the  true 
ellipse,  satisfactory  curves  will  easily  be  found. 

The  method  of  drawing  an  approximate  ellipse  using  a  five-centered  curve  will  now  be 
explained.    In  order  to  have  a  check  on  the  work,  it  is  advisable  to  first  draw  the  form  of  the 


Fig.  4. 


Fig.  5. 


Sec.  16-2cl 


ARCHES 


653 


true  ellipse  by  the  method  given  above.  Let  AD  and  CD  (Fig.  5)  be  the  given  semi-axes.  Join 
A  and  C,  and  through  B  draw  a  perpendicular  to  AC,  determining  E  and  0,  two  of  the  centers. 
From  0,  with  OC  as  radius,  draw  an  arc  CK  as  long  as  thought  suitable,  and  join  K  with  O. 
Make  KG  equal  to  AE.  Join  E  and  G.  At  the  center  of  EG  draw  a  perpendicular  to  jEJG, 
and  note  its  intersection  H  with  KO.  From  if,  with  radius  HK,  draw  an  arc  to  HE  (extended) ; 
and  from  E,  with  EA  as  radius,  complete  the  curve. 

2c.  Parabola. — The  equation  of  the  parabola.  Fig.  6,  is  as  follows: 

Divide  the  line  OR  into  any  number  of  convenient  equal  parts,  and  number  the  points  of  divi- 
sion 1,  2,  3,  etc.,  beginning  at  the  point  nearest  O.  Then  to  find  the  values  of  y,  for  the  various 
abscissas  x,  the  numbers  1,  2,  3,  etc.,  should  be  inserted  in  the  above  equation  for  values  of  Xy 
and  the  total  number,  which  in  the  illustration  is  6,  should  be  inserted  for  the  value  of  a. 


Fig.  6.  •  Fig.  7. 


A  very  simple  graphical  method  of  drawing  the  parabola  is  to  lay  off  on  the  vertical  line 
RS,  Fig.  7,  the  same  number  of  equal  divisions  as  are  made  on  the  horizontal  axis  OR,  and  from 
0  draw  radiating  lines  to  the  various  division  points  on  the  vertical  axis  RS.  From  the 
various  points  on  the  horizontal  line  OR  draw  vertical  lines  intersecting  the  radiating  lines 
from  0.  The  points  of  intersection  of  these  vertical  lines  with  corresponding  radiating  lines 
are  points  on  the  required  parabolic  curve. 

3.  Arrangement  of  Spandrels. — Arch  spandrels  may  be  entirely  filled  with  earth,  or  they 
may  be  left  more  or  less  open  and  the  roadway  supported  on  a  series  of  transverse  walls,  or  on 
a  complete  superstructure  of  columns,  girders,  beams,  and  slabs.  If,  as  is  rarely  the  case,  a 
heavy  or  massive  appearance  is  desired  in  open-spandrel  construction,  then  side  curtain  walls 
may  be  used  and  all  spandrel  openings  closed.  In  the  open-spandrel  type,  the  arch  ring  may 
be  either  solid  or  composed  of  two  or  more  longitudinal  ribs. 

With  filled  spandrels,  the  filling  material  is  held  in  place  laterally  by  retaining  walls  which 
rest  upon  the  arch  ring.  These  retaining  walls  may  be  of  either  the  gravity  or  the  reinforced 
type,  or  they  may  consist  of  thin  vertical  slabs  tied  together  by  reinforced-concrete  cross 
walls.  Solid  fillings  increase  the  weight  of  the  superstructure  and  make  necessary  thicker  arch 
rings  and  larger  foundations.  Open-spandrel  construction,  on  the  other  hand,  requires  a  rela- 
tively larger  amount  of  form  work.  At  the  present  cost  of  labor  and  materials  in  this  country, 
the  filled  type  of  arch  spandrel  is  preferable  from  the  standpoint  of  economy  for  all  arches  of 
moderate  rise  with  spans  less  than  about  100  ft.  and  also  for  flat  arches  of  greater  span  where 
the  ratio  of  rise  to  span  is  not  more  than  one-tenth.  Fortunately,  a  proper  artistic  appearance 
is  usually  obtained  in  satisfying  these  economical  requirements. 

4.  Piers  and  Abutments. — The  springing  lines,  or  springs  of  an  arch,  should  be  located  as 
near  the  foundation  as  conditions  will  permit.  This  will  often  make  possible  a  less  expensive 
design  for  the  abutments  and,  where  piers  are  employed,  will  reduce  the  overturning  effect 
on  the  piers  to  a  minimum. 

In  the  case  of  long  bridges  with  a  series  of  arches,  what  are  called  abutment  piers  should 
be  placed  at  frequent  intervals  (usually  every  five  or  six  spans)  so  as  to  act  as  an  abutment  in 


654 


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[Sec.  16-5 


case  of  failure  of  one  or  more  of  the  arches.  This  type  of  pier  is  made  of  sufficient  thickness 
to  resist  the  pressure  for  either  arch  standing  and  the  other  arch  removed,  and  for  both  arches 
standing.  The  ordinary  arch  pier  should  be  analyzed  for  one  adjacent  arch  without  live  load 
and  the  other  adjacent  arch  with  live  load  over  the  whole  span. 

Arch  bridges  of  four  and  six  spans  do  not  present  a  desirable  appearance.  For  esthetic 
effect,  an  odd  number  of  spans  should  be  selected  and  the  span  lengths  should  decrease  each 
way  from  the  center  of  bridge. 

The  depth  of  arch  foundations  and  the  shape  of  abutments  and  piers  is  dependent  upon 
local  conditions,  and  in  some  difficult  cases  have  to  be  chosen  after  thorough  study.  A  certain 
shape  of  abutment  or  pier  is  first  assumed;  and  this  is  then  reviewed  to  see  that  the  load  upon 
the  ground  does  not  exceed  the  allowable  and  that  it  is  well  distributed.  Great  saving  is 
effected  in  some  cases  by  the  use  of  hollow,  or  ribbed,  abutments  and  piers. 

5.  Depth  of  Filling  at  Crown. — In  making  a  preliminary  design  for  an  earth-filled  arch 
bridge,  it  is  necessary  to  know  approximately  the  required  crown  thickness  of  the  arch  ring  and 
also  the  amount  of  earth  filling  over  the  crown.  This  must  be  known  in  order  to  determine  the 
remaining  distance  from  the  crown  to  the  springing  line — that  is,  the  available  rise  for  the 
arch.  For  highway  bridges,  a  depth  of  filling  including  the  pavement  of  from  1  to  2  ft.  will  be 
sufficient;  but  for  railroad  structures  a  minimum  depth  of  from  2  to  3  ft.  below  the  ties  will  be 
needed  in  order  to  form  a  cushion  for  the  ties,  to  distribute  the  load,  and  to  absorb  the  shock 
from  passing  trains. 

6.  Loads. — The  dead  weight  of  the  arch  ring  itself  and  of  the  superimposed  material  con- 
stitute usually  the  principal  loads  on  an  arch  ring.  With  open-spandrel  construction,  the  dead 
loads  act  vertically  upon  the  arch  ring  or  arch  rib  through  the  transverse  walls  or  columns, 
and  are  hence  definitely  known.  With  filled  spandrels,  the  pressure  produced  on  the  arch  ring 
by  the  earth  filling  is  really  inclined  and  the  dead  load  cannot  be  so  accurately  determined. 

On  flat  earth-filled  arches,  it  is  better  to  consider  only  vertical  loads  as  acting  on  the  arch 
ring,  for  the  conjugate  horizontal  forces  are  small  and  may  be  neglected.  On  earth-filled  arches 
with  large  rise,  the  horizontal  thrusts  become  great,  especially  close  to  the  springing  lines,  and 
it  may  be  advisable  in  some  cases  to  take  these  horizontal  components  into  account.  The 
omission  of  these  horizontal  thrusts,  however,  is  always  on  the  side  of  safety. 

A  common  assumption  for  weight  of  earth  fill  where  the  actual  value  is  unknown  is  100  lb. 
per  cu.  ft.  When  sand  is  used,  its  weight  should  be  taken  at  120  lb.  Pavement  is  usually 
assumed  as  12  in.  thick  and  as  weighing  150  lb.  per  cu.  ft. 

The  live  load  to  be  used  in  the  investigation  of  an  arch  bridge  should  be  the  greatest  that 
comes  or  is  liable  to  come  upon  the  roadway.  Each  location  should  be  studied  and  the  live 
load  chosen  to  fit  the  requirements.  For  ordinary  conditions  a  standard  loading  is  commonly 
employed.    Wind  pressure  is  considered  only  on  light  or  exceptionally  high  structures. 

In  earth-filled  bridges  where  there  is  sufficient  thickness  of  filling  to  distribute  the  con- 
centrated loads  over  a  considerable  area  of  arch  ring,  uniform  live  loads  are  used  in  the  arch- 
ring  design.  City  highway  bridges  are  generally  designed  for  50-ton  electric  cars  and  for  such 
bridges,  with  spans  of  200  ft.  or  more,  a  uniform  load  of  1200  lb.  per  lin.  ft.  is  usually  taken  on 
each  railway  track  together  with  a  uniform  load  of  80  lb.  per  sq.  ft.  over  the  remaining  area  of 
roadway  and  sidewalks.  For  spans  between  100  and  200  ft.,  the  loads  are  taken  proportionally. 
The  loads  specified  above  for  city  bridges  may  be  reduced  by  about  20%  to  apply  to  the  arch 
rings  of  light  country  bridges.  The  load  on  each  street  railway  track  is  generally  assumed  to 
cover  a  width  of  9  ft. 

In  addition  to  the  above  loads,  city  bridges  and  bridges  on  thoroughfares  likely  to  be  used 
for  heavy  hauhng  should  be  designed  to  carry  20-ton  trucks,  with  axles  about  10  ft.  c.  to  c, 
14  tons  on  rear  axle  and  6  tons  on  front  axle;  wheels  about  5  ft.  c.  to  c. 

Because  of  the  permanent  character  of  concrete  bridges  it  may  be  wise  to  provide  a  larger 
margin  for  increase  of  loading  than  is  above  suggested,  or  than  is  usually  allowed  in  steel-bridge 
design.    Fortunately,  in  the  case  of  concrete-arch  bridges  a  large  increase  can  be  provided  for 


Sec.  16-6] 


ARCHES 


655 


with  only  a  slight  increase  of  expense  due,  of  course,  to  the  controlling  influence  of  the  dead 
load. 

Following  is  an  extract  from  the  report  of  a  Committee  on  Reinforced  Concrete  Highway- 
Bridges  and  Culverts,  American  Concrete  Institute,  presented  at  the  Annual  Convention  at 
Chicago,  Feb.  17,  1914: 

Class  "A"  Bridges. — Main  thoroughfares  leading  from  large  towns.  In  view  of  the  extensive  introduction 
of  the  heavy  motor  trucks  and  traction  engines,  and  the  probable  general  use  of  such  vehicles  in  the  future,  it  is 
recommended  that  bridges  on  main  thoroughfares  and  other  roads  which  are  likely  to  be  used  for  heavy  hauling, 
be  designed  to  carry  20-ton  trucks,  with  axles  about  10  ft.  c.  to  c,  14  tons  on  rear  axle  and  6  tons  on  fore  axle; 
wheels  about  5  ft.  c.  to  c.  Outside  of  the  large  cities  it  is  recommended  that  only  one  such  vehicle  be  assumed 
to  be  on  the  bridge  at  any  one  time;  the  likelihood  of  more  than  one  being  on  the  bridge,  in  a  position  to  produce 
maximum  stresses  at  the  same  time,  is  so  remote  that  this  assumption  is  considered  safe.  It  is  advised  that  such 
very  heavy  loads  be  considered  as  occupying  only  the  ordinary  width  of  the  road,  about  8  ft.  in  width  and  about 
35  ft.  in  length.  Congested  traffic  of  heavily  loaded  wagons  or  motor  trucks  will  rarely  impose  a  load  of  more  than 
100  lb.  per  sq.  ft.  over  a  considerable  area.  The  above-mentioned  20-ton  truck  gives  a  load  of  about  140  lb.  per 
sq.  ft.,  on  the  area  actually  occupied,  but  it  is  considered  extravagant  to  assume  that  a  large  bridge  is  covered  with 
•such  heavy  loads.  One  hundred  pounds  per  square  foot  is  thought  ample  to  assume  for  the  loading  of  spans  more 
than  60  ft.  long  in  designing  the  trusses  or  main  girders.  It  is  thought  to  be  safe  to  reduce  this  assumed  load  in  the 
case  of  longer  spans,  to  the  following  amounts: 

Length  of  Assumed  load 

span  (ft.)  (lb.  per  sq.  ft.) 
80  90 

100  80 

125  75 

200  and  over  70 

with  all  intermediate  spans  in  proportion. 

The  greatest  load  that  is  liable  to  be  imposed  on  a  bridge  sidewalk  occurs  when  there  is  some  excitement  in 
the  neighborhood  which  attracts  a  large  crowd,  and  for  which  the  bridge  affords  an  especially  good  point  of  view. 
In  that  case  the  crowd  forms  a  compact  mass  against  the  railing,  not  more  than  4  ft.  deep,  making  a  load  seldom 
exceeding  100  lb.  per  sq.  ft.  over  a  very  considerable  space.  The  remaining  portion  of  the  sidewalk  may  be  covered 
by  a  moving  crowd  which  can  scarcely  weigh  more  than  40  lb.  per  sq.  ft.  It  may  be  advisable,  sometimes,  to 
so  design  sidewalk  slabs,  that  if  a  street  car  or  motor  truck  accidentally  gets  upon  the  sidewalk,  it  will  not  go 
through.  Such  accidents  are  so  rare,  that  it  is  thought  safe  to  allow  materials  to  be  stressed  somewhat  beyond 
the  elastic  limit  in  such  cases. 

Class  "B"  Bridges. — Although  it  is  impossible  to  determine  beforehand,  especially  in  the  newer  parts  of  the 
country,  whether  any  given  road  is  to  be  used  for  heavy  traffic,  it  seems  extravagant,  at  least  in  the  cases  of  larger 
spans,  to  design  bridges  to  carry  much  heavier  loads  than  can  be  expected  to  come  upon  them.  It  is  recommended 
that  bridges  of  this  class  be  designed  to  carry  15-ton  trucks,  with  axles  10  ft.  apart,  5  tons  on  the  front  and  10  tons 
on  the  rear  axle.  This  will  allow  for  a  considerable  overloading  of  existing  motor  trucks.  It  is  further  recom- 
mended that  only  one  truck  be  assumed  to  be  on  the  bridge  at  one  time,  in  designing  the  floor  system,  that  it  be 
assumed  to  cover  a  width  of  8  ft.  and  a  length  of  35  ft.  and  that  the  remainder  of  the  bridge  be  covered  with  a 
load  of  about  90  lb.  per  sq.  ft.,  for  spans  up  to  60  ft. 

For  longer  spans,  the  trusses  and  main  girders  should  be  designed  for  the  following  loads: 

Length  of  Assumed  load 

span  (ft.)  (lb.  per  sq.  ft.) 

80  80 

100  70 

125  65 

150  60 

200  and  over  65 

with  intermediate  spans  in  proportion. 

Sidewalks  should  be  designed  to  carry  the  same  loads  as  in  the  case  of  Class  "A"  bridges. 

Special  Bridges. — City  bridges  and  bridges  carrying  traffic  connected  with  mines,  quarries,  lumber  regions, 
mills,  manufactories,  etc.,  require  special  consideration  and  should,  of  course,  be  designed  to  carry  any  load  which 
can  reasonably  be  expected  to  pass  over  them,  bearing  in  mind  the  likelihood  of  heavy  traction  engines  and  motor 
trucks  coming  into  extensive  use  in  the  not  distant  future. 

Bridges  Carrying  Electric  Cars. — Electric  traction  is  still  in  its  infancy  and  nobody  is  able  to  forecast  its  futiu-e 
development.  It  seems  probable,  however,  that  it  will  not  be  profitable  to  run  cars  weighing  more  than  50  tons 
each,  at  a  speed  that  would  be  permitted  on  any  public  road.  If  very  high  speeds  are  desired,  the  traction  company 
will  doubtless  be  required  to  operate  over  its  own  right-of-way.    It  is  recommended  that  bridges  carrying  either 


656 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-7 


urban  or  interurban  electric  cars  be  designed  to  carry  50-ton  cars  on  two  trucks,  spaced  30  ft.  c.  to  c,  each  truck 
having  two  axles  spaced  7  ft.  c.  to  c.  The  Committee  sees  no  reason  for  changing  the  customary  practice  of  assum- 
ing that  an  axle  load  is  distributed  over  three  ties. 

For  railroad  bridges,  Cooper's  Standard  Loadings  are  generally  specified,  the  particular 
loading  to  be  used  depending  upon  the  location  of  the  line  and  the  future  traffic  that  may  be 
expected.  As  regards  the  arch  ring  in  earth-filled  arches,  where  the  thickness  of  filling  is  suffi- 
cient to  distribute  the  concentrated  loads  over  a  considerable  area,  an  equivalent  uniform 
loading  per  linear  foot  per  track  is  generally  substituted.  A  load  of  700  lb.  per  sq.  ft.  is  common 
for  railroad  traffic  on  spans,  say,  over  80  ft.  in  length.  A  uniform  load  of  1000  lb.  per  sq.  ft. 
is  frequently  adopted  for  shorter  spans.  The  impact  of  live  loads  is  not  usually  considered 
except  for  the  floors  in  all  arches  of  open-spandrel  construction.  Braking  or  tractive  stresses 
are  important  only  for  bridges  on  heavy  grades. 

A  concentrated  load  should  be  assumed  to  be  distributed  downward  through  the  fill  on  a 
30-deg.  slope  with  the  vertical  starting  from  the  ends  of  the  ties.^  An  axle  load  is  assumed 
as  distributed  over  three  ties  in  the  direction  of  the  track. 

7.  Empirical  Rules  for  Thickness  of  Arch  Ring. — Various  empirical  formulas  have  been 
developed  for  the  trial  thickness  of  arch  ring  at  the  crown  and  are  an  aid  to  the  judgment. 

F.  F.  Weld^  gives  the  following  formula: 

fi      V         10       200  400 

where 

h  =  crown  thickness  in  inches. 
I  =  clear  span  in  feet. 

w  =  live  load  in  pounds  per  square  foot,  uniformly  distributed.  , 
w'  =  weight  of  dead  load  above  the  crown  of  the  arch  in  pounds  per  square  foot. 

W.  J.  Douglas  gives  the  following  tabulated  formulas  for  different  highway  spans,  the 
values  of  h  being  given  in  feet : 

Under  20  ft.  h  =  0.03(6  +  I)* 

20  to  50  ft.  h  =  0.015(30  +  Z)* 

50  to  150  ft.  h  =  0.00010(11,000  +  Z2)f 

Over  150  ft.  h  =  0.016(75  +  1)% 

*  For  railroad  arches,  add  25%. 
t  For  railroad  arches,  add  20  % . 
t  For  railroad  arches,  add  15%. 

Joseph  P.  Schwada  gives  the  following  formula  which  is  founded  on  a  rational  basis  but 
has  been  checked  with  results  from  actual  designs: 


^  ~  57.6(r 


where 


h  =  crown  thickness  in  feet. 

I  =  clear  span  in  feet. 

r  =  rise  of  intrados  in  feet. 

F  =  depth  of  fill  at  crown  in  feet  (not  including  track  and  ballast  or  pavement). 
B  =  weight  of  track  and  ballast  or  pavement  in  pounds  per  square  foot. 
w  =  uniform  live  load  in  pounds  per  square  foot. 

The  following  paragraphs  and  Figs.  8  and  9  are  from  Mr.  Schwada's  article  in  Eng.  News:^ 

In  Fig.  8  is  shown  the  application  of  the  formula  for  crown  thickness  to  a  series  of  railroad  arches  for  ratios  of 
rise  to  span  from  H  to  H  and  for  conditions  as  noted  in  the  figure.  For  convenience  the  coefficients  of  stress  for 
certain  spans  are  arranged  in  tabular  form.  Intermediate  values  can  be  determined  and  the  crown  thickness  for 
any  other  conditions  easily  obtained. 

1  See  teste  by  M.  L.  Engeb,  Eng.  Rec.,  Jan.  22,  1916,  p.  106. 

2  Eng.  Rec.,  Nov.  4,  1905,  p.  529. 

»  Eng.  News,  Nov.  9,  1916,  p.  880. 


Sec.  16-7] 


ARCHES 


657 


To  adapt  the  formula  for  crown  thickness  to  highway  arches  a  slight  change  must  be  made  in  the  value  of 
coefficients  for  short  spans,  because  of  the  light  loads  involved  and  because  of  a  desire  to  obtain  thicknesses  which 
are  practical.    The  coefficients  for  /c  for  spans  up  to  about  60  ft.  therefore  differ  from  the  coefficients  for  the  same 


"d-Wghf  of  ballast  and  track  tSi^OOIh/sqft 
r-Dirtfill-e.Oi 
W'  Uniform  live  load:  Ej^uiva/ent  to  Coopers 
E50  reduced  through  3'af fill  and Jjallast 
6001b.  per  sq.  in.  


ZO      30     40     50      60     10     80  90 
Span  in  feet 

Fig.  8. 


wo     I/O  120 


B  -  Weight  of  pavement =0 
F  -  Fill  on  crown  =  ^.0' 
w  ^Uniform  live  load  =W0*/5q  ft. 
fc  =550lb.per  sq.  in.  


£0     30     40      50      60      70      80     90     100     I/O  \Z0 
Span    j'n  feet 


Fig.  9. 


spans  for  railroad  arches.  For  spans  over  60  ft.  the  coefficients  are  the  same.  A  complete  table  of  values  for 
highway  arches  is  given  in  Fig.  9,  with  an  application  to  a  series  of  highway  arches  for  conditions  shown  in  the 
figure.  ^2 


658 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-8 


To  illustrate  the  application  of  the  formula  to  a  highway  arch  assume:  span,  90  ft.;  rise,  12  ft.;  weight  of 
pavement,  100  lb.  per  sq.  ft.;  fill,  1  ft.;  live  load,  300  lb.  per  sq.  ft.;  unit  stress,  fc,  550  lb.  per  sq.  in.  Then  K  = 
0.71.    Assume  depth  at  crown  to  be  23  in.  =  1.92  ft.    According  to  the  expression, 

90  X  90 


h  = 


[5  +  12.0  +  15.36  +  6  +  15]  =  1.91  ft.  =  23  in. 


57.6  X  10.08  X  0.71  X  550 

If  the  resulting  thickness  does  not  check  the  assumed  thickness,  another  trial  must  be  made. 

In  applying  the  formula  for  crown  thickness  it  should  be  understood  that  fc  in  the  expression  represents  an 
approximate  maximum  value  of  stress  which  one  may  reasonably  expect  to  obtain  if  the  arch  is  designed  according 
to  the  rules  for  curvature  and  thickness  followed  in  the  design  of  the  arches  here  considered.  The  maximum 
value  of  stress  for  these  arches  varied  from  575  lb.  per  sq.  in.  to  650  lb.  per  sq.  in.,  with  an  average  value  of  about 
625  lb.  per  sq.  in.    A  value  of  550  lb.  per  sq.  in.  to  600  lb.  per  sq.  in.  for  fc  is  suggested  for  use  in  the  formula. 

The  empirical  rules  given  above,  should  be  used  only  for  trial.  The  exact  shape  of  the 
arch  ring  and  the  thickness  at  different  sections  must  be  determined  by  analysis. 

8.  Approximate  Formula  for  Best  Shape  of  Arch  Axis. — Victor  H.  Cochrane  has  derived 
equations^  giving  approximately  the  best  shape  of  axis  for  both  open-spandrel  and  filled-spandrel 
arches.    The  equations  are  given  in  Art.  32  of  this  section. 

9.  Proper  Thickness  of  Arch  Ring  in  the  Haunch  for  Given  Thicknesses  at  Crown  and 
Springing. — Victor  H.  Cochrane  has  analyzed  a  series  of  typical  arches^  so  chosen  as  to  be 
applicable  to  any  span  length,  rise-ratio  (ratio  of  rise  to  span),  thickness  at  crown  and 
springing,  and  manner  of  loading.  The  characteristics  of  these  typical  arches  are  given  in 
Art.  33  of  this  section. 

10.  Dead  Loads  and  Their  Action  Lines. — After  a  trial  arch  ring  has  been  assumed,  the 
dead  loads  may  be  determined. 

Assume,  for  example,  a  railway  earth-filled  arch.    The  earth  filling  and  ballast,  ties,  and 
rails  should  be  reduced  to  an  equivalent  height  of  masonry,  as  shown  in  Fig.  10.    If  the  earth 
filling  is  taken  at  120  lb.  per  cu.  ft.  and  the  ballast,  ties,  and  rails  at  150  lb.  per  sq.  ft.  of  roadway, 
then  since  the  earth  filling  reaches  1  ft.  above  the  extrados  at  the  crown,  the  vertical  distance  ah 
120 

should  be  laid  off  equal  tOT^  =  0.8  ft.    In  a  similar  manner  the  distance  he  should  be  laid 


off  equal  to        =  1  ft 


150 


Points  d  and  /  should  be  determined  for  the  loading  at  c,  and  similar 

points  should  also  be  found  for  other  places  along 
the  arch  ring,  a  sufficient  number  being  taken  to 
fully  determine  the  curved  line  /e.  This  line  is 
called  the  reduced-load  contour. 

The  arch  with  its  load  should  now  be  divided 
by  vertical  lines  into  trapezoids,  or  what  are  nearly 
so.  For  testing  the  trial  arch  by  the  approximate 
method  (presented  in  the  following  article),  the 
horizontal  distance  between  springing  lines  may  be 
conveniently  divided  into  divisions  of  equal  hori- 
zontal length.  Fig.  10  shows  eight  divisions  on 
each  side  of  the  crown. 

The  next  step  is  to  determine  the  area  and 
center  of  gravity  of  each  trapezoid.  With  the 
area  known,  the  load  corresponding  to  each  trapezoid  is  found  by  multiplying  by  the  weight 
of  a  cubic  foot  of  concrete,  the  arch  considered  being  included  between  two  longitudinal  vertical 
planes  1  ft.  apart.  The  center  of  gravity  for  each  of  the  trapezoids  may  be  found  as  follows: 
Extend  AB,  Fig.  10,  so  that  BE  =  CD,  and  in  the  opposite  direction  extend  CD  so  that  CF  = 
AB.    The  intersection  of  EF  and  the  median  GH  is  the  center  of  gravity  sought. 

11.  Approximate  Method  of  Testing  Trial  Arch. — Since  the  dead  load  usually  controls 
the  shape  of  the  arch  ring,  it  is  desirable  to  test  the  trial  arch  for  this  loading,  employing  an 

1  Proc.  Engineers'  Society  of  Western  Pennsylvania,  vol.  32,  No.  8. 


Sec.  16-12] 


ARCHES 


659 


approximate  graphical  method.  In  the  method  referred  to,  that  form  of  arch  in  which  the  Une 
of  pressure  and  the  arch  axis  most  closely  approach  each  other  is  considered  to  be  the  best  that 
can  be  designed. 

There  are  two  classes  of  theories  of  the  stability  of  the  masonry  arch — the  line-of-thrust 
theories  and  the  elastic  theories.  The  line-of-thrust  theories  do  not  consider  the  elastic  proper- 
ties of  the  material  and  are  usually  employed  for  arches  made  up  of  wedge-shaped  stones, 
called  voussoirs.  For  instance,  stone  arches  are  generally  calculated  by  these  theories  and  the 
stability  of  the  arch  ring  is  considered  as  depending  upon  the  friction  and  the  reaction  between 
the  several  arch  stones.  Various  assumptions  are  made  in  arriving  at  these  different  line-of- 
thrust  theories,  and  the  results  derived  from  them  are  not  so  accurate  as  where  the  elastic 
properties  of  the  material  are  employed.  They  may  be  made  use  of,  however,  in  determining 
the  proper  shape  of  the  arch  ring  before  applying  the  elastic  theory  to  monolithic  arches. 

If  an  equilibrium  polygon  is  passed  through  the  centers  of  the  arch  ring  at  the  crown  and 
springing,  this  line  will  be  very  near  the  true  line  of  pressure.  In  the  trial  arch  mentioned 
above,  if  the  equilibrium  polygon  and  the  arch  axis 
do  not  closely  approach  each  other  there  will  surely 
be  another  shape  of  arch  ring  which  will  fulfill  this 
condition,  and  hence  have  probably  lower  maximum 
stresses  resulting  from  the  live  and  dead  loads.  Thus, 
the  method  of  obtaining  the  best  form  of  arch  is  to 
find  for  what  form  the  line  of  pressure  for  the  dead 
load  and  the  arch  axis  most  nearly  coincide.  It 
should  be  clear  that  this  method  will  aid  greatly  in 
getting  pretty  near,  at  any  rate,  to  the  proper  form 
for  the  arch  before  applying  the  elastic  theory. 

In  order  to  pass  an  equilibrium  polygon  through 
the  centers  of  the  arch  ring  at  the  crown  and  spring- 
ing, the  load  line  should  first  be  laid  off  as  shown  in 
Fig.  11  and  then  any  convenient  pole  0'  selected  in 
the  horizontal  through  the  point  k  in  the  load  line,  this 
point  representing  the  end  of  the  load  nearest  the 
crown.    The  next  step  is  to  draw  the  rays  to  the  force 

polygon  and  then  construct  the  corresponding  equilibrium  polygon  beginning  at  the  center  of 
the  arch  ring  at  the  skewback  (point  A).  If  now  the  first  and  last  strings  are  prolonged  to 
an  intersection  at  B,  a  vertical  line  is  determined  which  contains  the  resultant  of  the  loads 
occurring  over  the  left  half  of  span. 

The  equilibrium  polygon  which  we  have  constructed  does  not  pass  through  the  center 
of  the  arch  ring  at  the  crown  and  is  not  the  one  required.  We  do  know,  however,  that  the  first 
string  which  passes  through  A  must  intersect  the  last  string  in  the  vertical  through  B  and  that 
the  last  string  must  be  horizontal  due  to  symmetrical  loading.  Drawing  a  horizontal  line 
through  the  center  of  the  arch  ring  at  the  crown  determines  the  point  C  which  is  the  intersection 
of  the  first  and  last  strings  of  the  equilibrium  polygon  required.  A  line  drawn  through  m  of 
the  force  diagram  parallel  to  CA  determines  the  true  pole  0  on  the  horizontal  through  k.  If 
the  force  diagram  is  now  completed  for  this  pole,  the  required  equilibrium  polygon  may  be 
easily  drawn.  The  line  of  pressure  is  seen  to  follow  the  arch  axis  very  closely  and  the  trial 
arch  will  be  accepted  for  analysis. 

In  both  preliminary  and  final  analysis  the  arch  ring  should  be  laid  out  to  a  scale  of  1  in. 
=  3  ft.,  and  care  should  be  used  in  the  drafting  work  so  as  to  have  the  dimensions  exact  and 
the  lines  sharp. 

12.  Use  of  Temporary  Hinges  in  Arch  Erection. — Temporary  hinges  were  employed  by 
the  late  George  S.  Morison  in  the  construction  of  arches;  they  have  also  been  used  in  a  number 
of  European  bridges.    In  arches  with  a  rise  less  than  one-fourth  the  span,  these  hinges  materially 


Jrue  pole 


660 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-13 


decrease  stresses  in  the  arch  due  to  the  ehmination  of  all  dead-load  bending  stresses  (including 
arch  shortening  produced  by  dead-load  compressive  stresses)  in  addition  to  stresses  from  shrink- 
age or  settlement.  Concrete  should  be  poured  in  joints  to  close  hinges  only  after  full  dead  load 
is  on  the  structure  and  the  shortening  and  shrinkage  stresses  have  taken  place. 

13.  Use  of  Reinforcement  in  Concrete  Arches. — It  would  seem  from  purely  theoretical 
considerations  that  but  little  could  be  gained  by  the  use  of  reinforcement  in  a  concrete  arch 
since  the  direct  compression  usually  controls  to  such  an  extent  that  the  allowable  stress  in  the 
concrete  permits  of  but  a  small  unit  tensile  stress  in  the  steel.  From  a  broader  viewpoint, 
however,  it  is  clear  that  the  steel  adds  greatly  to  the  reliability  of  the  construction  and  makes 
possible  a  higher  working  stress  in  the  concrete  than  could  properly  be  employed  in  the  design 
of  plain-concrete  structures.  Higher  working  stress  produces  a  thinner  arch  ring,  and  conse- 
quently less  dead  load  and  lighter  abutments.  Undoubtedly,  a  large  saving  may  result  from 
this  cause  in  the  case  of  long-span  arches. 

A  considerable  portion  of  an  arch  ring  is  subject  to  both  positive  and  negative  moments, 
and  for  this  reason  the  reinforcement  should  be  placed,  for  some  distance  at  least,  near  both 
upper  and  lower  surfaces.  The  general  practice  is  to  carry  both  rows  of  steel  throughout  the 
entire  span  thereby  eliminating  any  possibility  of  failure  due  to  an  inadequate  provision  for 
tensile  stresses.  On  account  of  the  heavy  compressive  stress  in  arch  rings,  the  upper  and  lower 
reinforcement  should  be  tied  together  to  prevent  buckling. 

The  percentage  of  longitudinal  steel  in  arch  rings  is  to  a  certain  extent  arbitrary.  An 
amount  of  steel  between  }4,  and  1%%  of  the  ring  at  the  crown  seems  to  be  good  practice  in  the 
ordinary  full-barrel  arch-ring  design  although  the  exact  amount  depends  upon  the  loading  and 
the  form  of  arch  selected,  and  must  be  finally  tested  by  computation.  Transverse  rods  at 
right  angles  to  the  longitudinal  are  generally  used  to  prevent  cracks  in  the  concrete  and  to 
distribute  the  loads  laterally.    Web  reinforcement  is  not  required  in  ordinary  construction. 

14.  Classification  of  Arch  Rings. — Arches  may  be  classified  as  hinged  or  hingeless.  A 
hingeless  arch  is  one  having  fixed  ends,  while  a  hinged  arch  may  have  a  hinge  at  the  crown,  a 
hinge  at  each  end,  or  a  hinge  at  each  end  and  one  at  the  crown.  Arches  of  one  and  two  hinges 
are  not  used  to  any  extent  in  masonry  construction  since  the  three-hinged  arch  offers  the  ad- 
vantage of  more  definitely  fixing  the  line  of  pressure  throughout  the  ring  and  thus  makes  pos- 
sible a  saving  of  material.  Hinges,  however,  are  often  an  expensive  detail  and  the  three-hinged 
arch  is  by  no  means  so  common  as  the  concrete  arch  having  fixed  ends.  Friction  on  hinges  is 
also  an  important  consideration. 

Three-hinged  arches  are  treated  in  Arts.  43  to  47  inclusive. 

ANALYSIS  OF  THE  ARCH  BY  THE  ELASTIC  THEORY^ 

15.  Deflection  of  Curved  Beams. — Deflection  formulas  for  curved  beams  (in  which  the 
radius  of  curvature  is  large  as  compared  with  the  depth)  are  employed  in  the  development  of 
arch  theory. 

Let  AB^  Fig.  12,  be  any  portion  of  a  curved  beam  in  its  unstrained  form  and  A'B  the  same 
portion  in  its  strained  form,  assuming  the  beam  rigidly  fixed  at  B.  Let  X  —  X  and  Y  —  Y 
be  rectangular  axes  with  origin  at  A,  and  denote  the  components  of  A' as  Aa;  and  A?/.  AO, 
tangent  to  the  arch  axis  at  A,  moves  through  the  angle  k.  Formulas  below  give  the  following 
values:  (1)  angular  change  of  AO,  (2)  component  A.r  of  A',  (3)  component  A?/  of  A'. 

^  -  x:  s 

1  Method  of  analysis  as  given  in  Turneaure  and  Maurer's  "  Principles  of  Reinforced  Concrete  Construc- 
tion," 2nd  Edition,  pp.  335  to  344. 


Sec.  16-16] 


ARCHES 


661 


Fig.  12. 


The  smaller  the  elementary  lengths  of  beam  considered,  the  more  accurately  will  the  above 
formulas  apply.  In  the  derivation  of  the  formulas  the  values  of  M  and  /  have  been  regarded 
as  constant  quantities  for  each  particular  elementary  length  considered.  Since  this  is  not 
true  in  practice  on  account  of  each  element  having  appreciable  length,  a  close  approximation  to 
the  actual  M  and  1  for  a  given  element  may  be  obtained  by  taking  the  values  of  the  bending 
moment  and  moment  of  inertia  at  the  mid-point 
of  s.  Distances  x  and  y  should  also  be  measured 
to  this  point.  As  in  simple  beams,  M  is  considered 
positive  when  it  tends  to  increase  the  compression 
on  the  back  of  the  arch.  The  minus  sign  is  used 
in  formula  (2)  because  the  effect  of  a  positive 
value  of  M  in  any  element  causes  an  upward  de- 
flection— that  is,  a  minus  value  of  Ay,  considering 
only  the  effect  of  bending  in  the  element  in  ques- 
tion. 

16.  General  Procedure  in  Arch  Analysis. — A 

concrete  arch  with  fixed  ends  is  statically  indeter- 
minate. There  are,  in  all,  six  unknown  quantities — three  at  each  support  (the  vertical  and 
horizontal  components  of  the  reaction,  and  the  bending  moment;  or,  what  is  the  same  thing, 
the  magnitude,  direction,  and  point  of  application  of  the  reaction) — and  it  is  possible  to  de- 
termine only  three  unknowns  by  the  principles  of  statics.  The  three  additional  equations  may 
be  found  from  the  following  conditions: 

The  change  in  span  of  the  arch  =  Ax  =  0 

The  vertical  displacement  at  one  end  relative  to  the  other  end  =  Ay  =  0 

The  angle  between  the  tangents  to  the  arch  axis  at  the  two  ends  of  the 
arch  remain  unchanged,  or  Zfc  =  0 

These  three  conditions  must  be  true  since  the  arch  is  fixed  at  the  abutments. 

Instead  of  actually  finding  the  components  of  the  reactions  and  the  moments  at  the  sup- 
ports as  outlined  above,  it  is  simpler  for  sym- 
metrical arches  to  take  the  origin  of  coordinates 
at  the  crown  and  find  the  thrust,  shear,  and 
moment  at  that  point.  With  these  three  un- 
knowns determined,  each  half  of  arch  may  then 
be  treated  as  statically  determinate.  ^ 

The  analysis  of  a  symmetrical  arch  con- 
sists in  finding  the  thrust,  shear,  and  bending 
moment  at  the  crown  and  at  intermediate  sec- 
tions in  the  arch  ring  or  arch  rib,  and  then  find- 
ing the  stresses  resulting  therefrom.  (The 
method  of  finding  stresses  on  an  arch  section, 
knowing  moment  and  thrust,  is  explained  in 
Sect.  9.)  The  thrust  is  here  taken  to  be  the 
normal  component  of  the  resultant  force  on 
the  section,  and  the  shear  is  the  component 
at  right  angles  to  the  normal.  The  bending 
moment  will  be  considered  positive  when  it  tends  to  increase  the  compression  on  the  back  of 
the  arch,  this  being  the  same  convention  as  for  beams. 

A  horizontal  thrust  is  produced  at  the  crown  when  the  arch  is  loaded  symmetrically.  For 
non-symmetrical  loading,  an  inclined  pressure  acts  at  the  crown,  but  its  horizontal  component 
is  called  the  horizontal  thrust  for  that  loading.    Its  vertical  component  is  the  shear  at  the  crown. 

1  For  unsymmetrical  arches,  see  Art.  28. 


662 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-17 


Assume  the  arch  as  cut  at  the  crown  and  consider  each  half  to  act  as  a  cantilever  sustaining 
exactly  the  same  forces  as  exist  in  the  arch  itself. 

The  external  forces  holding  a  semi-arch  in  equilibrium  (Fig.  13)  are  the  loads  Fi,  P2,  etc., 
the  horizontal  thrust  He,  the  vertical  shear  7c,  and  the  reaction  at  the  skewback  Ra. 

After  He,  Vc,  and  Mc  have  been  computed,  the  line  of  pressure  (accurately  enough  re- 
presented by  the  equilibrium  polygon)  can  be  constructed  by  help  of  the  force  polygon.  Fig. 
13.  The  value  of  Mc  definitely  determines  the  point  of  application  of  He  and  makes  the  con- 
struction of  the  exact  line  of  pressure  possible.  (For  a  positive  value  of  Me,  the  thrust  He 
acts  above  the  arch  axis.)  From  this  line  of  pressure  and  the  accompanying  force  polygon  may 
be  obtained  the  thrusts,  shears,  and  bending  moments  at  intermediate  points  of  the  arch.  The 
force  polygon  gives  directly  the  thrusts  and  shears,  while  the  line  of  pressure  makes  possible 
the  determination  of  the  bending  moment  at  any  section,  the  bending  moment  being  equal  to 
the  resultant  pressure  at  the  given  point  multiplied  by  the  perpendicular  distance  from 
the  arch  axis  to  the  line  of  pressure.  Usually  the  line  of  pressure  is  drawn  to  serve  only  as  a 
check  on  the  computations,  and  the  bending  moments  at  the  various  points  are  determined 
algebraically. 

The  line  of  pressure  of  an  arch  is  a  continuous  curve,  but  differs  very  little  from  an  equi- 
librium polygon  for  the  given  loads.  Fig.  13.  In  fact  this  curve  becomes  tangent  to  the  equi- 
librium polygon  between  the  angle  points.  The  greater  the  number  of  loads,  the  nearer  the 
polygon  approaches  the  line  of  pressure. 

With  He,  Ve,  and  Mc  determined,  all  external  forces  are  known  except  the  reaction  at  the 
skewback,  and  this  is  determined  by  the  closing  line  of  the  force  polygon.  An  equilibrium 
polygon  may  then  be  constructed  as  already  mentioned,  the  first  side  being  in  the  line  of  Re 
produced,  the  second  parallel  to  the  ray  5,  and  so  on  until  the  last  side  through  q  gives  the 
position  of  i^o- 

17.  Notation. — The  following  notation  will  be  employed: 


Let      s  =  length  of  a  division  of  the  arch  ring  measured  along  the  arch  axis. 
nh  =  number  of  divisions  in  one-half  the  arch. 

I  =  span  of  arch  axis. 
Co  =  average  unit  compression  in  concrete  of  arch  ring  due  to  thrust. 
tc  =  coefficient  of  linear  temperature  expansion. 
tD  =  number  of  degrees  rise  or  fall  in  temperature. 
Ec  =  modulus  of  elasticity  of  concrete. 

At  the  crown,  let 

He  =  horizontal  thrust. 
Vc  ==  vertical  shear. 
Rc  =  resultant  of  Hg  and  Vc- 
Mc  —  bending  moment. 

At  any  point  on  the  arch  axis,  with  coordinates  x  and  y  referred  to  the  crown  as  origin,  let 
N  =  thrust  (normal)  on  radial  section. 
S  =  shear  on  radial  section. 

R  =  resultant  force  on  radial  section,  resultant  of  A'^  and  S. 
Xo  =  eccentricity  of  thrust  on  section,  or  distance  of  A'^  from  the  arch  axis. 
t  =  depth  of  section. 

I  =  moment  of  inertia  of  section  including  steel  =  /c  +  nls- 
A  =  area  of  section  including  steel  =  Ac  -\-  nAs. 
Po  =  steel  ratio  for  total  steel  at  section. 

d'  =  embedment  of  steel  from  either  upper  or  lower  surface. 
M  =  moment  =  Nxq. 

mL  =  moment  at  any  point  on  left  half  of  arch  axis  of  all  external  loads  (Pi,  P2,  etc.)  between  the  point 
and  the  crown. 

mR  =  moment  at  any  point  on  right  half  of  arch  axis  of  all  external  loads  between  the  point  and  the  crown. 
m  =  moment  at  any  point  on  either  half  of  arch  axis  of  all  external  loads  (Pi,  P2,  etc.)  between  the  point 
and  the  crown. 


Sec.  16-18] 


ARCHES 


663 


18.  Formijlas  for  Thrust,  Shear,  and  Moment. — When  the  arch  ring  is  so  divided  into  sec- 
tions that  I  is  a  constant,  then  the  following  formulas  apply: 


Loading: 


He  = 
Vc  = 
Mc  = 


nh'SimL  +  mR)y  -  X(mL  +  mR)'Ly 

2[nS2/2  - 
S(mL  -  mR)x 
2  2x2 

S(mL  +  thr)  —  2He'Z,y 


(4) 
(5) 
(6) 


2nh 

M  =  Mc  +  HcV  +  VcX  -  rriL  (7) 
M  =  Mc  +  HcV  -  VcX  -  ruR  (8) 
All  values  of  mL,  mR,  x,  and  y  should  be  substituted  as  positive.    All  summations  refer  to  one-half  of  the 
arch  axis.    Positive  value  of  Vc  indicates  that  the  line  of  pressure  slopes  upward  toward  the  left;  a  negative 
value,  downward  toward  the  left.    Positive  value  of  Mc  indicates  that  the  thrust  He  acts  above  the  arch  axis. 
Signs  preceding  terms  Mc  and  VcX  in  formulas  (7)  and  (8)  depend  upon  the  results  of  (5)  and  (6). 
Temperature: 

I  tdDluhEe 


2[ri/.S2/2_(Sy)2] 
Hcl^y 


(tD  should  be  inserted  as  +  for  a  rise;  —  for  a  drop.) 


(9) 


(10) 

"A 

M  =  Mc  +  Hey  (11) 
The  value  of  to  should  be  inserted  as  plus  for  a  rise  of  temperature;  minus  (  — )  for  a  drop.    Signs  preceding 
He  in  formulas  (10)  and  (11)  depend  upon  the  result  of  formula  (9).    Sign  preceding  Mc  in  formula  (11)  depends 
upon  the  result  of  formula  (10).    Thus  for  fall  of  temperature,  thrust  and  moment  are  of  opposite  sign  from  those 
for  a  rise.    I  =  span  of  arch  axis. 
Rib  shortening: 

I  Calnh 


He  = 
Mr.  = 


S  2[71aS2/2 


M  =  Mc  +  HcV 

Values  of  moments  and  thrusts  for  rib  shortening  are  of  same  sign  as  for  temperature  fall. 


(12) 

(13) 
(14) 

=  span  of  arch  axis. 


I    1  /  ^y-"  • 

I  \/ Distance  01003  Arch  Axis, 
j    ^>^i  from  Skewback 

I  / 

/ 

Fig.  14. 


19.  Division  of  Arch  Ring  for  Constant  j. — The  graphical  method  shown  in  Fig.  14  is 

usually  employed.  AB  is  drawn  to  any  con- 
venient scale  equal  in  length  to  one-half  the  arch 
axis.  The  curve  EF  is  then  drawn  through 
points  whose  ordinates  are  the  values  /  and 
whose  abscissas  are  the  corresponding  distances 
along  the  arch  axis  from  the  skewback.  (In 
order  to  make  the  drawing  clear,  the  ordinates 
and  corresponding  abscissas  which  determine 
the  curve  EF  are  not  shown.)  A  length  AB.  is 
then  assumed,  a  perpendicular  hC  erected  at  its 
center,  and  the  lines  AC  and  CU  determined. 
Starting  from  point  i?,  lines  are  drawn  parallel 
alternately  to  AC  and  CU^  as  shown  in  Fig.  14. 
Only  three  or  four  trials  will  usually  be  required 
to  divide  the  line  AB  into  the  desired  number 

of  divisions.    The  base  of  each  triangle  thus  formed  corresponds  to  s  and  its  altitude  to  /. 

Since  all  the  triangles  are  similar  by  construction,  the  term  y  is  constant  throughout. 

A  convenient  modification  of  the  above  method  is  to  draw  a  second  curve  E'F'  below  AB^ 
using  the  same  ordinates  as  for  EF.  AH  is  then  assumed  as  before  and  the  perpendicular  CC 
erected  at  its  center.  Starting  with  C,  diagonals  and  verticals  are  drawn  alternately  making 
the  diagonals  parallel  to  AC.  This  method  offers  the  advantage  of  drawing  all  the  diagonals 
parallel  to  the  same  line. 


664 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-20 


20.  Loadings  to  Use  in  Computations. — Arches  should  be  analyzed  for  live  load  over 
three-eighths  of  the  span,  five-eighths  of  the  span,  the  middle  one-fourth  of  the  span,  and  the 
end  three-eighths  of  the  span.  These  uniform  loadings  are  only  approximations  to  the  true 
loadings  which  produce  the  maximum  stresses.  The  exact  loadings  to  cause  maximum  con- 
ditions may  be  found  by  the  use  of  influence  lines. 

21.  Use  of  Influence  Lines. — It  is  common  practice  in  arch  design  to  consider  the  live 
load  as  extending  over  certain  definite  portions  of  the  span  and  to  assume  that  these  loadings 
produce  the  maximum  effects.  For  example,  it  is  often  assumed  that  by  loading  either  the 
whole  span  or  the  half  span  the  greatest  possible  stresses  at  any  given  section  are  obtained.  In 
general  this  assumption  is  only  a  very  rough  approximation,  and  considerable  inaccuracy  may 
result  from  such  a  method  of  procedure.  In  fact,  in  the  case  of  large  and  important  structures, 
the  only  satisfactory  way  to  analyze  for  maximum  stresses  is  by  what  might  be  called  a  unit- 
load  or  influence-line  method.  By  this  method  the  arch  is  first  analyzed  for  a  load  of  unity 
at  the  several  load  points  and  then  influence  lines^  are  drawn  for  either  moment  and  thrust  or 
for  fiber  stress. 

The  position  of  the  live  load  on  an  arch  to  cause  maximum  stress  at  any  given  section  can- 
not be  determined  in  advance  in  the  common  method  of  analysis.  An  investigation  will  show 
that  different  loadings  are  required  for  sections  similarly  located  in  arches  of  different  propor- 
tions. The  only  accurate  method,  then,  is  to  draw  a  proper  number  of  influence  lines  as  above 
described.  In  arches  continuously  loaded  no  definite  load  points  exist  at  which  to  place  the 
load  of  unity  in  influence-line  analysis,  but  in  arches  of  this  class  points  may  be  chosen  for  this 
purpose  sufficiently  close  together  to  give  any  desired  degree  of  accuracy. 

22.  Internal  Temperature  Investigations. — Comparatively  few  experiments  have  been 
made  which  furnish  data  on  the  internal  temperature  range  in  concrete  structures.  Undoubt- 
edly the  most  important  are  those  completed  under  the  direction  of  the  Engineering  Experiment 
Station  at  Ames,  Iowa,  on  two  highway  arch  bridges  of  the  earth-filled  type.  These  experi- 
ments^  are  described  in  detail  in  Bulletin  30  of  the  Iowa  State  College  of  Agriculture  and  Me- 
chanic Arts  where  a  summary  is  also  given  of  the  other  tests  that  have  been  made  on  inter- 
nal temperature  variation. 

The  writers  of  the  bulletin  conclude  that  "to  render  an  arch  structurally  safe,  provision 
should  be  made  (in  the  latitude  where  the  bridge  tests  were  conducted)  for  stresses  induced 
by  a  temperature  variation  of  at  least  40°F.  each  way  from  an  assumed  temperature  of  no  stress. 
Particular  circumstances  may  demand  that  a  greater  variation  be  used  for  drop  in  temperature 
to  prevent  the  appearance  of  cracks.  This  will  always  remain  largely  a  matter  of  judgment 
with  the  designing  engineer." 

23.  Shrinkage  Stresses. — Shrinkage  stresses  are  at  present  ignored  in  arch  analysis,  as  the 
shrinkage  coefficients  on  actual  arches  have  not  been  determined. 

24.  Deflection  at  Any  Point. — The  deflection  at  any  point  in  an  arch  may  be  found  by 
formula  (2),  Art.  15,  or 


The  arch  should  be  assumed  as  cut  at  the  point  in  question,  and  either  portion  of  the  arch  may 
be  considered.  The  cantilever  selected  should  be  subjected  to  exactly  the  same  forces  as 
exist  in  the  arch  itself. 

If  the  deflection  of  the  crown  of  a  symmetrical  arch  is  desired,  the  value  of  M  due  to  load- 
ing for  any  section  of  the  left  cantilever  may  be  found  from  formula  (7),  Art.  18;  or,  substi- 
tuting this  value  in  the  above  equation,  we  have 


Ay  =  - 


s 


~EJ 


Ay  =  - 


EJ 


1  See  Art.  48a,  Sect.  7;  also  Art.  34  of  this  section. 

2  By  Messrs.  C.  S.  Nichols  and  C.  B.  McCullough, 


Sec.  16-25] 


ARCHES 


665 


For  temperature  changes,  formula  (11)  of  Art.  18  may  be  substituted  in  place  of  formula  (7),  or 

Ay  =  -  ^  (Mc^x  +  Hc^^xy) 
_  _  tctnlinh'Exy  —  ^xXy) 

25.  Method  of  Procedure  in  Arch-ring  Design. — The  main  steps  that  need  to  be  taken  in 
the  design  of  an  arch  ring  may  be  enumerated  as  follows: 

1.  Assume  a  thickness  for  the  arch  ring  at  the  crown  and  at  the  springing,  using  empirical  formulas,  if  desired, 
as  an  aid  to  the  judgment. 

2.  Lay  out  the  curve  assumed  for  the  intrados. 

3.  Lay  out  a  curve  for  the  extrados  to  give  as  nearly  as  possible  the  assumed  ring  thickness  at  the  springing. 

4.  Draw  the  arch  axis  between  the  extrados  and  intrados. 

5.  Divide  the  arch  axis  into  an  even  number  of  divisions  such  that  the  ratio  ^  is  constant  for  all. 

6.  Compute  the  dead  and  live  loads,  and  indicate  these  loads  properly  on  the  drawing. 

7.  Compute  He,  Vc,  and  Mc  at  the  crown  for  the  different  conditions  of  loading. 

8.  Draw  the  force  polygons  for  the  different  conditions  of  loading  and  the  corresponding  equilibrium  polygons, 
or  lines  of  pressure. 

9.  Determine  the  thrusts,  shears,  bending  moments,  and  eccentric  distances  at  the  centers  of  they  divisions 

of  the  arch  ring  for  the  different  conditions  of  loading. 

10.  Compute  the  thrust  and  moment  at  the  crown  due  to  variation  in  temperature;  also  the  moments  on 
the  various  sections,  and  the  corresponding  thrusts  and  shears  by  resolving  the  crown  thrust  into  tangential  and 
radial  components. 

11.  Where  necessary,  compute  the  thrust  and  moment  at  the  crown,  and  the  thrust,  shear,  and  moment  at 
various  sections  due  to  rib  shortening. 

12.  Combine  the  thrusts,  shears,  and  moments  due  to  the  different  conditions  of  loading  with  the  thrusts, 
shears,  and  moments  due  to  temperature  and  rib  shortening.  (The  results  usually  show  that  the  shearing  unit 
stresses  are  very  small  and  need  not  be  considered.) 

13.  Compute  the  maximum  stresses — compression  in  the  concrete  and  tension  in  the  steel — due  to  the  thrusts 
and  moments.  If  the  stresses  are  either  too  small  or  too  large,  the  dimensions  or  even  the  shape  of  the  arch  ring 
must  be  changed  and  the  computations  repeated. 

26.  Uncertainty  as  to  Fixedness  of  Ends  of  Arch. — This  uncertainty  can  be  reduced  or 
entirely  eliminated  by  taking  the  skewback  for  purposes  of  analysis  at  a  plane  where  the  ends 
of  the  arch  are  virtually  fixed.  Whenever  the  abutments  are  of  such  a  form  that  there  is  no 
pronounced  change  of  section  at  the  springing  lines,  then  the  analysis  should  include  the  whole 
structure  down  to  the  point  where  the  distortion  due  to  the  live  load  on  the  arch  will  be  in- 
appreciable.   In  some  cases  this  may  be  the  very  bottom  of  the  abutment. 

27.  Skew  Arches. — Skew  arches  may  be  treated  exactly  as  right  arches,  the  span  being 
taken  parallel  to  the  center  line  of  roadway  and  not  at  right  angles  to  the  springing  lines  of  the 
arch. 

28.  Unsymmetrical  Arches. — Unsymmetrical  arches  are  sometimes  desirable  in  the  end 
spans  of  a  series  of  two  or  more  arches  in  order  to  reduce  material  in  abutments,  and  at  the 
same  time,  to  provide  ample  waterway  area  over  streams.  Also,  arches  of  this  type  are  often 
necessary  under  other  conditions,  as,  for  example,  when  a  river  in  a  deep  ravine  is  bordered  by 
a  railway  requiring  maximum  clearance  near  the  abutments.  ^ 

Formulas  for  unsymmetrical  arches  depend  upon  the  location     Section  near  \ 
of  the  coordinate  axes. 

28a.  Origin  of   Coordinates  Between  Divisional 
Lengths. — In  the  analysis  of  unsymmetrical  arches,  the  entire 

arch   ring  should  be  divided  into  a  sufficient  number  of  —j 

divisions  to  obtain  the  desired  degree  of  accuracy.    The  origin  y 
of  coordinates  may  then  be  taken  at  the  center  of  any  one  of  the  Fig.  15. 

sections  occurring  between  the  divisional  lengths,  but  for  con- 
venience in  scaling  the  values  of  x  and  i/,  this  origin  should  be  placed  at  one  of  the  sections 
rear  the  crown.    The  X  and  Y  axes  should  be  drawn  perpendicular  and  parallel  respectively 


666 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-286 


to  this  section  so  as  to  permit  the  thrust  at  the  section  to  be  determined  directly  without  com- 
position and  resolution  of  forces.    Fig.  15  shows  how  these  axes  should  be  drawn. 

The  flexure  formulas  for  Ho,  Vo,  and  Mo  for  unsymmetrical  arches,  considering  the  origin 
of  coordinates  near  the  crown,  are  exceedingly  complex  and  inconvenient  for  use  in  practice. 
The  best  plan  is  to  use  formulas  as  given  below  and  to  solve  simultaneously  for  the  above  values 
after  the  numerical  values  of  the  coefficients  are  substituted.  Following  are  the  formulas  to 
be  solved  in  this  way: 

Loading: 

Ho^y^  +  Vo(7:xLVL  -  'Lxrvr)  +  ilfoSy  -  -Lmy  =  0 

Ho^'LxLyL  —  'LxRyR)  +  FoSx^  +  Mo(2a;L  —  Sxfl)  —  'LmLxL  +  ^mRXR  =  0 
Ho'Sy  +  VoiXxL  —  I^xr)  +  nMo  -  Zm  =  0 

Ml  =  Mo  +  HoyL  +  Voxl  —  mh 

Mr  =  ilfo  +  HoyR  —  Voxr  —  mR 

All  values  of  mL,  mR,  xL,  xr,  yh,  and  yR  should  be  substituted  as  positive.  The  subscripts  L  and  R  refer  to 
summations  to  left  and  right  of  the  chosen  section  respectively.  No  subscript  indicates  that  summation  is  for 
entire  arch.  Positive  value  of  Mo  indicates  that  the  thrust  Hq  acts  above  the  arch  axis.  Considering  the  chosen 
section  as  nearly  vertical,  a  positive  value  of  Fo  indicates  that  the  line  of  pressure  slopes  upward  toward  the  left; 
a  negative  value,  downward  toward  the  left.  Signs  preceding  terms  Mo,  Voxl,  and  YoXR  in  the  last  two  formulas 
depend  upon  the  signs  of  Mo  and  Fo  resulting  from  the  three  simultaneous  equations. 

Temperature: 

Ho-Ly"^  +  FoCSxLJ/L  -  '^xRyR)  +  MoSy  -  ^  •  tctnlEc  =  0 

Hoil^xLyL  -  I^xrur)  +  Fo2a;2  +  Mo(2xL  -  Sxfl)  =  0 
HoSy  +  FoCSxL  -  Sxfl)  +  nMo  =  0 

Ml  =  Mo  +  HoyL  +  Foxz, 

Mr  =  Mo  +  HoyR  —  Voxr 

The  value  of  to  should  be  inserted  as  plus  (  +  )  for  a  rise  of  temperature;  minus  (  — )  for  a  drop.  Signs  pre- 
ceding terms  Mo,  HoyL,  HoyR,  VoxL,  and  Vqxr  in  the  last  two  formulas  depend  upon  the  signs  of  Mo,  Ho,  and  Fo 
resulting  from  the  three  simultaneous  equations.    I  =  span  or  arch  axis  measured  parallel  to  X  axis. 

Rib  shortening: 

Ca 

Rib  shortening  causes  the  same  efifect  as  a  lowering  of  the  temperature.  Solving  for  to  gives  equivalent 
temperature  drop. 

286.  Origin  of  Coordinates  at  Crown. — Assuming  that  by  ''crown  section" 
is  meant  a  section  at  the  highest  point  of  the  arch,  the  following  formulas  result,  where  q 

equals  (^jj  ^  divided  by  ^jj  ^• 

Loading: 

Hcil^y^L  +  l^VR^q)  +  Vcil^xLyL  -  ^XRyRq)  +  Md^yL  +  Sj/flg)  -  2mL2/L  -  ZmRyRq  =  0 
Hci'^xLVL  —  ^XRyRq)  +  FcCZxL^  +  'LxR'^q)  +  Mc(SxL  -  2xflg)  -  I^mLXL  +  ^mRXRq  =  0 
Hei^yL  +  ^yRq)  +  Vci^xL  -  ^XRq)  +  M^nL  +  URq)  -  l^mL  -  ^mRq  =  0 

Ml  =  Mc  +  HcyL  +  VcXL  —  mL 

Mr  =  Mc  +  HcyR  -  VcXR  -  mR 

Temperature: 

HcC2:yL^  +  S2/ft2Q)  +  Fc(SxL2/L  -  "S-XRyRq)  +  Mc^'LyL  +  ^yRq)  -  ^—  '  =  0 


HciZxLVL  -  ZxRyRq)  +  Vd^XL^  +  Sxiz^g)  +  Mc(SxL  -  Sxflg)  =  0 
Hci'^yL  +  Sl/fls)  +  Vdl^xL  -  ZxRq)  +  MdnL  +  nRq)  =  0 
Ml  =  Mc  +  HcyL  +  V^xl 
Mr  =  Mc  +  HcyR  -  VcXR 

Rib  shortening: 

Ca 

E7t. 


All  values  of  mL,  mR,  xl,  xr,  yL,  and  yR  should  be  substituted  as  positive. 


Sec.  16-28c] 


ARCHES 


667 


28c.  Origin  of  Coordinates  at  Left  Springing.- 

dinates  x  and  y  should  be  measured.  The  directions  Hi,  Vi, 
considered  as  positive  in  the  formulas  given  below.  Values 
of  y  measured  below  the  axis  X  —  X  should  always  be  con- 
sidered as  negative. 


-Fig.  16  shows  how  the  coor- 
and  Ml  are  shown  for  values 

Y 


Loading: 


Hi'Ly'^  -  ViZxy  -  MiZy  +  Xmy  = 
HiZxy  —  ViXx^  -  MiZx  +  Hmx  = 
Hi-2y  -  ViT^x  -  nMi  +  Sm  =  0 


in  which 


Then 


^  ab  —  cd 
^  ~  ae  —  cf 

a  =  'Ex'Zy  — 
b  =  XmxXy  - 
c  =  l^x'^'Sy  - 


Hi 


Ml 


n'Sxy 
-  'ExXmy 
I.x'Lxy 


d  =  l.m'Zy 
e  =  2x22/2 
/  =  n22/2  - 


-  n'Lmy 

-  -Lxylly 
(22/)2 


M  =  Ml  +  Fix  -  Hiy  -  m 
All  values  of  m  and  x  should  be  substituted  as  positive.  Values  of  y  below  the  X  —  X  axis  should  be  taken  as 
negative.  The  summations  refer  to  entire  arch.  Positive  value  of  Mi  indicates  that  the  reaction  acts  to  the  left 
of  the  arch  axis  at  the  springing.  Positive  values  of  Hi  and  Vi  indicate  that  the  reaction  acts  upward  to  the  right. 
Signs  preceding  terms  M\,  Vix,  and  Hiy  in  the  last  formula  depend  upon  the  signs  of  Mi,  Vi,  and  Hi  resulting  from 
the  preceding  equations. 
Temperature:  , 

//i22/2  -  7i2x2/  -  Mi2y  =  --tetDlEc 


HiZxy 
HiXy  - 

a 

Hi  =  -' 


■  ViZx^ 
Fi2x  - 


-  Afi2x  = 
nMi  =  0 


cf 


Vi  = 


k-Zx  -  Hu 


Ml  = 


HiZy  -  ViZx 


in  which 


k  = 


tctDlEc 


Then 


M  =  Ml  +  Fix  -  Hiy 

The  value  of  to  should  be  inserted  as  plus  (  +  )  for  a  rise  of  temperature;  minus  (  — )  for  a  drop.  Signs  pre- 
ceding terms  Mi,  Fi,  and  Hi  in  the  last  formula  depend  upon  the  signs  of  Mi,  Fi,  and  Hi  resulting  from  the  pre- 
ceding equations.    I  =  span  of  arch  axis  measured  horizontally;  that  is,  parallel  to  X  axis. 

Rib  shortening: 

Ca 

Ectc 


tD 


Rib  shortening  causes  the  same  effect  as  a  lowering  of  the 
temperature.  Solving  for  tD  gives  equivalent  temperature 
drop. 

29.  Arch  Structure  of  Two  Spans  with  Elastic 
Pier.i — A  structure  of  this  type  is  shown  in  Fig.  17. 


The  points  indicated  as  fixed  may  be  the  bottoms  of  the  pier  and  abutments,  or  they  may 
be  at  intermediate  sections,  depending  upon  where  the  designer  considers  the  structure  fixed. 
The  horizontal  section  A- A  where  arches  and  pier  join  is  the  section  considered.  In  Fig.  18 
the  top  of  the  pier  is  shown  in  detail. 

1  An  arch  structure  of  more  than  two  spans  and  with  elastic  piers  may  readily  be  analyzed  by  the  ellipse-of- 
elasticity  method  explained  in  vol.  Ill  of  Hool's  "Reinforced  Concrete  Construction." 


668 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-29 


What  may  be  called  the  skewbacks  of  the  arches  are  shown.  The  weight  of  the  material 
between  the  skewbacks  and  the  section  A-A  need  be  considered  only  in  finding  the  resultant 
thrusts  on  the  pier  sections.  The  origin  of  coordinates  x  and  y  for  each  arch  is  taken  at  the 
middle  point  C  of  the  section  A-A  instead  of  at  the  center  of  the  skewbacks. 

The  following  notation  is  employed: 

Let  XL,  VL  =  coordinates  of  any  point  on  the  axis  of  the  left  arch  referred  to  the  center  of  the  section 

A-A  as  origin.  Values  of  yh  should  be  considered  plus  when  measured  above  the  axis 
X-X,  and  as  negative  when  measured  below  that  axis. 
XR,  VR  =  coordinates  of  any  point  on  the  axis  of  the  right  arch  referred  to  the  center  of  the  section 
A-A  as  origin.  Values  of  yR  should  be  considered  plus  when  measured  above  the  axis 
X-X,  and  as  negative  when  measured  below  that  axis. 
yp  =  depth  of  any  point  on  the  vertical  axis  of  the  pier  below  the  section  A-A.  All  values 
positive. 

mL,  mR  =  moment  at  any  point  on  axis  of  left  arch  and  right  arch  respectively  of  all  external  loads 
between  the  point  in  question  and  the  top  of  the  pier. 
MLy  Mr,  Mp  =  moment  at  any  point  on  axis  of  left  arch,  right  arch,  and  pier  respectively. 

nL,  nR,  np  =  number  of  j  divisions  in  the  left  arch,  right  arch,  and  pier  respectively. 

CL,  cR,  CP  =  values  of  j  for  left  arch,  right  arch,  and  pier  respectively. 

Hi,  Vi  =  horizontal  and  vertical  components  of  the  thrust  from  the  left  arch  at  the  top  of  pier. 

Ml  =  moment  at  section  A-A  due  to  thrust  from  left  arch  =  vertical  component  of  thrust 
from  left  arch  multiplied  by  the  distance  from  the  point  C  (the  center  of  the  section)  to  where 
this  thrust  produced  cuts  the  section  A-A. 
Hi,  Vi  =  horizontal  and  vertical  components  of  the  thrust  from  the  right  arch  at  the  top  of  pier. 
Mi  =  moment  at  section  A-A  due  to  thrust  from  right  arch. 
H3  =  resultant  shear  on  section  A-A  =  Hi  —  H2. 
V3  =  resultant  thrust  (normal)  on  section  A-A  =  Vi  +  V2. 
M3  =  resultant  moment  on  section  A-A  =  Mi  —  M2. 

The  arrows  in  Fig.  18  indicate  what  are  considered  positive  values  of  the  quantities. 

The  following  six  equations  for  loading  may  be  solved  simultaneously  for  the  values  of 
Hi,  7i,  Ml,  H2,  Vi  and  M<,\ 

Loading: 

cUMiHyL  —  HiZyL^  -\-  ViZxLyL  -  'LmhyL)  =  -  cR{Mii:yR  -  HilLyR^  +  ViUxrvr  -  1,mRyR) 
MillXL  —  Hi'ZxLyL  +  Vi'LxL^  —  l^mLxL  =  0 
MiXxR  —  Hi'LxRyR  +  V21:,xr'^  —  ZmRXR  =  0 

CLinLMi  —  HiZyL  -\-  Vi'ExL  —  XmL)  =  —  cRinRM--  —  Hi'S^yR  +  ViZxR  —  "Lvir) 
cp[(il/i  -  M2)Syp  +  {Hi  -  i72)S2/p2]  ^  cL[Mi-ZyL  -  HilLyh^  +  ViLxLVL  -  ^mLyL] 
cp[np(Mi  —  M2)  +  (Hi  —  i72)S2/p]  =  -  chinhMi  -  H1S2/L  +  FiSxL  -  Smi] 

Bending  Moment  at  any  point: 

Ml  =  Ml  —  HiyL  +  ViXL  —  mL 
Mr  =  M2  —  HiyR  +  V2XR  —  mp 
Mp  =  (Ml  -  M2)  +  (Hi  -  H2)yp 
Values  of  yL  and  yp  should  be  considered  plus  when  measured  above  the  axis  X-X,  and  as  negative  when 
measured  below  that  axis.    The  values  of  H3,  V3,  and  Mz  may  be  obtained  from  the  following  relations: 
Hz  =  Hi  -  Hi  Vz=  Vi  +  Vi  Mz  =  Ml  -  Mi 

All  values  of  mL  and  mp  should  be  substituted  as  positive. 

For  arch  bridges  symmetrical  about  the  center  line  of  pier,  the  labor  involved  in  solving 
the  simultaneous  equations  mentioned  above  will  be  greatly  reduced. 

All  the  simultaneous  equations  given  above  pertain  to  the  unknown  forces  acting  at  the 
section  A-A.  With  these  completely  determined,  however,  the  moment  and  thrust  at  any 
section  may  be  found  in  same  manner  as  for  the  single  symmetrical  arch.  Each  of  the  three 
members  must  be  considered  separately  and  each  subjected  to  exactly  the  same  force  that  is 
found  to  act  upon  it  at  the  top  of  pier  in  the  monolithic  structure. 

When  the  two  arch  spans  are  equal,  either  arch  may  be  analyzed  for  temperature  and  rib 
shortening  stresses  in  the  same  manner  as  for  a  single  arch  having  immovable  or  fixed  supports. 


Sec.  16-30] 


ARCHES 


669 


COCHRANE'S  FORMULAS  AND  DIAGRAMS  FOR  USE  IN  THE  DESIGN  OF  SYMMET- 
RICAL ARCHES  IN  ACCORDANCE  WITH  THE  ELASTIC  THEORY^ 

30.  Accuracy  of  Formulas  and  Diagrams. — The  formulas  and  diagrams  in  this  chapter 
are  of  sufficient  accuracy  to  use  for  the  final  design  in  many  cases,  and  in  practically  all  instances 
they  will  afford  a  means  of  determining  the  form  and  dimensions  of  the  arch  with  assurance  that 
the  final  analysis  will  show  that  but  slight  changes,  if  any,  are  required. 

31.  Difficulties  and  Uncertainties  Involved  in  Applying  the  Elastic  Theory. — There  art 
many  reasons  for  concluding  that  the  use  of  rigidly  exact  theoretical  formulas  for  arch  design 
is  wholly  unwarranted,  and  that  if  by  making  certain  reasonable  practical  assumptions  we  can 
devise  greatly  shortened  methods  of  design,  we  are  quite  justified  in  so  doing.  For,  in  the 
first  place,  the  elastic  theory  as  applied  to  hingeless  arches  is  based  on  the  assumption  that  the 
ends  of  the  arch  are  rigidly  attached  to  immovable  abutments,  so  that  a  section  of  the  arch  at 
the  skewback  or  springing  is  subject  neither  to  vertical  or  horizontal  displacement  nor  to  rota- 
tion. This  assumption  is  never  in  entire  agreement  with  actual  conditions,  and  is  only  admis- 
sible as  an  approximation  in  cases  where  the  piers  or  abutments  will,  by  reason  of  their  size 
and  the  character  of  the  foundations,  be  subject  to  but  slight  distortions  or  movements.  There 
are  other  approximate  assumptions  made  in  deriving  the  working  formulas,  such  as  that  the 
material  is  homogeneous,  that  the  modulus  of  elasticity  is  constant,  and  that  the  effect  of  the 
radius  of  curvature  may  be  neglected.  Furthermore,  it  is  necessary  to  replace  the  definite 
integrals  of  the  three  equations  of  condition  by  summations.  But  this  is  not  all.  Even  if  the 
thrusts  and  moments  at  any  section  for  any  given  condition  of  loading,  etc.,  could  be  found 
with  certainty  by  the  elastic  theory  the  resultant  stresses  could  not  even  then  be  exactly 
determined,  on  account  of  the  approximate  character  of  the  flexure  formulas  and  the  uncertain 
tensile  stresses  in  the  concrete.  Finally,  it  may  be  pointed  out  that  the  live  load  itself  is  subject 
to  much  uncertainty,  both  as  to  its  amount  and  its  distribution,  and  that  the  effect  of  variations 
in  temperature,  while  in  many  cases  quite  severe,  cannot  in  the  present  state  of  our  knowledge 
concerning  the  matter  be  determined  with  any  great  degree  of  certainty.  Ihe  effect  of  the 
shrinkage  of  the  concrete  is  even  more  uncertain.    These  i 

and  other  like  considerations  justify  the  use  of  approxi-  V-'--5x--t-''^^<4^ 

mate  short-cut  methods  such  as  those  proposed  in  this  y-X^M^^L  \ 

chapter.  z^^^^*^-  H  J^^^s^^ 

32.  Best  Shape  of  Arch  Axis. — Using  the  notation  '^/^^^^             I  ^ 
as  shown  in  Fig.  19;  also  H"   ^  '  

r  =  rise  ratio  =  y  '  Fig.  19. 

u  =  ratio  of  thickness  at  any  point  to  thickness  at  the  crown  =  ^. 

to 

te 

Us   =  J- 
to 

then  the  equations  derived  giving  approximately  the  best  shape  of  arch  axis  for  both  open- 
spandrel  and  filled-spandrel  arches  may  be  expressed  as  follows: 

For  open-spandrel  arches: 

tan  d   =  (3  +  5r) 

6  +  or 

1  Taken  verbatim,  for  the  greater  part,  from  paper  on  the  "  Design  of  Symmetrical  Hingeless  Concrete 
Arches "  presented  before  The  Engineers'  Society  of  Western  Pennsylvania  by  Victor  H.  Cochrank;.  This 
paper  was  published  in  the  Nov.,  1916,  issue  of  the  Proc,  vol.  32,  No  8,  pp.  647-713.  Diagrams  on  pp.  682- 
685  inclusive  were  supplied  by  Mr.  Cochrane  and  take  the  place  f^f  formulas  presented  in  the  original  paper. 


670 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-33 


For  filled-spandrel  arches: 


4rl 


tan  d  = 


4r 


1  +  3r 


(1  +  7.5r) 


O.Zb         0  50  075 
Values  ofv=%i 


Fig.  20. 


33.  Variation  in  Thickness  of  Arch  Ribs. — Mr.  Cochrane  made  a  number  of  complete 
designs  and  investigated  a  number  of  designs  found  in  technical  literature,  in  order  to  determine 
what  the  thicknesses  of  the  arch  should  be  at  various  points  in  the  haunch  to  give  the  same  fiber 
stresses  as  at  the  crown  and  the  springing;  or  in  other  words,  to  determine  the  variation  in  u 

with  respect  to  y  =  —  for  equal  maximum  stresses  throughout  the  arch  ring.    Plotting  the 
s 

values  of  v  as  abscissas  with  the  values  of  u  as  ordinates,  curves  were  obtained  of  which  those 
shown  in  the  full  lines  OAB  and  OCD  in  Fig.  20  are  typical.  In  each  case  it  was  found  that 
a  certain  portion  of  the  haunch  might,  so  far  as  the  stresses  were  concerned,  have  been  made 
thinner  than  the  crown  section.  It  was  also  found  in  each  case  that  the  thinnest  section  required 
is  at  about  the  quarter  point,  and  that  between  this  point  and  the  springing  the  thickness  should 
increase  almost  uniformly.    It  is  easy  to  see  why  this  should  be  the  case,  since  the  moments 

^  due  to  rib  shortening  and  temperature  variations  are 
small  near  the  quarter  point  and  greatest  at  the  crown 
or  springing.  A  slight  increase  of  thickness  was  required 
near  the  crown,  as  shown  at  X  in  OCD,  in  some  arches 
of  large  rise-ratio  designed  for  a  relatively  heavy  live 
load. 

An  arch  of  this  shape  would  be  unsightly  and  diffi- 
cult to  build,  and  consequently  about  the  best  that  can 
be  done  is  to  make  the  arch  rib  of  uniform  thickness,  or 
but  slightly  increasing  thickness,  from  the  crown  to  about 
the  quarter  point,  and  to  increase  the  thickness  almost 
uniformly  from  this  point  to  the  springihg.  The  point  at  which  the  thickness  should  begin 
to  increase  rapidly  is  nearer  the  springing  in  arches  of  large  rise-ratio  carrying  heavy  live  loads 
than  in  flat  arches  carrying  light  live  loads.  The  dashed  curve  OFD  in  Fig.  20  represents  an 
arch  of  the  former  kind  and  the  curve  OEB  an  arch  of  the  latter  kind,  these  curves  representing 
the  actual  thicknesses  to  be  used  instead  of  the  possible  minimum  thicknesses  shown  by  OCD  and 
OAB.  The  flatter  arches  generally  require  a  greater  relative  thickness  at  the  springing  than 
do  those  with  large  rise-ratios. 

These  conclusions  led  to  the  selection  of  a  number  of  typical  curves  showing  the  variation 
of  u  with  respect  to  v  for  various  values  of  Us.  These  curves  are  shown  in  Diagram  1  and  are 
designated  as  Types  ^3.25,  A3,  A2.75,  -^2.5,  A2.25,  A2,  Ai.75  and  A1.5,  the  subscript  in  each  case 
denoting  the  value  of  Us  for  that  type.  These  curves  were  chosen  after  a  careful  study  of 
existing  well-designed  arches,  and  it  is  believed  that  the  arch  thicknesses  required  in  any  given 
case  will  be  closely  represented  by  some  one  of  them;  we  have  only  to  select  the  one  best  suited 
to  the  given  conditions. 

Since  in  each  case  the  typical  arch  has  a  greater  thickness  in  the  haunches  than  would  be 
required  to  keep  the  extreme  fiber  stresses  within  desired  limits,  we  reach  the  important  conclu- 
sion that  it  is  unnecessary  to  compute  the  stresses  in  any  hut  the  crown  and  springing  sections. 
The  writer  has  yet  to  find  a  single  well-designed  arch  having  thicknesses  corresponding  closely 
to  those  represented  by  one  of  these  typical  curves,  in  which  the  stresses  at  the  crown  and 
springing  are  not  very  nearly  the  maximum  found  anywhere  in  the  arch,  provided  the  arch- 
shortening  effect  is  considered.  Perhaps  the  only  good  reason  for  computing  the  stresses  any- 
where except  at  these  two  sections  is  in  order  to  determine  whether  the  amount  of  the  steel 
reinforcement  may  be  reduced  near  the  quarter  point. 

Many  arches  have  been  built  having  a  much  greater  relative  thickness  in  the  haunch  than 


Sec.  16-33] 


ARCHES 


671 


indicated  by  these  diagrams,  but  such  practice  is  not  to  be  recommended.  Not  only  do  such 
arches  require  more  material  than  necessary,  but  on  account  of  the  thicker  haunches  have 
greater  arch-shortening  and  temperature  stresses  at  the  crown  and  springing  sections  than  do 
those  having  thicknesses  corresponding  to  the  diagrams.    Thickening  the  haunch  does  not 


Diagram  1 


O       0.10      O.ZO     030     040     Q50    0.60    070     0.80     Q90  /.GO 
^a/ues      of     /?<7f/o  v 
Assumed  thickness  of  typical  arches. 


seem  to  improve  the  appearance  of  the  arch.  It  is  therefore  clearly  advisable  to  make  the 
haunch  as  thin  as  practicable. 

If  the  half  axis  is  divided  into  ten  equal  sections  the  ratio  of  the  depth  of  the  arch  at  the 
center  of  each  section  to  the  depth  at  the  crown  is  given  in  the  following  table : 


672  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  16-33 


Table  1. — Thicknesses  of  Typical  Arches 


Value  of 

Values  of  u 

=  —  for  tvoe 

to 

r  -  — 

s 

Al.6 

Al.75 

A2 

A.2,25 

^2.75 

As 

A3. 25 

0 

1 

.000 

1.000 

1 

.000 

1 . 000 

1 .000 

1 

.000 

1 

.000 

1.000 

0.05 

1 

007 

1.006 

1 

.005 

1 .004 

1 . 003 

1 

002 

1 

.001 

1 .000 

0.15 

1 

.021 

1.018 

1 

.015 

1 . 012 

1 .009 

1 

006 

1 

003 

1.000 

0.25 

1 

035 

1.030 

1 

.025 

1 . 020 

1 .015 

1 

010 

1 

005 

1.000 

0.35 

1 

049 

1.042 

1 

035 

1.028 

1.023 

1 

021 

1 

023 

1.030 

0.45 

1 

063 

1.054 

1 

048 

1.048 

1.057 

1 

070 

1 

083 

1.101 

U .  Oo 

1 

077 

1  n79 

1  .  U/  z 

1 

085 

1.105 

1.133 

1 

165 

1 

193 

1  OQ1 

0.65 

1 

095 

1.125 

1 

168 

1.215 

1.269 

1 

328 

1 

385 

1.455 

0.75 

1 

145 

1.223 

1 

311 

1.403 

1.508 

1 

625 

1 

737 

1.865 

0.85 

1 

245 

1.393 

1 

547 

1.700 

1.862 

2 

025 

2 

185 

2.355 

0.95 

1 

406 

1.621 

1 

837 

2.055 

2.277 

2 

495 

2 

709 

2.932 

1.00 

1 

500 

1.750 

2 

000 

2.250 

2.500 

2 

750 

3 

000 

3.250 

We  can  readily  obtain  a  formula  for  the  areas  of  the  vertical  faces  of  these  typical  arches. 
This  forrnula  is 

.      182.2  +  18.6Sus  +  5ASus^  ^ 


The  value  of  s,  the  length  of  the  half  axis,  may  be  determined  by  scaling  from  a  drawing,  or 
it  may  be  taken  by  interpolation  from  the  following  table: 


Table  2. — Lengths  of  the  Half  Arch  Axis  s  in  Terms  of  the  Span  Length 


Kinds  of  arches 

Values  of  s  for  rise-ratio  r  = 

0.10 

0.15 

0.20 

0.25 

0.30 

Open-spandrel  arches  

Filled-spandrel  arches  

0.513Z 
0.515Z 

0.529Z 
0.534i 

0.551^ 
0.559^ 

0.577Z 

0.607Z 

Table  3  gives  values  of  -j"  (referred  to  as  j  in  preceding  chapters  for  the  typical  arches,  the 
half  axis  in  each  case  divided  into  10  parts).    7o  =  moment  of  inertia  at  the  crown. 

Table  3 


Type 

Value  of  Y 

^1.6 

0 

0769  s  -V-  7o 

Ai.78 

0 

0732  s  -^  7o 

A, 

0 

0699  s  /o 

^2.25 

0 

0672  s  -^  /o 

-^2.  5 

'  0 

0647  s  h 

^2.75 

0 

0626  s  7o 

^3 

0 

0606  s  7o 

^1.26 

0 

0586  s  -i-  7o 

The  approximate  value  of  s  may  be  taken  from  Table  2  above. 


Sec.  16-34]  ARCHES  673 

The  following  table  gives  the  location  of  the  centers  of  divisions  having  a  constant  ratio 

As 

Y".  These  points  will  be  referred  to  for  convenience  as  "division  centers,"  or  "centers  of 
divisions." 

Table  4. — ^Location  of  Centers  of  Divisions  Having  a  Constant  Ratio 

As  .  . 

-J-  (10  divisions) 


Point  at  center 
of  division. 

Values  oi  v  = 

=  —  for  type 
s 

No.  from  crown 

Al.Tb 

A  2 

A2.25 

A  2. 5 

A2.75 

A3 

A3. 25 

1 

0.039 

0.037 

0.036 

0.034 

0.033 

0.032 

0.031 

0.030 

2 

0.119 

0.112 

0.107 

0.102 

0.098 

0.095 

0.092 

0.089 

3 

0.201 

0.190 

0.180 

0.172 

0.165 

0.159 

0.153 

0.149 

4 

0.286 

0.270 

0.255 

0.243 

0.232 

0.222 

0.214 

0.208 

5 

0.374 

0.352 

0.332 

0.316 

0.301 

0.287 

0.275 

0.265 

6 

0.464 

0.436 

0.411 

0.389 

0.370 

0.353 

0.338 

0.325 

7 

0.558 

0.522 

0.491 

0.466 

0.443 

0.423 

0.405 

0.389 

8 

0.657 

0.614 

0.578 

0.549 

0.524 

0.502 

0.481 

0.463 

9 

0.766 

0.722 

0.684 

0.652 

0.625 

0.600 

0.578 

0.558 

10 

0.912 

0.890 

0.872 

0.856 

0.842 

0.829 

0.817 

0.806 

To  find  the  distances  from  the  crown  to  the  division  centers,  multiply  the  above  coefficients 
by  the  length  of  the  half  axis.    These  coefficients  apply  to  an  axis  of  any  shape. 

Table  4  was  computed  on  the  basis  of  a  1  %  crown  reinforcement,  but  it  may  be  used  for 
plain  arch  ribs,  since  the  moments  and  thrusts  are  changed  but  little  on  account  of  a  consider- 
able change  in  the  location  of  the  division  centers. 

34.  Influence -line  Diagrams. — The  formulas  used  in  figuring  the  influence-line  values  of 
Diagrams  2  to  13  inclusive  were  the  same  as  given  in  Art.  18. 

The  use  of  these  influence-line  diagrams  requires  little  explanation.  The  designer  having 
determined  by  means  of  the  diagrams  referred  to  in 
Art.  35  (or  otherwise)  the  approximate  actual  or  rela- 
tive thicknesses  at  crown  and  springing,  selects  the 
typical  arch  best  suited  to  the  particular  case,  and 
reads  from  the  diagrams,  by  interpolation  if  necessary, 
the  values  of  the  moments  and  thrusts  at  crown  and 
springing.  Having  these  values  he  constructs  influence 
line  diagrams  to.  any  desired  scale  and  reads  off  from 
these  the  moments  and  thrusts  due  to  the  specified  con- 
centrated loads.  If  no  concentrated  loads  are  speci- 
fied, or  if  uniform  loads  may  be  substituted  for  the 
concentrated  loads,  the  influence  lines  are  not  needed 
and  the  diagrams  of  Art.  35  are  used  instead. 

It  will  be  noted  that  the  maximum  live-load  mo- 
ments at  the  crown  and  springing  sections  are  determined  by  four  typical  arrangements  of  the 
live  load  designated  in  Fig.  21  as  loadings  1,  2,  3  and  4.  Loadings  1  and  2  are  for  the  maxi- 
mum positive  and  negative  moments  at  the  crown  respectively,  and  when  combined  cover  the 
entire  span.  Loadings  3  and  4  are  for  the  maximum  positive  and  negative  moments  at  the 
springing  section,  respectively,  and  when  combined  likewise  cover  the  span.  In  the  figure,  k 
represents  the  ratio  of  the  length  loaded  to  the  span  length.  Loadings  1,  3  and  4  are  contin- 
uous, while  loading  2  is  discontinuous, 
43 


i 


L0/1D/NG  J 

for  Max  ■*  M.  a-/  Crown 

llllllllllllllll 


LOADING  2 
For  Max  -Al.  a-f  Crown 


L  0/1  DING  3 
For  Max.  +  M  dSprn^ 

mil  miiil  \ 


LOAD/A/G4 
For  Max  - M.  atSpr'n'^ 


Fig.  21. — Typical  loadings  for  maximum 
moments  at  crown  and  springing. 


674  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  16-34 


Sec.  16-34] 


ARCHES 


675 


Sec.  16-34] 


ARCHES 


077 


678 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-34 


Sec.  16-34] 


ARCHES 


679 


680 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-34 


An  inspection  of  the  moment  diagrams  reveals  an  unexpectedly  small  variation  in  the  value 
of  the  ratio  k  for  each  loading,  the  variation  being  greater  with  respect  to  the  rise  than  with 
respect  to  the  type  of  arch.  It  appears  that  using  approximate  average  values  for  k,  the  maxi- 
mum positive  moment  at  the  crown  occurs  when  the  live  load  covers  one-fourth  of  the  span  at 
the  middle,  and  the  maximum  negative  moment  occurs  when  the  load  covers  the  two  end  three- 
eighths.  The  maximum  positive  moment  at  the  springing  is  produced  by  a  load  covering  five- 
eighths  of  the  span  beginning  at  the  opposite  end,  and  the  maximum  negative  moment  occurs 
when  the  load  covers  the  adjacent  end  three-eighths  of  the  span.  It  may  be  stated  further  that 
loading  1  and  loading  4  combined  produce  loading  3,  and  that  one-half  of  loading  2  is  the  same 
as  loading  4. 

Another  striking  fact  is  that  for  any  given  type  of  arch  the  coefficients  for  moments  vary 
only  slightly  with  respect  to  the  rise-ratio.  Hence  we  may  say  that  the  moments  for  any  typical 
arch  of  given  span  length  are  practically  independent  of  the  rise-ratio. 

As  the  ratio  of  springing  thickness  to  crown  thickness  increases,  the  arch  axis  remaining 
the  same,  the  moments  at  the  springing  increase  and  the  moments  at  the  crown  decrease,  as 
might  be  expected.  The  change  in  the  moments  as  the  arch  axis  changes  in  form,  the  ratio  Us 
remaining  the  same,  may  be  seen  by  comparing  the  diagrams  for  an  open-spandrel  arch  with 
those  for  a  filled-spandrel  arch  having  the  same  ratio  u^.  Table  5  presents  a  typical  case.  The 
positive  moments  at  crown  and  springing  increase  as  the  arch  axis  departs  farther  from  the 
parabolic  form  and  becomes  more  nearly  elliptical,  while  the  negative  moments  at  crown  and 
springing  decrease. 

Evidently  the  areas  enclosed  by  a  moment  influence  line  above  and  below  the  line  of  zero 
moments  are  a  measure  of  the  maximum  moments  due  to  a  uniform  live  load  on  the  span. 
The  algebraic  sum  of  the  positive  and  negative  areas  is  a  coefficient  of  the  moments  due  to 
live  load  over  the  entire  span.  It  is  evident,  therefore,  from  an  inspection  of  the  diagrams  that 
the  moments  for  live  load  over  the  whole  span  are  generally  much  smaller  numerically  than  the 
maximum  moments,  and  are  always  positive  at  crown  and  springing. 

Another  interesting  fact  is  that  for  arches  of  the  same  type  (that  is,  having  the  same  ratio 
Us),  but  having  axes  of  different  form,  the  arithmetical  sum  of  the  positive  and  negative  moments 
is  practically  the  same.  For  example,  take  an  open-spandrel  and  a  filled-spandrel  arch  of  the 
s.ame  rise-ratio  r  =  0.2  and  the  same  thickness-ratio  Us  =  2.5  (Diagrams  4,  7,  9  and  12),  and  the 
moments  are  as  follows: 


Table  5. — Comparison  of  Moments  for  Type  Aa.s  Open-Spandrel  and 
Filled-Spandrel  Arches  (r  =  0.20) 


Section 

Kind  of  moment 

Open-spandrel  arch 

Filled-spandrel  arch 

Crown 

Max.  +  moment  

Algebraic  sum  

Arithmetical  sum  

+0. 00474 
-0.00378w;Z2 

+0. 00096^^^2 
0.00852t(;Z2 

+0 . 00637w;^2 
-0. 00302 w;Z2 

+0.003357/;Z2 
0.00939i(;Z2 

Springing 

Max.  +  moment  

Max.  —  moment  

Algebraic  sum  

Arithmetical  sum  

+0.02990^^;^2 
-0.02330w;^2 

+0.00660w;^2 
0 . 05320w;Z''' 

+0.04110w;Z2 
-0.01750w;Z2 

+0 . 02360w;^2 
0.05860w;Z2 

Thus  while  the  maximum  positive  moments  are  more  than  one-third  greater  for  the  filled 
spandrel  arch  than  for  the  open-spandrel  one,  the  arithmetical  sums  of  the  moments  are  only 


Sec.  16-35] 


ARCHES 


681 


one-tenth  greater.  These  two  arch  axes  differ  widely,  and  hence  for  two  axes  differing  but  little 
we  may  assume  that  the  arithmetical  sum  of  the  maximum  positive  and  negative  moments  is 
the  same  for  each  arch.  This  fact  leads  to  an  easily  applied  approximate  method  for  correcting 
the  known  moments  for  an  assumed  axis  to  suit  an  actual  arch  having  its  axis  differing  in  form 
from  the  assumed  axis.    This  method  is  given  in  Art.  36. 

The  moments  in  any  typical  arch  due  to  unit  loads  are  proportional  to  the  span  length, 
while  the  thrusts  are  the  same  for  all  span  lengths.  The  shears  at  the  crown  are  nearly  inde- 
pendent of  the  rise  and  are  the  same  for  all  span  lengths.  The  thrusts  at  the  crown  increase  as 
Us  increases,  and  also  as  the  arch  axis  approaches  an  elliptical  form,  and  very  approximately 
inversely  as  the  rise-ratio  r. 

35.  Diagrams  for  Moments,  Thrusts,  and  Average  Stresses. — The  notation  used  in 
Diagrams  14  to  21  inclusive  is  as  follows: 


I 

the  span  length  of  the  arch  axis  in  feet. 

h 

the  rise  of  arch  axis  in  feet. 

r 

the  rise-ratio  h/l. 

y 

the  ordinate  of  the  arch  axis  at  any  point  the  abscissa  of  which  is  cl. 

Us 

ratio  of  the  thickness  at  springing  to  the  thickness  at  crown. 

Mc 

moment  at  crown  in  foot-pounds. 

To 

thrust  at  crown  in  pounds. 

Ms 

moment  at  springing  in  foot-pounds. 

Ts 

thrust  at  springing  in  pounds. 

Vs 

approximate  dead  load  vertical  end  reaction,  or  one-half  dead  weight  of  span  in  pounds. 

Wc 

weight  of  arch  at  the  crown,  plus  average  weight  of  arch  superstructure  at  the  crown  in  pounds  per 

lineal  foot  of  span. 

w 

live  load  in  pounds  per  lineal  foot  of  span  (not  necessarily  the  same  for  all  positions  of  the  live  load). 

te 

the  coefficient  of  linear  expansion  due  to  temperature  changes. 

tD 

change  in  temperature  in  degrees  Fahrenheit. 

E 

modulus  of  elasticity  of  concrete  in  pounds  per  square  foot. 

lo 

the  moment  of  inertia  of  the  arch  rib  at  the  crown  in  feet^. 

fa 

average  direct  stress  throughout  arch  in  pounds  per  square  foot. 

Sac 

direct  stress  at  crown  section  in  pounds  per  square  foot. 

From  what  has  been  said  the  use  of  these  diagrams  will  be  readily  understood.  Following 
is  a  summary  of  the  steps  required  in  designing  an  arch  by  the  use  of  the  diagrams.  It  is 
assumed  that  the  arch  superstructure  has  been  designed,  and  that  the  dead  load  per  lineal 
foot  at  the  crown,  exclusive  of  the  arch  rib,  is  known;  also  that  the  span  and  rise  of  the  axis 
have  been  fixed. 

1.  Assume  a  crown  thickness  in  accordance  with  one  of  the  empirical  formulas  in  use,  or  by  comparison 
with  a  previous  design,  and  compute  the  total  dead  load  per  lineal  foot  of  span  at  the  crown  (=  w^). 

2.  Assume  the  arch  type,  or  the  thickness-ratio  Us.  For  open-spandrel  arches  this  ratio  will  usually  be  from 
1.5  to  2.5,  and  for  fiUed-spandrel  arches  from  2  to  3.25. 

3.  Determine  from  the  diagram  the  dead-load  thrusts  and  the  maximum  positive  and  negative  moments  and 
corresponding  thrusts  at  the  crown  and  springing  due  to  live  load,  temperature  variation  and  arch  shortening,  and 
calculate  the  extreme  fiber  stresses  due  to  the  proper  combinations  of  moments  and  thrusts.  If  the  stresses  so 
found  are  too  great  or  too  small,  change  the  thickness  at  the  crown  or  at  the  springing,  or  both,  and  repeat  the  above 
operation.  The  second  trial  will  usually  be  sufficient.  If  the  thicknesses  originally  assumed  are  not  correct,  the 
fact  will  usually  be  revealed  before  the  first  set  of  calculations  is  completed. 

4.  Lay  out  the  assumed  arch  axis  as  per  Art.  32  and  divide  it  into  10  or  more  equal  parts,  locating  the  center 
of  each  division.  At  the  points  thus  found  lay  off  the  lialf  thickness,  as  given  in  Diagram  1  or  in  Table  1,  above  and 
below  the  assumed  axis,  and  through  the  points  thus  determined  pass,  as  nearly  as  practicable  through  all  the  points, 
segmental,  three-centered,  or  five-centered  curves.    A  set  of  railroad  curves  is  useful  for  this  purpose. 

5.  Compute  the  dead  loads  at  the  panel  points  or  at  suitable  intervals  and  lay  out  an  equilibrium  polygon 
passing  through  the  crown  and  springing,  the  value  of  the  horizontal  thrust  being  first  computed  as  for  a  three- 
hinged  arch  and  used  as  the  pole  distance  for  the  force  polygon  (see  Art.  11). 

6.  By  trial  alter  the  shape  of  the  arch  axis  so  that  it  will  fit  the  dead-load  equilibrium  polygon  as  nearly  as 
practicable,  lay  out  the  arch  thicknesses  again,  and  determine  the  radii  of  the  intradosal  and  extradosal  curves. 

7.  If  the  actual  axis  departs  considerably  from  the  assumed  axis,  scale  the  dead-load  thrusts  from  the  force 
polygon  and  correct  the  maximum  live-load  moments  by  the  method  given  in  Art.  36,  revising  the  stresses  and 
changing  the  thicknesses  if  necessary.    This  last  step  will  seldom  be  required. 


682 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-35 


684 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-35 


Sec.  16-35] 


ARCHES 


685 


686 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-36 


36,  Approximate  Method  of  Correcting  Maximiun  Moments  when  Actual  Arch  Axis 
Deviates  from  Assumed  Axis. — It  has  been  found  that  for  any  given  typical  arch — that  is, 
for  an  arch  having  a  constant  ratio  Us — the  resistance  line  for  live  load  over  the  entire  span 
crosses  the  arch  axis  at  about  the  same  horizontal  distance  from  the  center  line  of  the  span, 
regardless  of  the  shape  of  the  arch  axis.  Also  it  has  been  found  that  for  two  arch  axes  of  the 
same  type  and  which  differ  but  little,  the  arithmetical  sum  {Si)  of  the  maximum  positive  and 
negative  moments  is  the  same  for  each  arch.  Making  use  of  these  facts,  the  formulas  given 
below  were  obtained. 

In  Fig.  22,  the  line  CABS  represents  the  axis  of  an  open-spandrel  arch  of  type  A 2. 5  and 
rise-ratio  =  0.2,  while  CDES  represents  the  axis  of  a  type  A-i.^  filled-spandrel  arch.  The 


Fig.  22. — Resistance  lines  for  an  open-spandrel  and  a  filled  spandrel  arch;  live  load  over  whole  span. 

vertical  scale  is  times  the  horizontal.  The  resistance  lines  for  full  live  load  are  QABN 
and  ODEP,  respectively,  and  it  will  be  seen  that  the  intersection  points  A  and  D  are  about 
equidistant  from  the  center  line,  as  are  also  B  and  E.  It  appears,  then,  that  if  the  full-load 
resistance  line  for  one  axis,  as  CABS,  is  known,  the  resistance  line  for  another  axis,  as  CDES, 
may  be  approximately  determined  by  passing  the  parabola  ODEP  through  the  two  points 
D  and  E  having  the  abscissas  Xi  and  X2  the  same  as  for  the  known  intersection  points  A  and 
B,  and  the  ordinates  yi  and  yo,  referred  to  C  as  origin. 

Let  d  =  the  rise  of  the  required  resistance  line  for  live  load  over  the  entire  span  (parabolic). 

di  =  the  corresponding  known  term  for  the  assumed  arch. 

a  =  the  vertical  intercept  between  the  arch  axis  and  the  required  resistance  line  at  the  crown. 
b  =  the  vertical  intercept  at  the  springing. 
Hi  =  horizontal  thrust  for  known  resistance  line  QABN. 
Mp'  =  known  maximum  positive  moment  at  crown  or  springing  for  the  assumed  axis  CABS. 
Mn   =  known  maximum  negative  moment  at  crown  or  springing  for  the  assumed  axis  CABS. 
Afp  and  Mn  =  corresponding  terms  for  the  actual  axis  CDES. 


arithmetical  sum  of  the  moments  Mp'  and  Mn'  —  Mp'  —  Mn'. 


Then 


Mp 


Hia~  +  S 
a 


2 


Hia^  -  S: 


2 


Sec.  16-36] 


ARCHES 


687 


For  the  springing  moments  substitute  b  for  a  in  these  formulas. 

These  formulas  will  give  close  approximations  to  the  true  values  of  the  moments  even  if  the 
axis  used  deviates  considerably  from  the  assumed  axis. 

Illustrative  Problem. — The  design  will  be  that  of  the  132-ft.  arch,  Kansas  River  bridge  at  Lawrence, 
Kan.  This  is  a  rather  flat  open-spandrel  arch.  Typical  half  sections  of  the  span  are  shown  in  Fig.  23.  Follow- 
ing are  the  dimensions: 

Z  =  132  h  =  16  :.  r  =  0.121 

fo  =  2.5  te  =  5.63  Us  =  2.25 

The  live  loads  are  as  follows: 


HALr- SECTION  AT  HAUNCH       HALF-SECTION  AT  CROIVN 

Fig.  23. 


Live  Loads 


Member  loaded 

Portion  of  structure  loaded 

Track 

Remainder  of 
roadway  (18  ft.) 

Sidewalks 

For  roadway  floor  slabs,  fascia-girders,  canti- 
lever beams,  cross-girders,  spandrel  columns 
and  approach  girder  spans. 

Electric  railway  loading 
(assumed  to  occupy  a 
transverse     width  of 
12  ft.). 

20-ton  road  roller 
or 

200  lb.  per  sq.  ft. 

150  lb.  per  sq.  ft. 

Electric  railway  loading 
(assumed  to  occupy  a 
transverse     width  of 
12  ft.). 

60  lb.  per  sq.  ft. 

50  lb.  per  sq.  ft. 

Or  the  equivalent  uniform  loads  given  below. 

3500  lb.  per  lin.  ft.  span 

50  lb.  per  sq.  ft. 

40  lb.  per  sq.  ft. 

J  lie  vviieei  luaus  are  snuwii  iii  rig.  ^•±. 

The  working  stresses  assumed  are  given  on  page  688. 


37300 
37500 

37500 
37SOO 

37500 
37SOO 

37SOO 
37SOO 

37500 
37500 

9  9 

O  O     Q  O    E'TC,  Of? 

ki  23' 

\s\  8'  \s]^£' 

/I  continuous  line  of  150,000 /b.  cans  mfh  ax/e  hods  as  abovre.       2 ax/es  on/y. 
Liv^e  Load  for  E/ecfr/c  Ry.  Track 


t 


ZO-Ton  Road  Roller 
Fig.  24. 


688 


CONCRETE  ENGINEERS'  HANDBOOK 
Working  Stresses  in  Pounds  per  Square  Inch 


[Sec.  16-36 


Member 

Kind  of  stress 

Stress 

Floor  slabs  

600 
16,000 

Tension  in  steel  

Arch  rings  

Compression  on  concrete,  including  L.  L.,  D.  L.,  rib  shortening  and  temperature  (for 

600 
800 

Es  =  30,000,000       Ec  =  2,000,000       n  =  15        tc  =  coefficient  of  expansion  =  0.0000055. 

In  order  to  employ  the  formulas  it  is  necessary  to  use  a  uniform  live  load  in  lieu  of  the  concentrated  loads 
shown  in  Fig.  24  for  the  electric  railway  track.  It  is  difficult,  if  not  impracticable,  to  work  out  equivalent  uniform 
loads  for  arches  such  as  are  in  use  for  simple  beam  and  truss  spans.  It  will  usually  be  sufficiently  accurate  for  prac- 
tical purposes  to  use  the  average  weight  per  lineal  foot  of  car.    Hence  we  assume  the  uniform  load  as  follows: 

Average  weight  of  car   =  ^  ^^'^^f^  _  3,490 


Uniform  load  on  roadway. 
Uniform  load  on  sidewalks. 


(30 


43 
12)  X  60 
10  X  50 


=  1,080 
=  500 


Total   5,070  1b. 

Then  we  have  wl   =  5,070  X  132  =      669,000  lb. 

and  wl^  =  5,070  X  132^  =  88,340,000  ft.-lb. 
It  will  be  assumed  to  begin  with  that  rough  preliminary  calculations  have  been  made  from  which  it  is  found 
that  the  crown  thickness  to  may  be  assumed  =  2.5,  and  the  ratio  Ug  =  2.25.    The  first  step  is  to  compute  the  dead 
load  per  lineal  foot  at  the  crown  (wc),  thus: 

Weight  of  track,  paving,  and  paving  base  on  sand  fill   4,000 

Weight  of  concrete  in  floor  slabs,  fascia  girders  and  side  walls   3,170 

Weight  of  cantilever  brackets,  per  foot  of  span   1,300 

Weight  of  sand  fill   2,880 

Weight  of  railings   800 

Weight  in  conduit  spaces   250 

Weight  of  arch  rib,  24  X  2.5  X  150   9,000  ' 


Total  Uc  =   21,400  lb. 

Dead  Load. — From  Diagram  14,  Tc  (or  He) 

=  (1.135)(21,400)(132)  =  3,210,000  lb. 
Vs  =  (0.600)  (21,400)  (132)  =  1,700,000  lb. 
Ts  =  3,630,000  lb. 
Live  Load,  Max.  +  Mom.  at  Crown. — From  Diagram  15, 
Tc  =  (0.524)  (669,000)  =  351,000  1b. 
Mc  =  (0.00445)  (88,340,000)  =  +  393,000  ft.-lb. 
Line  Load,  Max.  —  Mom.  at  Crown. — From  Diagram  15, 
Tc  =  (0.545)  (669,000)  =  365,000  1b. 
Mc  =  (  -  0.00391)  (88,340,000)  =  -  345,000  ft.-lb. 
Live  Load,  Max.  +  Mom.  at  Springing. — From  Diagram  16, 
Ts  =  (0.746)  (669,000)  =  499,000  lb. 
Tc  =  (0.775)  (669,000)  =  518,000  lb. 
Ms  =  (0.0282)  (88,340,000)  =  +  2,490,000  ft.-lb. 
Live  Load,  Max.  —  Mom.  at  Springing. — From  Diagram  16, 
Ta  =  (0.431)  (669,000)  =  288,000  lb. 
Tc  =  (0.295)  (669,000)  =  197,000  lb. 
Ms  =  (-  0.024) (88,340,000)  =  -  2,120,000  ft.-lb. 
The  arch  is  reinforced  with  24  lines  of  V/i-in.  square  bars  at  top  and  bottom.    The  centers  of  the  bars  are 
from  the  face  of  the  arch,  or  1  ft.  from  the  axis  at  the  crown.    Hence  the  moment  of  inertia 
J.   _  (24)(2.5)3  ,  (24)(2)a.56)(l)2(15) 


12        '  144 
The  equivalent  area       at  the  crown  = 

2.5 +[<2«lj»],24,=  67.8  s,.(t. 
Fall  0/  Temperature  of  40°. — 

tctoE  =  (0.0000055)  (40)  (288,000,000) 
-  63,400  lb.  per  sq.  ft. 


=  39.05 


Sec.  16-36] 


ARCHES 


689 


From  Diagram  19, 
Tc  = 

Mc  = 


(29.9)  (63,400)  (39.05) 

(16)  (16) 
(20.1)  (289,000)  (16) 


=  -  289,000  lb. 
=  +  929,000  ft.-lb. 


100 

Ts  =  (1.09  -  1.75  X  0.121)  (289,000)  =  -  254,000  lb. 
Ms  =  +  929,000  -  (16)  (289,000)  =  -  3,695,000  ft.-lb. 
Average  Stresses. — From  Diagrams  20  and  21 
For  dead  load, 

^3,210,000n 


fa  =  (0.88)  (- 


67.8 


0  =  41, 


700  lb. 


For  L.  L.  producing  max.  +  moment  at  crown, 

/,-(0.87)(M)  =  4500  1b. 
ForL.  L.  producing  max.  —  moment  at  crown, 


/365,000\ 
/a=  (0.90)(-^)  = 


4800  lb. 


ForL. L.  producing  max.  +  moment  at  springing 
'518,000\ 


6700  lb. 


/a  =  (0.87)  (-^^  3  / 
For  L.  L.  producing  max.  —  moment  at  springing, 

(0.89)  (1§|»)  =  2600  lb. 
For  temperature  drop  of  40°, 

fa 


(0.83)(™)  =  -  3500  1b. 


67. 

For  each  combination  of  loading,  the  arch-shortening  thrusts  and  moments  bear  the  same  ratio  to  the  thrusts 
and  moments  due  to  a  fall  of  40°  in  temperature,  as  does  the  total  average  stress  to  the  stress  IcIdE  (  =  63,400  lb.). 

I.    Summary  for  Maximum  +  Moment  at  Crown 
(a)  D.  L.,  L.  L.  and  Arch  Shortening 


Thrust 

Moment 

Average 
stress 

D.  L  

+  3,210,000 
+  351,000 
-  200,000 

+  41,700 
+  4,500 
-  2,400 

L.  L  

Arch  S  

Total  

+  393,000 
+  642,000 

+  3,361,000 

+  1,035,000 

+  43,800 

(&)  D.  L.,  L.  L.,  Temperature  Variation,  and 
Arch  Shortening 

Thrust 

Moment 

Average 
stress 

D.  L.  and  L.  L. . 
Temperature.  .  . 
Arch  S  

Total  

+  3,561,000 

-  289,000 

-  185,000 

+  393,000 
+  929,000 
+  593,000 

+  46,200 

-  3,500 

-  2,200 

+  3,087,000 

+  1,915,000 

+  40,500 

II.    Summary  for  Maximum  —  Moment  at  Crown 
(a)  D,  L.,  L.  L.,  and  Arch  Shortening 


Thrust 

Moment 

Average 
stress 

D.  L  

+  3,210,000 
+  365,000 
-  201,000 

+  41,700 
+  4,800 
-  2,400 

L.  L  

-345,000 
+  646,000 

Arch  S  

Total  

+  3,374,000 

+  301,000 

+  44,100 

It  appears  from  the  above  that  there  is  no  negative  moment  at  the  crown. 
41 


690 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-36 


III.    Summary  for  Maximum  +  Moment  at  Springing 
(a)  D.  L.,  L.  L.,  and  Arch  Shortening 


Thrust 

Moment 

Average 
stress 

D.  L  

+  3,630,000 
+  499,000 
-  184,000 

+  41,700 
+  6,700 
-  2,500 

L.  L  

Arch  S  

Total  

+  2,490,000 
-2,675,000 

+  3,945,000 

-  185,000 

+  45,900 

(6)  D.  L.,  L.  L.,  Temperature  Variation,  and 
Arch  Shortening 

Thrust 

Moment 

Average 
stress 

D.  L.  and  L.  L. . 
Temperature.  .  . 
Arch  S  

Total  

+  4,129,000 
+  254,000 
-  197,000 

+  2,490,000 
+  3,695,000 
-2,860,000 

+  48,400 
+  3,500 
-  2,700 

+  4,186,000 

+  3,325,000 

+  49,200 

IV.    Summary  for  Maximum  —  Moment  at  Springing 
(a)  D.  L.,  L.  L.,  and  Arch  Shortening 


Thrust 

Moment 

Average 
stress 

D.  L  

+  3,630,000 
+  288,000 
-  168,000 

+  41,700 
+  2,600 
-  2,300 

L.  L  

Arch  S  

Total  

-2,120,000 
-2,450,000 

+  3,750,000 

-4,570,000 

+  42,000 

(6)  D.  L.,  L.  L.,  Temperature  Variation,  and 
Arch  Shortening 

Thrust 

Moment 

Average 
stress 

D.  L.  and  L.  L.. 
Temperature.  .  . 
Arch  S  

Total  

+  3,918,000 

-  254,000 

-  155,000 

-2,120,000 
-3,695,000 
-2,257,000 

+  44,300 

-  3,500 

-  2,100 

+  3,509,000 

-8,072,000 

+  38,700 

The  following  table  gives  the  approximate  extreme  fiber  stresses  in  pounds  per  square 
inch  computed  from  the  above  thrusts  and  moments  on  the  assumption  thai  the  concrete 
takes  no  tension : 


Case  1(a) 

Case  1(6) 

Case  IV(a) 

Case  IV(6) 

580 

750 

420 

730 

Sec.  16-37] 


ARCHES 


691 


The  stresses  computed  by  this  method  will  be  found  to  be  somewhat  less  than  those  figured 
by  the  exact  method,  but  if  some  arbitrary  allowance  should  be  made  for  the  dead-load 
moments  the  difference  would  be  less.  A  good  rule  for  figuring  the  arbitrary  allowance  for 
dead-load  moments  (in  case  the  arch  axis  is  made  to  fit  the  dead-load  equilibrium  polygon) 
is  to  assume  an  eccentricity  of  application  of  the  dead-load  thrust  above  or  below  the  axis 
equal  to  one-fortieth  the  depth  of  section. 

DETAILS  OF  ARCH  BRIDGES 

37.  Spandrel  Details  in  Earth-filled  Bridges. — The  filling  material  in  solid-spandrel 
bridges  is  held  in  place  laterally  by  retaining  walls  which  rest  upon  the  arch  ring.  These  retain- 
ing walls  may  be  of  either  the  gravity  or  the  reinforced  type,  or  they  may  consist  of  thin  vertical 
slabs  tied  together  by  reinforced-concrete  cross  walls.  In  the  usual  type  of  solid-spandrel 
construction,  the  sidewalk  rests  upon  the  earth  filling,  which  is  the  type  shown  in  Figs.  25  A  and 
26.    Where  the  counterforted  type  of  spandrel  wall  is  employed,  sidewalks  are  sometimes 


Fig.  25 a. — Details  of  Pine  Street  bridge,  Lima,  Ohio. 


cantilevered  beyond  the  faces  of  the  arch  ring,  as  illustrated  in  Fig.  27.  The  faces  of  spandrel 
walls  may  be  entirely  plain,  or  panels  of  approximately  a  triangular  shape  may  be  formed, 
either  by  indenting  the  portion  above  the  arch  ring  or  by  nailing  beveled  strips  to  the  form- 
work.    Brick  and  stone  are  used  in  some  cases  as  a  facing  for  arch  rings  and  spandrel  walls. 

Figs.  25A  and  25B  show  a  portion  of  a  flat-arch  bridge  designed  for  the  city  of  Lima,  Ohio. 
The  spandrel  walls  are  of  the  reinforced  cantilever  type. 

A  bridge  with  gravity  spandrel  walls  is  shown  in  Fig.  26.  The  brick  facing  for  the  arch 
ring  and  the  cast  concrete  and  brick  belt  courses  should  be  noted.  The  spandrel  walls  rest 
partly  on  the  brick  facing  and  partly  on  the  concrete  portion  of  the  arch,  and  are  keyed  into 
the  concrete  portion  by  means  of  a  projection  which  fits  into  a  6  by  12-in.  groove  in  the  arch. 

A  counterforted  type  of  spandrel  wall  is  shown  in  Fig.  27.  These  walls  are  12  in.  thick 
and  are  reinforced  on  both  faces  with  a  double  system  of  rods.  The  counterforts  occur  at 
about  9-ft.  intervals,  and  cantilever  brackets  are  placed  at  these  counterforts  to  support  the 
sidewalks.    The  following  description  is  taken  from  Engineering  Record,  Feb.  22,  1913. 

The  entire  width  of  the  arch  ring  between  outside  faces  of  spandrel  walls  is  35  ft.,  and  the  roadway  above  is 
39  ft.  wide,  thus  giving  an  overhang  of  2  ft.  on  each  side  of  the  bridge  between  the  curb  lines.  This  2-ft.  overhang 
constitutes  the  concrete  gutter  of  the  roadway  and,  as  such,  will  be  subject  to  heavy  concentrated  wheel  loads  com 


692 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-37 


ing  upon  the  cantilever  section.  It  was,  therefore,  built  as  a  heavily  reinforced  concrete  beam.  This  beam  is 
2  ft.  9  in.  wide,  having  a  depth  of  15  in.  at  the  spandrel  wall  and  10  in.  at  the  curb,  and  is  reinforced  with  fourteen 
^i-in.  rods,  with  additional  reinforcement  at  the  brackets. 

The  bridge  is  designed  for  trolley  traffic,  and  provision  is  made  for  the  trolley  poles  by  anchoring  sections  of 
10-in.  cast-iron  water  pipe  in  the  brackets  of  the  piers  and  abutments.  Drainage  is  provided  by  means  of  6-in. 
cast-iron  drains  in  the  gutters  over  the  piers. 


1!  'ii^-^".s"Laj  Bolt 

SecTion 

Details  of  Railfng 


Fig.  255. — Details  of  Pine  Street  bridge,  Lima,  Ohio. 

Details  of  the  arch  bridge  over  the  Olentangy  River  on  King  Avenue,  Columbus,  Ohio, 
is  shown  in  Figs.  28 A,  285,  and  28C.  The  type  of  spandrel  walls  without  pilasters  over  piers 
should  be  noted.  Since  the  space  beneath  each  sidewalk  is  hollow,  the  inner  wall  was  designed 
as  a  slab  with  the  principal  steel  placed  horizontally  between  cross  walls.  The  longitudinal 
walls  under  the  car  track  were  employed  to  prevent  the  usual  settlement  of  the  track  when 
laid  on  a  new  fill.  The  ties  were  laid  directly  on  top  of  these  walls  and  earth  filling  was  dumped 
both  sides  of,  and  also  between,  the  longitudinal  walls. 


Sec.  16-37] 


ARCHES 


693 


Side  Elevation  Section  A-A 

Fig.  27. — Counterforted  spandrel  wall,  highway  bridge  at  Ansonia,  Conn. 


694 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-38 


Drains  should  be  placed  on  each  side  of  the  roadway  of  a  concrete  bridge  at  intervals  of 
30  to  40  ft.  when  the  roadway  is  level  and  about  every  100  ft.  when  on  a  grade.  These  drains 
should  have  a  diameter  of  not  less  than  3  in.  The  minimum  area  of  a  drain  in  square  inches 
may  be  computed  by  the  formula 

A 

^=200 

where  A  =  area  of  the  surface  drained  in  square  feet. 

One  type  of  expansion  joint  in  a  simple  cantilever  wall  is  shown  in  Fig.  29. 


Elevation 

Fig.  28 a. — Elevation  of  west  end  of  Olentangy  River  bridge  on  King  Avenue,  Columbus,  Ohio. 


Fig.  28B. — Details  of  west  abutment,  Olentangy  River  bridge  on  King  Avenue,  Columbus,  Ohio. 


38.  Spandrel  Details  in  Open-spandrel  Bridges. — The  general  types  of  open-spandrel 
bridges  have  been  described  in  Art.  3.  Figs.  30  to  35  inclusive  will  serve  to  illustrate  details 
of  some  of  these  types. 

Fig.  30  shows  a  full-barreled  arch  reinforced  with  typical  Melan  trusses  made  up  of  3  by 
3  by  ^{e-in.  angles  and  2}i  by  }i-m  lattice  bars.  The  floor  system  is  carried  on  a  series  of 
transverse  spandrel  walls  and  the  floor  slab  is  provided  with  expansion  joints  as  shown.  The 
sidewalks  leave  an  overhang  of  about  3  ft.  and  are  supported  on  cantilever  brackets.  The 


Sec.  16-38] 


ARCHES 


695 


e8-6 

Half  Plan  of  Pier 


[j  U  U  J  U  L 


U  u  J  J  l] 


Half  Sec+ion  at  Pier 


Fig.  28C, — Details  of  Olentangy  River  bridge  on  King  Avenue,  Columbus,  Ohio. 


Sheet  Lead  ■  ■ 
j' "  thick 

Top  of   

batter  of 
spandrel  wall 


Inside  Elevation 
of  Expansion  Joint 


•  Sheet 
asphalt  ^ 
or  its 
equivalent 

■■■  Bottom  of 
batter  erf 
spandrel  wall 


.  Sheet  Lead 
/  'thick 


Section  A-A 


i'.i" Soft  wood 
Strip 

Sheet  Lead _ 
^' thick- 


Sheet 
"^^  '  Asphalt 

Section  B-B 

Fig.  29. — Details  of  expansion  joint  in  highway  arch  bridge  over  Chattahoochee  River  at  Columbus,  Georgia* 


696 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-38 


Longitudinal  Section 


  8o'-o"   ■> 

Half  Section  through  Crown  of  llO-foot  Arch 


Fig.  31. — Details  of  Penn  Street  viaduct,  Reading,  Pa. 


Sec.  16-38J 


ARCHES 


697 


Expansion  Joint 


Bottom  of  file  to  be  flush 
*y/fh  slab  at  high  points 


y^sbesfos 


^,.4 "Ha If  Tile  fz'long 


Board 
S" Sheet  Iron  --" 
Downspout  extend- 
ing thru  arch  rinj 


6      Strip  of/lsbestos  Board 

-3"  Drain  Tile 

?"°fods,  6"c  ioc.  £'3"ionj 
along  expansion  joint 


Section  throu'gh  Expansion  Joint 
at  Center  Drain 


'■■•■s"''f?ods  /3'lonj 


s''o/?od  lO' lonq 
8 

Mole  for  Trolley  Pole  ^ 


l"''lfo.ds  4'-9"  lon^ 


4Lo''.'.-^ '-I'"- Pods  b^nf up 

from  bottom  of 
Section  B-B  cantilever 

4'.6". 


Section  C-C 


rrtx 

■  ■ 


Section  A-A 


,3 ' Tile  Drain 


6",^" Strip  of 
Asbestos  Board 


-r--^T-+-^-^4 


,rr, 


Section  E-E 
Section  D-D 

Fig.  32^.— Details  of  the  Dallas-Oak  Cliff  viaduct,  Dallas,  Texas. 


698 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-38 


Sec.  16-38] 


ARCHES 


699 


Fig.  34. — Wisconsin  approach  to  high  wagon  bridge  at  Winona,  Minn. 


700 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-38 


Fig.  35. — Bridge  over  ravine  on  Mississippi  River  Boulevard,  St.  Paul,  Minn. 


Sec.  16-38] 


ARCHES 


701 


Longitudinal  Sectior; 

FiQ.  37.— Elk  Run  bridge  across  Cedar  River,  W.  C.  F.  &  N.  Ry, 


702 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-39 


cantilever  section  of  the  sidewalk  is  cast  in  units  5  ft.  long  and  laid  in  place.  Tile  conduits  are 
provided  under  each  sidewalk  for  necessary  wires,  and  a  4-in.  gas  pipe  and  12-in.  water  main 
are  laid  in  specially  designed  reinforced-concrete  troughs  beneath  the  roadway. 

Transverse  spandrel  walls  with  openings  to  save  material  are  shown  in  Figs.  32A  and  32B. 
The  method  of  carrying  the  sidewalk  should  be  noted. 

The  curtain  walls  between  columns  in  Fig.  33  were  considered  simply  as  a  bracing  system. 
The  columns  were  designed  to  carry  all  loads,  but  doubtless  the  curtain  walls  help  to  distribute 
the  total  loading.  In  taking  the  loading  for  the  arch  rings,  it  was  assumed  that  the  loadiag 
from  columns  was  equally  distributed  over  12  ft.  of  arch  ring  instead  of  having  two  loads  con- 
centrated on  an  arch  ring  16  ft.  wide. 

39.  Piers  and  Abutments. — The  resistance  offered  by  piers  to  the  passage  of  water  varies 
with  the  type  of  starling.  Experiments  show  that  the  value  in  this  respect  of  the  different 
shapes  of  piers  is  in  the  following  order:  first,  elliptical  horizontal  sections;  second,  rectangular 
body  with  starlings  formed  by  two  circular  arcs,  tangent  to  the  sides  and  described  on  the  sides 
of  an  equilateral  triangle;  third,  rectangular  body  with  semicircular  starlings;  fourth,  rectangular 
body  with  triangular  starlings,  the  angle  at  the  nose  being  90  deg. ;  and  fifth,  rectangular  body 
without  starlings. 

The  ordinary  type  of  abutment  in  earth-filled  arches  is  shown  in  Figs.  36  and  37.  What 
might  be  called  a  buttressed  abutment  is  shown  in  detail  in  Fig.  2SB.  Fig.  38  represents  a 
very  wide  abutment  in  which  a  network  of  rods  has  been  employed  to  make  the  entire  abutment 
act  as  a  unit.    Hollow  piers  for  ribbed-arch  structures  are  shown  in  Figs.  31  and  33. 


Fig.  38. — Abutment  of  causeway  arch  construction,  Galveston,  Texas. 


40.  Railing  and  Ornamental  Details. — A  spindle  balustrade  is  the  common  type  of  railing. 
In  such  railings  the  spindles  or  balusters  are  usually  the  only  members  which  are  not  cast  in 
place.  Expansion  joints  should  be  provided  each  side  of  the  posts  and  also  over  the  spandrel 
joints.  Railing  and  ornamental  details  of  various  kinds  are  shown  in  Figs.  25B,  2SC,  30  and 
S2B. 

CONSTRUCTION  OF  ARCHES 

41.  Arch-ring  Construction. — Arch  rings  with  span  lengths  less  than  about  90  ft.  are 
usually  constructed  in  longitudinal  ribs  3  or  4  ft.  wide,  or  in  fact  of  such  a  width  that  one  entire 
rib  can  be  poured  in  approximately  1  day's  time.  In  narrow  arches  the  entire  arch  ring  is 
sometimes  poured  at  one  operation.  This  method  of  construction  has  been  successfully  used 
for  much  greater  spans  than  90  ft.  but,  unless  special  care  is  taken  to  make  the  centering  very 
stiff,  the  construction  of  any  one  rib  may  defo'rm  the  arch  center  to  such  an  extent  as  prac- 
tically to  strike  the  center  under  the  completed  ribs.  Of  course,  the  ribs  should  be  poured 
continuously  from  each  abutment  toward  the  crown  so  as  to  obtain  a  symmetrical  loading  on 
the  falsework  and  thus  eliminate  distortion  of  the  centering  so  far  as  possible. 


Sec.  16-41] 


ARCHES 


703 


For  spans  of  90  ft.  or  over  it  is  usually  preferable  to  construct  an  arch  ring  or  arch  rib  by 
what  is  known  as  the  alternate  block  or  voussoir  method.  The  arch  is  constructed  in  transverse 
blocks  of  such  size  that  each  block  can  be  completed  at  one  pouring,  or  with  about  a  day's 
work.    Obviously  this  method  reduces  shrinkage  stresses  in  the  arch  ring  to  a  minimum. 

For  the  best  results  the  blocks  should  be  poured  in  such  order  as  to  give  a  uniform  settle- 
ment of  the  centering,  and  also  prevent  the  crown  of  the  arch  from  rising  as  the  lower  arch 
loads  are  placed.  If  blocks  close  to  the  crown  section  are  not  placed  before  the  blocks  at  the 
haunch  and  springing  sections,  the  centering  will  rise  at  the  crown  and  the  placing  of  the  crown 
loads  will  be  likely  to  cause  cracks  at  the  middle  of  the  haunch.  Even  in  the  construction  of 
an  arch  by  the  longitudinal-rib  method,  a  temporary  loading  of  the  crown  is  often  necessary. 

The  order  followed  in  the  construction  of  the  Philadelphia  and  Reading  R.  R.  bridge  across 
the  Delaware  River  at  Yardley,  Pa. — an  earth-filled  bridge  with  clear  span  of  90  ft.  9  in. — is 
shown  in  Fig.  39,  the  sections  being  concreted  in  the  alphabetical  order  shown.  The  section 
D  is  the  keying  section,  and  the  section  E  a  haunching  section  (quite  unusual  construction) 
which  was  added  after  the  lower  portion  of  the  arch  ring  was  completed.  The  part  of  the  arch 
ring  close  to  the  springing  lines  was  placed  monolithic  with  the  piers  and  abutments,  making 


Fig.  39.  Fig.  40. 

what  is  called  an  umbrella  form  for  the  piers.  In  large  arches  this  umbrella  type  of  construction 
is  frequently  adopted.  The  pier  forms  in  such  cases  are  more  expensive,  but  this  increase  in 
expense  for  the  piers  is  usually  more  than  offset  by  the  saving  in  the  falsework  for  the  arch 
ring. 

Fig.  40  shows  the  method  of  constructing  the  Larimer  Avenue  bridge  at  Pittsburgh — a 
bridge  of  the  open-spandrel  type,  with  two  ribs,  having  a  clear  span  of  approximately  300  ft. 
The  blocks  were  placed  in  alphabetical  order  and  later  the  keys  between  them  were  concreted 
to  make  the  closure. 

In  constructing  an  arch  rib  or  arch  ring  by  the  alternate  block  method  the  individual 
sections  or  block  spaces  are  closed  off  at  the  ends  by  timber  bulkheads.  On  the  steepest  slopes 
of  the  lagging  these  bulkheads  adjoining  keying  sections  are  held  in  place  by  temporary  struts 
between  voussoirs.  ^  top  form  is  usually  needed  for  the  block  sections  near  the  piers  and  abut- 
ments.   This  top  form  should  be  laid  up  as  the  concreting  progresses. 

If  arch  reinforcement  for  large  arches  is  put  in  place  in  long  lengths,  the  settlement  and 
deformation  of  the  centering  during  the  pouring  of  the  concrete  will  cause  buckling  of  the  steel 
which  will  prevent  the  reinforcement  from  lying  in  its  theoretical  position.  For  this  reason 
steel  lengths  should  not  exceed  about  30  ft.  and  the  splicing  should  occur  in  the  keyways.  An 
effort  should  be  made  to  stagger  the  splices  of  adjacent  rods  and  to  locate  the  splices  where  the 
tension  in  the  steel  is  a  minimum. 

The  upper  reinforcement  in  arch  rings  may  be  kept  in  position  either  by  means  of  spacing 
boards  nailed  to  props  or  by  the  steel  being  wired  directly  to  transverse  timbers  supported  above 
the  surface  of  the  finished  concrete.  In  the  first  method  mentioned,  the  props  and  spacing 
boards  must  be  knocked  out  as  the  concrete  is  brought  up  with  likelihood  of  disturbing  the  steel. 

When  steel  ribs  (either  rolled  sections  or  built-up  lattice  girders)  are  used  as  arch  reinforce- 
ment, great  care  should  be  taken  to  fix  the  ribs  in  the  proper  position,  and  in  this  position  they 


704 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-42 


should  be  braced  until  the  concrete  is  placed.  The  use  of  such  ribs  is  known  as  the  Melan 
system. 

Spandrel  walls  for  earth-filled  arches  are  either  built  on  top  of  the  arch  ring,  or  include  a 
portion  of  the  arch,  the  bottom  inner  edge  of  the  spandrel  retaining  wall  lapping  a  short  dis- 
tance over  the  completed  arch  ring. 

42.  Centering. — The  bent  type  of  timber  falsework  is  the  type  of  centering  generally 
employed  in  arch  construction  except  where  a  deep  gorge  is  to  be  spanned  or  where  a  large 
clearance  under  the  arch  is  necessary  while  the  bridge  is  under  erection.  Timber  arches,  Howe 
trusses  and  bowstring  trusses  are  sometimes  employed  when  it  is  impossible  to  use  the  bent 
type  of  centering,  but  these  forms  are  expensive  to  build,  deform  badly  under  loading,  and  have 
but  small  salvage  value.  Before  using  any  of  these  types,  consideration  should  be  given  to  the 
use  of  steel  centers. 


Fig.  41. — Common  form  of  timber  centering  for  arches  of  low  rise. 


42a,  Timber  Centers. — simple  and  common  form  of  timber  centering  for  arches 
of  low  rise  is  shown  in  Fig.  41.  The  lagging  had  not  been  placed  at  the  time  this  photograph 
was  taken,  but  some  of  the  joists  for  supporting  the  lagging  were  already  in  place.  The  joists, 
of  course,  extended  from  abutment  to  abutment  and  were  supported  by  transverse  bents  of 
round  timber  resting  on  sills  the  full  length  of  each  bent.  The  falsework  rested  on  the  con- 
crete floor  of  a  spillway  channel  so  that  mud  sills,  piles,  or  specially  constructed  concrete 
footings  were  not  necessary.  Wedges  were  placed  at  the  bottom  of  the  posts  so  that  the  center 
might  be  lowered  conveniently  after  the  arch  ring  was  completed  and  ready  to  bear  its  load. 

The  centering  used  in  the  Third  Avenue  bridge  at  Cedar  Rapids,  Iowa,  is  shown  in  Fig. 
42.  In  a  paper  presented  before  the  Western  Society  of  Engineers,  April  13,  1914,  Barton  J. 
Sweatt  described  the  construction  of  this  centering  as  follows : 

The  falsework  for  supporting  the  arches  consisted  of  pile  bents,  the  first  bent  being  6  ft.  6  in.  from  the  face  of 
piers  and  abutments,  the  second  bent  12  ft.  6  in.  from  the  first,  and  the  intermediate  bents  were  14  ft.  6  in.  centers. 
Oak  piles  were  used  and  as  a  rule  were  driven  to  bed  rock,  the  spacing  was  6  ft.  0  in.  for  the  three  outside  piles  and 


Sec.  16-42a] 


ARCHES 


705 


8  ft.  0  in.  for  the  intermediate.  The  caps  used  were  12  by  12-in.  yellow  pine,  false  caps  6  by  10  in.,  joists  4  by  14 
in.,  spaced  24  in.  on  centers  and  the  lagging  was  2  by  8  in.  The  proper  curve  for  the  intrados  was  obtained  by 
the  use  of  2-in.  strips  out  to  the  proper  curve  and  tacked  to  the  regular  joists.  Oak  wedges  were  used  between  the 
main  and  false  caps.  These  wedges  were  placed  in  pairs  and  spaced  about  4  ft.  apart.  Small  wedges  were  used 
under  the  ends  of  the  joists  to  bring  them  to  the  proper  height. 

In  constructing  the  centering,  an  allowance  of  IVz  in.  was  made  for  camber  and  in.  for  settlement  after  the 
centering  was  removed.    The  actual  settlement  of  the  crown  after  removing  the  centering  was  %  in. 


Z' Circle  Strips. 
Z\l0"-2'-0'c.fO 


11 

4'jr/4  "Jo Is  ts  ■  ?4  "c.  io  c\  \ 
(f^of  double) 

2"  Filler.     ^  ^"B'x  l6'-o"  Yellow  P/ne  Shsefin^..         \  |.? 
6"xl0'L.^^ 
SjDriffs 


I "  Bolts 


Oair  Piles  .■rf 
driven  to 
rock 


Haff  Side  View  Secrion  showing  Half  erf  Center  Bent 

Fig.  42. — Centering  for  Third  Avenue  bridge.  Cedar  Rapids,  Iowa. 


All  Plumb  Posts,  Caps,  and  Stringers  -  6"k  8"  Yellow  Pine  Timber 
All  Batter  Posts-  4"x  6"  Y.P  Timber 
Arch  Pibs -  £"xiz''  Y.P  Timber 

Arch  Flooring- £''x  lo"  Y  P  Timber  ^ 

Other  Braces  -  Z''x  e"  YP  Timber  X 

 vi- 


FiG.  43. — Falsework  and  centering  for  Cleveland  Avenue  bridge,  Kansas  City,  Mo.    Note  structural  steel  girder 
carrying  the  center  of  the  span  to  allow  for  flood. 


An  article  in  Cement  Age,  March,  1912,  describes  the  construction  of  the  centering  shown 
in  Fig.  43  in  the  following  manner: 

The  centering  for  the  arch  consisted  of  four  pile  bents  of  four  piles  each,  and  two  center  pile  bents  of  five  piles 
each.  These  bents  were  capped,  top  of  caps  being  elevation  of  spring  line  of  arch,  and  four  lines  of  6  by  8-in. 
stringers  were  placed  continuous  from  abutment  to  abutment — the  ends,  at  elevation  of  the  spring  line,  bearing  4 

45 


706 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-42a 


in.  on  the  concrete  abutments.  At  completion  the  ends  of  stringers  were  bored  out  and  the  holes  in  the  abutments 
tilled  with  concrete.  On  these  four  lines  of  stringers  were  placed  a  set  of  pine  wedges  over  each  pile,  there  being 
four  and  five  sets  of  wedges  to  each  bent,  and  3  by  12-in.  timber  was  laid  on  the  wedges  over  each  bent  through  the 
width  of  the  arch.  On  these  3  by  12-iH.  timbers,  the  arch  bents  were  erected,  each  having  four  and  five  6  by  8-in. 
vertical  posts  V-braced,  with  6  by  8-in.  caps  set  edgeways,  top  of  caps  12  in.  below  intrados  of  arch.  On  these 
caps  were  placed  2  by  12-in.  ribs,  dapped  to  take  square  bearings  on  caps.  These  ribs  were  placed  18  in.  centers 
across  the  arch  and  were  cut  from  timber  of  sufficient  dimensions  to  make  them  lap  over  alternate  caps.  The  ribs 
were  covered  with  2-in.  planking  to  form  the  intrados  of  the  arch. 


Fig.  44. — Details  of  arcli  centers  for  proposed  renewal,  C.  R.  R.  Co.  of  N.  J. 

A  very  simple  and  accurate  method  of  laying  out  the  ribs  was  used  which  consisted  of  laying  out  the  full-size 
arch  intrados  radii  on  a  level  place  near  the  bridge  site.  The  timber  for  the  ribs  was,  therefore,  marked  by  a  full- 
size  drawing.  Probably  the  most  interesting  feature  of  this  arch  centering  was  the  simple  straight  work  giving 
maximum  strength  and  maximum  safety  in  every  respect  at  the  lowest  cost.  The  five  steel  floor  beams  of  the  old 
bridge  were  utilized  to  make  an  18-ft.  clear  opening  of  maximum  height  in  the  centering.  This  was  economical, 
as  it  saved  one  pile  bent  and  one  centering  bent,  but  its  main  purpose  was  to  allow  drift  to  pass  through  in  case  of 
high  water  during  construction. 

Figs.  44,  45,  46  and  47  show  timber  centers  similar  to  the  one  just  described. 


Sec.  16-42a] 


ARCHES 


707 


A  patented  type  of  centering  is  shown  in  Fig.  48,  known  as  the  Luten  arch  centering.  The 
idea  in  this  center  is  to  dispense  with  the  usual  wedges  employed  in  lowering  the  falsework. 
The  top  part  of  the  uprights  consists  of  two  thin  members  with  major  dimensions  transverse  to 
each  other.  These  are  arranged  in  the  form  of  a  T-column,  and  wired  together  at  frequent 
intervals.  Each  member  separately  is  made  too  light  to  carry  its  loading  so  that  clipping  the 
wires  permits  each  member  to  buckle,  which  lowers  the  center. 


e"  Beveled  Filler 
Stringers  not  notched 


■  8-6  ;'->k  8-6' 

Mud  Sills  if  required 


Elevation 

All  lumber  to  be  Yellow  Pine  unless 
othenvise  stated     All  bolts, with 
tnv  standard  C.  I  was  tiers     Lagging  to  be 
matched  and  dressed  to  a  oniform  thickness 
so  as  to  form  a  smooth  and  true  surface. 
/II/  lagging  to  be  z"x 4"  tongue  and  grooye 


Elev.  219.00 
All  sills  to  be  laid  On 
solid  surface  blocked 
where  necessary 


Wedge 
(  White  Oak) 


.Zx4  Lagging 


iritnninnninnririnnnnnnrinif 


Section  A- A 

Fig.  45. — Details  of  arch  centers  for  Center  Street  bridge,  Phillipsburg,  N.  J. 


W.  W.  Washburn  in  an  article  in  Concrete-cement  Age,  August,  1914,  writes  as  follows  in 
regard  to  the  centering  shown  in  Fig.  49: 

Since  Buffalo  Bayou  is  a  navigable  stream,  it  was  necessary  to  leave  an  opening  in  the  arch  centering  for 
the  passage  of  tugs  and  boats  during  construction.  This  opening  was  24  ft.  vertically  above  average  water  level 
and  38  ft.  wide.  Protection  piles  on  each  side  of  the  passageway  were  necessary,  consequently  the  total  span  of 
the  opening  in  the  arch  centering  was  49  ft.  To  carry  the  load  over  this  opening  nine  30-in.,  200-lb.  I-beams  were 
used.    These  I-beams  will  be  used  in  the  construction  of  other  bridges. 

Longitudinal  bracing  was  arranged  so  as  to  counter,  as  much  as  possible,  the  "bucking  up"  tendency  of  the 
centering  at  the  crown  as  the  arch  was  concreted.    On  account  of  the  arch  being  skewed,  special  study  was  given 


708 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-42a 


Sec.  16-42a] 


ARCHES 


709 


during  the  placing  of  braces,  etc.,  so  as  to  take  care  of  all  side  thrusts.  Struts  were  placed  diagonally  between 
bents  at  right  angles.    Spacing  of  centering  piles  was  such  that  no  pile  received  a  load  of  over  12  tons. 

Timber  centering  for  a  bridge  over  railroad  tracks  at  Fall  River,  Mass.,  is  shown  in  Fig.  50 
and  described  in  Engineering  Record,  April  26,  1913,  as  follows: 

In  building  the  arch  centering  it  was  necessary  to  provide  for  certain  requirements  that  necessitated  a  design 
similar  to  the  one  shown  in  the  accompanying  drawing. 

These  requirements  called  for  an  overhead  clearance  of  18  ft.  at  a  point  11  ft.  3  in.  from  the  property  lino,  a 
clear  span  of  40  ft.  between  inside  vertical  posts,  and  a  minimum  clearance  of  15  ft.  from  the  top  of  rail  to  the  under 


Fig.  47. — Falsework  for  bridge  over  Big  Muddy  River,  I.  C.  R.  R. 


2" Facing   


5>K   n'-9"  »•>}<••••    13'- ii' 

Level  Line  -a  ^1    


Section  parallel  to  Roadway 
{96' Span) 


Half  Cross  Section  ^ 
perpendicular  to 
Center  Line  of  Road 

Fig.  48. — Centers  of  Luten  Design  for  Cicott  Street  bridge  over  Wabash  River,  Logansport,  Ind. 


side  of  the  truss.  The  work  had  to  be  conducted  without  interruption  of  train  service.  The  uprights  supporting 
the  centering  were  carried  on  concrete  mud  sills  and  2-in.  tongue-and-groove  lagging  was  used  over  the  entire 
arch  ring.    The  centering  was  designed  for  a  deflection  equal  to  one  eight-hundredth  of  the  span. 

Figs.  51A  and  515  show  the  type  of  arch  centering  used  in  constructing  a  three-ribbed 
arch  on  the  Mississippi  River  Boulevard,  St.  Paul,  Minn.    Boxing  for  the  ribs  is  also  shown. 

Posts  in  timber  centering  have  sometimes  been  placed  approximately  normal  to  the  arch 
soffit,  but  such  instances  are  quite  rare.    Since  specially  constructed  footings  are  necessary 


710 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-42a 


for  inclined  members,  this  form  of  center  may  be  used  economically  only  when  rock  or  other 
suitable  foundation  lies  near  the  ground  surface. 

Sand  boxes  have  been  used  to  a  very  limited  extent  in  this  country  in  place  of  wedges  for 
the  striking  or  lowering  of  arch  centers.  These  boxes  have  given  satisfaction  in  most  instances, 
but  great  care  must  be  taken  to  keep  the  sand  dry  while  the  arch  ring  is  being  constructed. 
This  type  of  lowering  device  is  expensive,  but  the  extra  first  cost  may  be  offset  in  large  arches 
by  the  high  cost  of  striking  wooden  wedges. 


Fig.  49. — Details  of  arch  centering  and  supports  for  110-ft.  span  of  San  Jacinto  bridge,  Houston,  Texas.  Note 

size  of  opening  for  navigation. 


z" Sheathing 


<  -  4o'-o"-  3. 

 Clear  Span  82- 6  '  

■■■       ■                •■•    Concre-K  Mud  Sills  '  _ 

Fig.  50. — Highway  bridge  at  South  Park,  Fall  River,  Mass.,  over  tracks  and  right-of-way  of  the  N.  Y.,  N.  H.  & 

H.  R.  R. 


The  chief  disadvantage  of  using  sand  boxes  lies  in  the  fact  that  the  sand  will  compress  as  the 
weight  on  the  centering  increases.  The  amount  of  this  compressibility  is  considerable,  greatly 
increasing  deflection  unless  the  sand  is  put  under  an  initial  compression,  which  is  seldom  feasible. 

A  sand  box  used  in  the  main  arch  of  the  Edmondson  Avenue  bridge,  Baltimore,  is  shown  in 
Fig.  52.  The  center  was  lowered  by  allowing  the  sand  to  run  out  through  a  1-in.  circular  hole 
in  the  oak  bottom  of  the  steel-plate  cylinder.    This  hole  was  closed  by  a  wooden  plug  while 


Sec.  16-42a] 


ARCHES 


711 


Fig.  51B. — Rib  boxing  for  bridge  over  ravine  on  Mississippi  River  Boulevard,  St.  Paul,  Minn. 


}6"~ Diameter  Oak  Cy  I'm  den 


y±'^'-'-Felf  Paper 

Cylinder 


Oafr  Cylinder* 

Fig.  52. — Sand  box. 


712 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  l"6-42fe 


the  centering  supported  its  load.  A  disadvantage  in  the  use  of  sand  boxes  lies  in  the  fact  that 
the  centering  cannot  be  raised  before  the  arch  ring  is  poured  in  order  to  adjust  the  top  members 
to  the  curve  of  the  arch  intrados. 

In  the  design  of  large  arch  centers  an  uncertainty  exists  regarding  the  pressures  from  vous- 
soirs  placed  on  the  steepest  portions  of  the  lagging.  Either  of  two  assumptions  are  usually- 
made  as  to  the  forces  acting  on  the  centering  due  to  the  weight  of  such  voussoirs.  In  the 
common  method  of  design,  the  assumption  is  made  that  the  centering  sustains  only  the  radial 
components  of  the  voussoir  weights,  the  tangential  components  being  resisted  by  temporary 
struts  between  voussoirs  so  as  to  be  transferred  to  the  abutments.  The  more  accurate  method 
is  to  assume  that  tangential  pressures  (in  addition  to  the  radial  pressures)  act  on  the  centering 
which,  from  any  voussoir,  may  be  as  great  as  the  product  of  the  radial  component  and  the  coeffi- 
cient of  friction  between  the  voussoirs  and  lagging.  The  original  tangential  component  is 
then  reduced  by  this  amount. 

Since  a  timber  center  is  only  a  temporary  structure  and  has  a  high  salvage  value,  great 
accuracy  in  the  design  of  the  separate  members  is  not  necessary.  The  method  of  design  need 
only  be  such  that  the  size  of  each  member  is  well  on  the  safe  side.  Then,  too,  rigidity  is  quite 
as  important  as  strength,  so  that  all  things  considered,  close  figuring  is  out  of  the  question. 
Obviously  the  weight  of  centering  may  be  omitted  except  for  high  arches.  For  the  method  of 
designing  lagging,  joists,  and  posts  see  Arts.  65  and  66,  Sect.  2. 

As  a  rule,  only  hardwood  should  be  used  for  caps  and  sills,  although  long-leaf  pine  may  be 
sufficiently  hard  in  many  cases.  Wedges,  however,  should  be  made  of  hardwood  without 
exception.  It  is  always  advisable  to  reduce  the  number  of  joints  in  side-grain  compression  to 
a  minimum  on  account  of  the  low  bearing  value  of  timber  across  the  grain.  Steel  distributing 
plates  are  of  advantage  in  this  connection. 

Care  should  be  taken  to  prevent  lateral  displacement  of  vertical  posts  due  to  radial  pres- 
sure from  the  arch  ring.  This  may  be  avoided  either  by  proper  longitudinal  bracing  or  by 
notching  out  the  joists  and  shimming  them  tight  against  the  caps. 

Many  practical  notes  on  the  design  and  erection  of  falsework  may  be  found  in  Sect.  7 
of  the  "American  Civil  Engineers'  Pocket  Book." 

In  striking  arch  centers,  wedges  should  be  lowered  gradually  beginning  at  the  crown  and 
working  toward  the  springing  lines.  The  lowering  should  be  done  symmetrically  with  respect 
to  the  center  of  the  arch  ring.  In  a  series  of  arches,  centers  between  abutments  or  abutment 
piers  should  be  struck  simultaneously.  As  a  rule,  centers  should  not  be  struck  from  arches  in 
less  than  28  days  under  favorable  weather  conditions,  and  it  is  desirable  that  a  longer  period 
should  elapse  if  possible. 

426.  Steel  Centers. — Steel  centers  of  the  arch-trussed  type  should  receive  con- 
sideration when  arches  are  to  be  built  in  series  or  where  the  character  of  the  stream  or  crossing 
renders  timber  and  pile  falsework  impossible  or  expensive.  Undoubtedly  the  cost  of  a  steel 
center  is  usually  high,  but  if  it  can  be  used  a  number  of  times,  as  in  a  large  series  of  arches,  it 
may  not  prove  any  more  costly  than  timber. 

It  is  generally  recognized  that  there  are  some  well-defined  advantages  in  using  three- 
hinged  arch  centers.  In  the  first  place,  the  crown  deflection  using  steel  centers  is  usually  much 
less  than  that  obtained  by  employing  timber  falsework.  Furthermore,  it  is  possible  to  compute 
the  deflection  of  each  point  of  a  steel  center  with  some  degree  of  accuracy  while,  in  the  case  of 
a  wooden  center,  the  probable  settlement  at  each  bent  is  pretty  much  a  matter  of  guesswork. 
Steel  centers  also  have  the  additional  advantages  of  allowing  an  obstructed  opening  for  railroad 
or  other  traffic  and  of  eliminating  danger  from  flood  and  ice  in  the  construction  of  arches  over 
streams.  The  advantage  of  allowing  the  deflection  to  be  quite  accurately  computed  makes  it 
possible  to  give  the  centers  a  preliminary  camber  so  that  when  the  concrete  is  in  place  and  the 
centering  withdrawn,  the  arch  ring  will  assume  its  true  position. 

One  disadvantage  of  using  steel  in  arch  centering  lies  in  the  fact  that  it  is  materially  affected 
by  temperature  changes.  For  this  reason,  in  constructing  large  arches,  only  the  alternate  block 
method  should  be  employed. 


Sec.  16-426] 


ARCHES 


713 


The  steel  centering  used  in  constructing  the  three-span  earth-filled  arch  structure  which 
carries  Atherton  Avenue  in  the  City  of  Pittsburgh  across  the  four  tracks  of  the  Pennsylvania 
Railroad  is  shown  in  Fig.  53.  This  centering,  fabricated  by  the  Blaw  Steel  Cons.  Co.,  consisted 
of  steel  arch  trusses  spaced  5  ft.  5}i  in.  on  centers.  The  trusses  carried  timbers  and  lagging, 
and  were  supported  on  framed  trestle  bents  placed  close  to  the  pier  facfes.  Sufficient  trusses 
were  at  first  erected  to  concrete  one-half  the  width  of  each  arch  ring,  then  the  centers  were  shifted 
transversely  to  themselves  and  the  concrete  placed  for  the  second  half  of  the  structure.  The 
method  used  in  construction  and  the  details  of  the  arch  centering  are  described  in  Engineering 
and  Contracting,  Feb.  19,  1913,  as  follows: 

A  six-post  bent  was  erected  on  the  footing  shelf  of  the  pier,  the  idea  being  to  have  a  bent-post  under  each  arch 
rib.  On  the  bent  caps  over  each  post  was  placed  a  block  and  double  wedge  and  on  these  supports  a  12  by  12-in. 
plate  on  which  rested  the  ribs.    Between  each  pair  of  ribs  a  dolly  was  fastened  to  the  bent-caps. 


The  shifting  of  the  center  to  construct  the  second  half  of  the  arch  was  accomplished  as  follows:  Jacks  were 
set  up  on  the  bent-caps  alongside  the  dollies,  and  a  strain  taken  on  them  until  the  wedges  were  loosened  sufficiently 
to  be  easily  removed.  The  jacks  were  then  lowered  until  the  weight  of  the  centers  rested  on  the  dollies.  To  pre- 
vent the  lagging  and  cross-timbers  from  being  lifted  off  the  ribs  by  sticking  to  the  soffit  of  the  arch  ring,  one  end  of 
the  center  was  lowered  ahead  of  the  other  so  as  to  give  a  stripping  action  in  freeing  the  lagging.  When  lowered 
into  the  dollies  the  whole  center  was  shifted  sidewise  rubbing  on  the  dollies,  until  it  rested  on  the  six-post  bents  under 
the  second  half  of  the  arch.  The  jacks  were  then  placed  on  the  caps  of  the  second  bents  and  the  center  raised  and 
the  blocks  and  wedges  inserted.  A  steamboat  ratchet  was  used  to  pull  the  center  on  the  dollies.  Four  men 
working  8  hr.  shifted  a  center.  Incidentally  the  tie  rods  connecting  the  opposite  ends  of  the  ribs  were  found,  when 
planked  across,  to  provide  a  most  convenient  bridge  for  the  workmen  engaged  in  shifting  and  adjusting  the  centers. 

The  lateral  thrust  on  the  centers  due  to  their  skewed  position  was  taken  care  of  by  suitable  lateral  bracing 
of  the  ribs.  In  anticipation  of  the  center  rising  at  the  crown  in  concreting  from  the  haunches  upward,  the  ribs  were 
anchored  back  to  the  pier  masonry.  The  joining  carried  by  the  ribs  consisted  of  cross-timbers  over  which  were 
notched  stringers  with  curved  top  edges.  The  stringers  were  spaced  IV/i  in.  apart  and  were  lagged  with  ^^-in. 
boards.    The  bearings  of  the  stringer  ends  against  the  piers  were  formed  by  wedges. 

Steel  centering  employed  in  the  construction  of  the  South  Eighth  Street  Viaduct,  Allen- 
town,  Pa.  (a  two-ribbed  arch  structure  of  nine  120-ft.  spans)  is  shown  in  Fig.  54.  The  Engi- 
neering News,  April  17,  1913,  describes  this  centering  as  follows: 


714 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-426 


For  the  nine  120-f t.  arohes  three  full  sets  of  steel  arch  centers  were  used,  using  each  set  for  three  of  the  arches. 
Each  set  of  centers  consisted  of  two  independent-trussed  arches  of  the  outHnes  shown  in  Fig.  54,  each  arch  support- 
ing one  of  the  twin  concrete  arch  ribs  and  being  itself  made  up  of  two  steel  arch  ribs  interbraced  with  steel  struts. 
Across  the  upper  chords  of  these  steel  ribs,  which  were  curved  to  the  curve  of  the  concrete  arch,  was  bolted  the 
wooden  lagging  on  which  the  concrete  was  deposited.  The  twin  centering  arches  were  held  together  by  a  timber 
cross-beam  and  diagonal  steel  rods. 

The  arch  trusses  were  fabricated  in  six  sections  and  riveted  on  the  ground  into  semi-arches,  which  were  lifted 
by  derricks  into  place,  to  be  bolted  at  the  base  to  the  supporting  columns.  At  the  crown  it  was  riveted  solidly  in 
the  bottom  chord,  but  bolted  through  slotted  holes  at  the  upper  chord,  to  insure  the  stress  passing  through  the 
lower  chord. 


Fig.  55. — Arch  rib  forms  on  steel  centers  for  Brooklyn-Brighton  viaduct,  Cleveland. 

The  centers  were  supported  on  inclined  steel  columns  which  footed  on  concrete  steps  purposely  projected 
from  the  main  section  of  the  pier  and  cut  off  after  the  centers  were  struck.  The  base  plates  of  the  columns  rest  on 
cast-iron  wedges  which  in  turn  rest  on  I-beam  grillages,  footing  on  the  aforementioned  concrete  projection.  Be- 
tween the  column  base  and  the  projection,  10-ton  screw  jacks  are  interposed  to  aid  in  the  alignment  and  leveHng 
of  the  centers;  they  are  allowed  to  remain  in  place,  though  the  load  passes  directly  to  the  wedges  which  are  used 
for  striking  centers.  A  U-shaped  clamp,  made  of  a  1-in.  bolt  (not  shown  in  the  drawing)  is  passed  around  each 
pair  of  wedges  to  prevent  any  possible  lateral  motion.  A  similar  bolt  is  used  for  the  same  purpose  higher  up  on  the 
main  column. 


Sec.  16-43] 


ARCHES 


715 


The  unique  feature  in  the  steel  centering  used  in  constructing  the  Tunkhannock  Creek 
Viaduct  on  the  relocation  of  the  Delaware,  Lackawanna,  and  Western  Railroad  was  an  adjust- 
able panel  at  the  crown  of  the  steel  arch  trusses. 

Arch  rib  forms  on  steel  centers  are  shown  in  Fig.  55.  These  forms  were  used  in  constructing 
the  Brooklyn-Brighton  viaduct,  Cleveland. 

THREE-HINGED  ARCHES 

43.  General  Discussion. — An  arch  with  three  hinges  is  statically  determinate  and  conse- 
quently can  be  analyzed  much  more  readily  for  a  given  loading  than  is  possible  in  the  case  of  a 
fixed-ended  or  solid  arch.  Furthermore,  three-hinged  arches  do  not  need  to  be  analyzed  for 
temperature  changes,  the  hinges  allowing  contraction  and  expansion  of  the  ribs  without  causing 
any  stress  throughout  the  arch.  Obviously  this  statement  does  not  take  into  account  the  effect 
which  results  from  friction  on  the  hinges,  but  such  effect  is  usually  considered  to  be  negligible. 
Whether  or  not  hinge  friction  is  likely  to  cause  appreciable  error  in  the  analysis  of  three-hinged 
arches  is  still  a  matter,  however,  in  regard  to  which  there  seems  to  be  a  decided  difference  of 
opinion. 

Three-hinged  arches  are  especially  adapted  to  sites  where  abutments  and  piers  must  be 
founded  on  compressible  soil  or  on  piles.  The  hinges  permit  of  considerable  settlement  without 
failure  of  the  arch  or  without  causing  the  huge  cracks  which  are  sure  to  develop  in  a  fixed-ended 
structure  under  like  conditions.  Of  course,  a  solid  arch  may  be  designed  on  the  assumption 
that  the  abutments  are  yielding,  but  this  is  rarely  done  and 
such  computations  in  any  event  could  not  take  into  account 
such  settlement  as  might  come  from  an  unexpected  source. 

Hinges  in  arch-bridge  construction  are  likely  to  be  an 
expensive  detail,  especially  in  short-span  structures.  The 
claim  is  made,  however,  that  in  arches  of  large  span,  the 
saving  in  concrete  as  compared  with  the  fixed-ended  type 
much  more  than  pays  for  the  hinges. 

44.  Methods  of  Analysis. — Consider  first  the  general 
case  of  an  unsymmetrical  three-hinged  arch  subjected  to  a 
number  of  vertical  concentrated  loads.  By  referring  to 
Fig.  56,  it  is  seen  that  there  are  four  unknown  quantities — 
namely,  the  horizontal  and  vertical  components  of  each  reaction — and  four  independent 
equations  are  necessary  to  solve  for  these  unknowns.  We  have  the  following  three  equations 
from  statics: 

HV  =  algebraic  sum  of  the  vertical  components  =  0. 

ZH  =  algebraic  sum  of  the  horizontal  components  =  0. 

XM  =  algebraic  sum  of  moments  of  all  the  forces  about  any  point  =  0. 

The  additional  equation  may  be  obtained  from  the  fact  that  the  bending  moment  is  zero  at  the 
crown  hinge.    Thus  we  have  the  following  four  equations  with  respect  to  the  arch  of  Fig.  56. 

Fa  +       -  SP  =  0 
Ha  -  Hb  =0 

Taking  moments  about  the  left  hinge 

Heb  -  VbI  +  ^Pa  =  0 
Since  the  moment  at  the  crown  hinge  is  zero 

VaIi  -  Ha!  -  So'iP  {h  -  a)  =  0 
These  four  equations  may  be  solved  simultaneously  to  obtain  the  horizontal  and  vertical  com- 
ponents of  the  two  reactions. 


716 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-44 


The  calculations  may  be  simplified  by  resolving  each  reaction  into  a  vertical  force  and  a 
force  in  the  direction  of  the  closing  chord  (Fig.  57).  The  four  equations  in  this  case  are  as 
follows  (since  Ha  =  Hb  from  Fig.  56) : 

Fi  +  72  -  2P  =  0 
i^i  -  //2  =  0 
-  V2I  +  2Pa  =  0 
Vih  -  So''P  (Zi  -  a)  -//ir  -  0 

or 

Vih  -  2o'^P(Zi  -  a)  -  Hac  =  0 

(The  values  of  V  have  not  been  considered  in  the  first  equation  as  they  are  equal  and  opposite 
in  direction.)  With  the  components  of  either  reaction  determined  by  these  equations,  the  line 
of  thrust  may  be  drawn  throughout  the  arch  as  described  in  Art.  16  for  the  arch  with  fixed  ends. 

It  should  be  noted  that  the  values  of  Vi  and  V2  may  be  obtained  from  the  above  equations 
(or  by  using  SAf  =  0  at  both  points  A  and  B)  in  the  following  form: 

Vi  =1  SF(Z  -  a)  (1) 


I 

V2  =  \  ^Pa 


(2) 


These  forces  are  thus  identical  with  the  reactions  of  a  simple  beam  of  the  same  span  and  similarly 
loaded. 


Fig.  57. 


(3) 


The  bending  moment  at  any  point  K  (Fig.  57)  may  be  expressed  as  follows* 

M  =  VxX  -  llQ^'Pix  -  a)  -  Hav' 
=  Mk  -  HaV 

where  Mr  is  the  bending  moment  at  the  point  K  of  a  similarly  loaded  beam.  At  the  crown 
hinge,  letting  Mc  denote  the  moment  of  the  vertical  forces  about  the  point  C,  we  have 

M  =  Mc  -  Hac  =  0 

or 

Ms 

c 


(4) 


Equations  (1)  to  (4)  inclusive  are  the  formulas  commonly  employed  in  the  analysis  of  three- 
hinged  arches — supplemented,  of  course,  with  the  force  and  equilibrium  polygons  as  in  the  case 
of  arches  with  fixed  ends. 

For  symmetrical  arches,  Hi  and  H2  are  horizontal  and  the  line  of  thrust  need  be  drawn  for 
onlj^  one-half  the  arch  when  the  loading  is  symmetrical  about  the  crown  hinge.  In  such  a 
case  of  loading,  the  thrust  at  the  crown  hinge  is  horizontal  and  the  line  of  thrust  may  be  deter- 
mined by  trial  in  the  manner  described  in  Art.  11.  This  trial  method  gives  exact  results 
when  applied  to  a  three-hinged  symmetrical  arch  on  account  of  there  being  two  known  points 
(hinge  points)  on  the  line  of  thrust  for  each  half  of  arch. 


Sec.  16-45] 


ARCHES 


717 


The  computations  for  uniform  live  loading  are  extremely  simple  and  should  be  made 
separately  from  those  for  dead  load  or  concentrated  live  loads.  For  full  loading,  with  the 
crown  hinge  at  mid-span,  formula  (4)  gives 

H.=l-^  (5) 

where  w  is  the  uniform  load  per  foot.  The  following  equation,  determined  by  substituting 
in  formula  (3)  gives  the  bending  moment  at  any  point  (coordinates  x  and  y) : 

M  =  -^wx{l  -x)  -  -~-y  (6) 

(For  an  arch  of  parabolic  form,  M  =  0,  and  only  axial  stress  occurs  throughout  the  arch  for 
full  uniform  loading.)    With  only  one-half  of  the  span  loaded 

or  one-half  that  due  to  full  loading.  The  bending  moment  at  any  point  in  the  loaded  half 
equals 

1  1  7/;/2 

M  =  ^  wx{Zl  -4:x)  -^'—-y  (8) 


and  in  the  unloaded  half 


16  c 

TIT        1      7  1  '^^^ 


(In  equations  (8)  and  (9),  the  value  of  x  is  measured  from  that  end  of  the  arch  which  is  nearer 
to  the  point  in  question.) 

A  three-hinged  arch  is  commonly  analyzed  for  (1)  dead  and  uniform  live  load  over  the 
entire  span,  (2)  for  dead  and  uniform  live  load  over  the  right  half  of  span,  and  (3)  for  dead  and 
uniform  live  load  over  the  left  half  of  span.  Full  loading  gives  maximum  stresses  for  the  sections 
near  the  hinges,  while  the  half-span  loadings  give  the  greatest  stresses  near  the  quarter  points 
of  the  span.  The  usual  method  of  design  is  to  locate  the  hinges  at  the  proper  points  and  to 
draw  the  force  lines  representing  the  load  concentrations.  These  loads  can  be  determined  quite 
accurately  by  making  a  complete  design  ^ 

of  the  spandrels  prior  to  the  arch  design  ,        .  — r=y:^Tr^jC^        , .      -  ^     ^  u  ,' 

and  by  approximatmg  the  weight  of  the  /d?^'^'^'^  ^^'^^^^^ 

arch  ring — the  arch  ring,  however,  need  '^^^^'^^^^^^ 

not  be  drawn.    The  lines  of  thrust  for     ^-^^  ^   ^""rhx 

the  three  conditions  of  loading  stated  /    Pb—  ^  ...,.7t^^  ^  —   M  ^ 

above  are  then  drawn  as  shown  in  Fig.  * 
58.    With  the  lines  of  thrust  known,  it 

then  becomes  possible  to  determine  the  correct  thickness  of  the  arch  at  any  point  and  decide 
upon  a  suitable  arch  ring  which,  of  course,  should  not  differ  appreciably  in  weight  or  position 
from  the  arch  ring  previously  assumed  or  else  a  second  analysis  should  be  made. 

For  a  load  of  unity  at  the  point  L2  in  Fig.  59,  the  direction  of  one  of  the  reaction  lines  is 
given  by  the  line  connecting  the  two  hinges  to  one  side  of  the  load.  The  direction  of  the  other 
reaction  is  then  known.  It  is  thus  an  easy  matter  to  construct  influence  lines  similar  to  those  of 
Art.  34  and  determine  the  exact  maximum  loadings.  Method  of  constructing  influence  lines 
is  explained  in  Art.  48a,  Sect.  7. 

45.  Common  Type  of  Hinges. — The  most  common  form  of  arch  hinge  consists  of  a  struc- 
tural or  cast-steel  pin  bearing  on  two  steel  castings.  Hinges  of  this  type  are  shown  in  Figs. 
60  to  63  inclusive. 

46.  Methods  of  Construction.— Three  distinct  methods  of  construction  have  been  employed 
in  the  erection  of  three-hinged  arches:  (1)  casting  the  concrete  ribs  in  forms  on  the  ground  and 
then  hoisting  them  into  place;  (2)  erecting  structural-steel  reinforcement  to  be  employed  in 


718 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16- 


Thrust  at  section  K 
for  unif  had  at  *' 


for  un/t  /oacf  atL^.^^. 


\-7 


Shear  at  section  K 
for  unit  load  at  Lz- 


Fig.  59. 


K-— /?-j'''-->t-s-'- //-^'''■■->t<---  ii'-6''->r'--"  1 1 '-6  "■—>¥■—■•  ii'-e'- 


Z6-6  C-fOC-^. 


Half  Sec-Hon  A-A 


Anchor  Bolts 


n 

Plan  or 

Side  Elevation 
Cost  Steel  Hinges 

Fig.  60. — Details  of  Fourth  Street  bridge,  Paducah,  Ky. 


Sec.  16-47] 


ARCHES 


719 


the  arch  ribs  and  using  this  reiiiforconunit  to  support  the  weight  of  the  forms  and  phistic 
concrete  during  construction;  and  (3)  employing  the  usual  type  of  centering  and  casting  the 
ribs  in  place.  The  first  method  is  the  one  usually  followed.  Method  No.  2  is  of  advantage 
when  a  stream  to  be  spanned  is  subject  to  sudden  freshets  and  a  minimum  of  falsework  is 
required.    Method  No.  3  is  necessary  only  under  unusual  conditions. 

The  cheapest  type  of  the  three-hinged  arch  and  also  the  type  that  is  lightest  and  best 
adapted  to  the  use  of  hinges  is  one  of  detached  ribs  supporting  spandrel  columns.  Such  a  type 
of  arch  lends  itself  readily  to  the  unit  method  of  construction  should  this  form  of  erection 
be  desired,  and  also  eliminates  the  necessity  for  waterproofing  which  is  a  serious  problem  in  the 
case  of  a  solid  filled  arch. 


Abutmeni-    Hinge  Cast  Steet  Rib  Hinge 

Fig.  G1. — Pratt  Street  bridge  over  Jones'  Falls,  Baltimore,  Md. 


47.  Details  of  Design. — Figs.  60  to  63  inclusive  give  typical  details  of  three-hinged  arches. 

The  arch  shown  in  Fig.  60  is  founded  on  Ohio  River  mud,  Raymond  concrete  piles  being 
used  for  the  foundations.  The  reason  for  the  use  of  the  cast  hinges  in  this  case  is  thus  apparent, 
as  settlement  of  foundations  was  anticipated.  No  appreciable  settlem^ent,  however,  has  ever 
taken  place. 

The  two  halves  of  each  rib  of  the  bridge  shown  in  Fig.  61  were  designed  to  be  erected  simul- 
taneously, without  falsework,  by  derricks  on  opposite  sides  of  the  stream,  and  to  be  self-support- 
ing as  soon  as  the  crown-hinge  connection  was  made.  Temporary  sway  bracing  was  provided 
to  insure  lateral  stability  while  the  forms  were  being  built  and  filled  with  concrete. 


720 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  16-47 


Fig.  62. — Bridge  over  the  Vermillion  River  at  Wakeman,  Ohio. 


A 


Hinge  at  Abutmem-  Abutment 
FirG.  63. — Details  of  Moffett  Creek  arch,  Columbia  Highway,  Oregon. 


Sec.  16-47] 


ARCHES 


721 


The  three-hinged  arch  construction  with  cantilever  ends,  shown  in  Fig.  62,  is  unusual, 
but  was  found  to  be  more  economical  for  an  arch  of  this  type  and  dimensions  than  a  hingeless 
structure.  The  cantilever  ends  were  rendered  necessary  on  account  of  the  fact  that  there 
were  no  stable  foundations  for  abutments  at  the  top  of  the  fill  at  the  ends  of  the  bridge.  The 
cantilever  ends  decreased  the  dead-load  thrust  on  the  center  hinges  about  one-quarter  and 
decreased  considerably  the  angle  which  the  resultant  thrust  on  the  lower  hinges  made  with  the 
vertical,  thus  decreasing  the  size  of  abutment  required.  The  cost  of  the  hinges  necessary  for 
the  three-hinged  arch  was  very  considerably  less  than  the  cost  of  the  additional  steel  reinforcing 
in  the  arch  ring  required  to  take  care  of  the  additional  bending  moments  in  the  hingeless  arch. 
No  connection  whatever  was  needed  between  the  ends  of  the  cantilevers  and  the  abutments  on 
account  of  the  extremely  small  amount  of  vertical  motion  at  these  points.  A  common  type  of 
centering  was  used  in  constructing  the  arch  ribs  in  place.  The  cast-steel  hinges  were  entirely 
encased  in  concrete  after  the  centers  were  struck,  a  K-in.  plate  of  sheet  lead  having  been  placed 
at  the  center  of  each  hinge  to  allow  the  necessary  motion  of  the  arch  rib  under  live  load  and 
temperature  stresses.    In  this  way  all  possibility  of  corrosion  of  the  steel  hinges  was  avoided. 


46 


SECTION  17 
HYDRAULIC  STRUCTURES 

DAMS 

By  a.  G.  Hillberg^ 

A  dam  is  built  for  the  purpose  of  holding  back  a  certain  volume  of  water  and  usually  to 
raise  the  water  level  at  a  given  point,  so  as  to  create  a  fall  or  head.  Low  dams  designed 
to  permit  the  water  to  flow  over  them  are  termed  weirs,  while  higher  structures  are  called 
spillways.  Dams  designed  to  hold  back  the  water  and  not  intended  to  assist  in  passing  the 
discharge  are  classified  as  bulkheads. 

Dams,  as  a  rule,  can  be  divided  into  two  main  groups :  Fixed  and  movable.  The  former 
consist  of  masonry,  earth,  rock,  steel,  timber,  or  combinations  of  these  materials  and  are  de- 
signed as  immovable;  while  the  second  group  contains  movable  structures,  such  as  gates,  stop 
logs,  flashboards,  needles,  rollers,  etc.,  designed  to  be  removed  as  required. 

Often  dams  are  combinations  of  these  two  groups  as,  for  instance,  at  Keokuk,  Iowa,  where 
11-ft.  steel  gates  have  been  placed  on  top  of  a  32-ft.  spillway  dam  of  mass  concrete. 

1.  Preliminary  Studies. — Before  the  actual  designing  of  a  dam  can  be  undertaken,  a 
great  deal  of  knowledge  of  its  purpose  and  the  site  must  be  at  hand.  As  a  rule,  the  geological 
formation  is  the  deciding  factor  as  to  what  type  to  adopt,  while  very  often  the  hydrographical 
and  topographical  conditions  decide  the  height  of  the  structure. 

la.  Locating. — When  investigating  a  river  with  the  view  of  finding  a  suitable 
dam  site,  the  engineer,  naturally,  first  looks  for  the  narrow  canyons.  The  reason  for  this  is  the 
desire  to  get  as  short  a  structure  as  possible  and  also  because  the  rock  formation  in  such  a  narrow 
place  is  usually  firm  and  hard.  However,  the  writer  once  investigated  such  a  narrow  box-can- 
yon where  the  sides  consisted  of  good,  hard,  blue  limestone  and  thought  the  site  to  be  excellent, 
while  borings  afterward  showed  the  canyon  to  be  a  volcanic  split  in  the  rock,  probably  1500 
ft.  deep  below  the  river  bed. 

When  storage  is  required,  a  narrow  box-canyon,  while  offering  good  dam  sites,  may  not 
give  the  desired  reservoir  capacity.  It  is,  therefore,  often  necessary  to  investigate  a  number 
of  possible  dam  sites,  as  the  one  apparently  best  suited  may  not  have  any  rock  foundation  nor 
give  the  necessary  storage  capacity.  A  site,  which  at  first  does  not  seem  suitable,  might 
after  all  be  the  most  favorable  because  the  formation  is  solid  bedrock  located  not  far  below 
the  surface  and  the  basin  upstream  such  as  to  give  the  desired  capacity  with  a  structure  of  low 
height. 

lb.  Geological  Investigations. — These  investigations  must  be  very  thorough 
and  the  capital  spent  on  careful  explorations  will  be  saved  many  times  over  during  the  con- 
struction. The  first  matter  of  importance  is  to  know  whether  or  not  bedrock  can  be  reached. 
If  so,  then  it  is  important  to  know  whether  it  is  stratified,  decomposed,  or  homogeneous;  whether 
hard  or  soft;  or  whether  the  formation  is  primeval,  sedimentary,  or  volcanic. 

Such  data  can  be  obtained  only  through  core  borings  with  diamond  drills,  and  it  is  advisable 
to  test  the  holes  by  means  of  air  or  water  under  pressure.  In  one  case  the  exact  locations  of 
fissures  were  determined  by  having  two  gaskets  on  the  pipe,  so  that  air  under  pressure  could 

'  Hydraulic  Engineer,  New  York  City. 

723 


724 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-lc 


be  applied  to  any  predetermined  portion  of  the  hole.^  Should  it  be  found  that  the  forma- 
tion is  stratified  or  otherwise  permeable,  it  is  sometimes  necessary  to  grout  it. 

In  soft  foundations,  wash  borings  must  be  used  and  a  record  kept  of  the  materials  pene- 
trated. Even  here  the  main  point  is  whether  the  formation  is  permeable  or  not.  As  a  rule, 
clay  or  hard-pan  offer  good  foundations,  while  glacial  deposits  are  always  treacherous. 

Hard-pan  is  not  always  to  be  depended  upon  since,  if  saturated  with  water  under  high 
pressure,  it  will  often  disintegrate  into  yellow  clay  and  gravel. ^ 

As  soon  as  the  necessary  data  have  been  obtained,  a  subsurface  map  should  be  made. 
From  this  map  it  can  be  decided  what  type  of  dam  is  most  suitable  and  if  any  precautions  have 
to  be  taken  in  improving  the  foundations. 

Ic.  Selecting  a  Suitable  Type  of  Dam. — As  a  rule,  an  engineer  will  first  think 
of  a  gravity-section  dam,  but  if  bedrock  cannot  be  reached  this  type  is  out  of  the  question.  It 
is  also  usually  out  of  the  question  if  no  suitable  materials  for  concrete  are  available  at  the  site, 
because  hauling  materials  is  expensive.  For  such  conditions  dams  of  reinforced  concrete  are 
well  worth  investigating.  However,  the  type  of  dam  depends  directly  on  the  foundation 
conditions,  which  can  be  divided  into  two  groups:  Rock  foundations  and  soft  foundations. 

Rock  Formation. — A  type  of  dam  always  suitable  in  rock  formations  is  the  gravity-section. 
However,  if  the  site  is  narrow,  an  arched  dam  as  a  rule  shows  a  considerable  saving  in  material. 
A  still  greater  saving  can  sometimes  be  obtained  by  a  reinforced-concrete  dam. 

If  no  concrete  materials  are  available,  an  earthen  dam  might  be  the  solution,  but,  in  order 
to  make  it  tight,  there  must  be  both  clay  and  sand  or  gravel  available,  as  at  least  20%  of  clay 
is  necessary  to  make  it  tight. 

In  many  instances  rock-fill  dams  have  been  used,  but,  in  order  to  make  them  tight,  a  water- 
tight membrane  must  be  provided  on  the  upstream  side.  This  can  be  made  of  gravel,  sand, 
fine  sand  and  clay  graded  so  that  they  will  form  an  impervious  stratum.  Reinforced  con- 
crete has  also  been  used,  but  as  a  rule  it  is  cheaper  to  support  such  a  deck  on  concrete  buttresses 
rather  than  on  a  rock  fill.  To  place  a  core  wall  of  concrete  near  the  center  of  a  rock-fill  dam 
is  not  good  practice,  as  the  upstream  portion  of  the  rock  fill  is  then  submerged. 

If  good  timber  is  available  and  the  structure  to  be  built  is  not  too  high,  a  rock-fill  crib 
dam  will  often  be  worth  investigating. 

Steel  dams  are  structurally  all  right,  but  their  maintenance  is  high. 

Soft  Foundations. — In  soft  foundations,  gravity-section  dams  are  out  of  the  question,  but 
sometimes  engineers  have  put  low  gravity-section  structures  on  piling.  The  most  suitable  dams 
for  such  conditions  are  earthen  dams;  reinforced-concrete  structures  placed  on  continuous 
foundation  mattresses;  rock-fill  timber  cribs;  or  framed  timber  dams. 

Id.  Height  of  Structure. — Several  conditions  influence  the  height  of  a  dam. 
If  it  is  to  be  used  for  storing  water  for  irrigation,  the  reservoir  capacity  must  be  sufficient  to 
regulate  the  natural  flow  so  that  a  certain  area  can  be  irrigated;  if  built  in  connection  with 
a  hydro-electric  power  plant,  the  head  created  is  just  as  important  as  the  storage  or  the  regu- 
lation of  the  river  discharge;  if  a  low  diversion  dam,  it  must  be  high  enough  to  divert  water 
into  the  pipe  line,  flume,  or  ditch  at  all  stages ;  if  built  for  flood  protection,  it  must  have  suffi- 
cient capacity  to  retain  all  discharge  in  excess  of  the  maximum  carrying  capacity  of  the  river 
channel  below  the  dam,  etc. 

Very  often  the  interference  of  the  backwater  with  structures  of  immovable  character, 
such  as  operating  mills,  other  power  plants,  buildings,  railroads,  etc.,  will  limit  the  height  of 
a  dam. 

The  top  of  the  bulkhead  section  of  a  dam  should  always  be  higher  than  the  maximum 
water  level,  as  wave  action  will  occur  on  the  surface  of  the  reservoir.  Such  wave  action  is  a 
function  of  the  exposed  length  of  surface  and,  according  to  Stevenson 

H  =  1.5VT  +  (2.5  -  VT)  (ft.) 

1  C.  W.  Smith:  "Construction  of  Dams." 

2  "  Failure  of  Stony  River  Dam."  Eng.  Rec,  Jan.,  1914,  p.  115. 


Sec.  17-le]  HYDRAULIC  STRUCTURES  725 

where  H  =  height  of  wave  in  feet;  and  I,  length  of  exposed  water  surface  in  miles,  measured 
along  a  line  perpendicular  to  the  dam. 

D.  C.  Henny  gives  the  following  formula: 

H  =  0.075  (F  -  8.5)  (ft.) 

where  V  =  velocity  of  wind  in  miles  per  hour.  For  dams  designed  by  the  U.  S.  Reclamation 
Service,  the  following  wave  heights  have  been  used : 

Wind  velocity,  miles  per  hour.  Wave  height,  feet. 

35  2.00 

40  2.50 

44  2 . 50 

48  3.50 

50  3 . 50 

56  4.00 

75  5.00 

The  top  of  the  dam  should,  of  course,  be  somewhat  higher  than  the  wave  height,  especially 
if  it  is  an  earthen  dam,  which  might  be  severely  eroded  if  water  splashes  over  it. 

le.  Hydrographic  Investigations. — For  whatever  purpose  a  dam  is  built  an 
intimate  knowledge  of  the  river  and  its  drainage  basin  is  required.  The  best  possible  data 
to  work  on  are  actual  observations  on  the  river  itself,  such  as  are  kept  and  published  by  the  U.  S. 
Geological  Survey  and  by  the  various  State  engineering  offices. 

If  no  such  records  are  available  at  the  point  where  the  dam  is  to  be  built,  records  at  other 
points,  preferably  one  above  and  one  below  the  site,  can  be  made  use  of  and  a  rating  curve 
established.  Should  no  records  at  all  be  available  on  the  stream  itself,  the  best  method  is  to 
compare  it  with  adjacent  streams  on  which  records  have  been  kept. 

In  many  cases  it  is  necessary  to  resort  to  runoff  calculations,  basing  them  on  the  rainfall. 
Such  computations  are  always  very  unreliable  and  should  be  made  and  used  with  the  greatest 
caution.    The   best   available   method   is   that   developed   by  Vermeule.^ 

E  =  F(15.50  +  0.16i^)  (in.) 

where  E  =  yearly  losses  due  to  evaporation;  F  =  (0.05T  —  1.48),  where  T  =  mean  yearly 
temperature  in  degrees  Fahrenheit;  and  R  =  yearly  rainfall  in  inches.  Vermeule  found  by 
investigating  the  rivers  in  the  East,  especially  those  in  New  Jersey,  that  the  monthly  relation 
between  evaporation  (including  absorption  by  crops,  etc.)  and  rainfall  was  as  follows: 

December  e=0.42  +  0.10r  June  e  =  2.50  +  0.25r 

January  e  =  0.27  +  O.lOr  July  e  =  3.00  +  0.30r 

February  e  =  0.30  +  O.lOr  August  e  =  2.62  +  0.25r 

March  e  =  0.48  +  O.lOr  September  e  =  1.63  +  0.20r 

April  e  =  0.87  +  O.lOr  October  e  =  0.88  +  0.12r 

May  e  =  1.87  +  0.20r  November  e  =  0.66  +  O.lOr 

Each  of  these  monthly  evaporations  is  to  be  multiplied  by  f  =  (0.05^  —  1.48),  where  t  = 
average  monthly  temperature  in  degrees  Fahrenheit. 

Where  gage  records  are  available  they  should  be  worked  up  as  shown  in  Fig.  1,  giving  the 
rating  curve,  the  gage  heights,  and  the  duration  per  year  of  each  gage  height.  The  longer  the 
record,  the  better  the  average  will  be. 

It  is  of  great  importance  to  determine,  as  correctly  as  possible,  the  maximum  discharge 
that  can  possibly  occur.  As  the  records  given  might  not  cover  a  sufficiently  long  period  of  time 
to  embrace  such  a  maximum  discharge,  a  cautious  designer  should  increase  the  given  maximum 


New  Jersey  Geological  Survey,  1894. 


726 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-1  / 


from  20  up  to  50%,  and  even  then  have  sufficient  freeboard  to  safeguard  the  bulkhead  portion 
from  being  overtopped. 

1/.  Capacity  of  Reservoir. — As  soon  as  the  dam  has  been  located  definitely  and 
the  reservoir  surveyed,  a  capacity  diagram  should  be  made  as  shown  in  Fig.  2.    Such  a  diagram 


is  obtained  by  determining  the  areas  enclosed  by  each  contour,  calculating  the  mean  areas 
between  any  two  contours  and  multiplying  by  the  distance  iDetween  them.  A  table  should  also 
be  made  giving  the  areas  and  capacities.  For  convenience  the  unit  measure  is  1  acre-foot  which 
equals  43,560  cu.  ft.    Such  a  diagram  is  approximate  only,  as  it  is  based  on  the  assumption  that 


Capacities   In  acre-feet 


Fig.  2. 


the  water  level  is  horizontal;  while,  as  a  matter  of  fact,  it  is  a  modified  parabola  tangent  to  the 
horizontal  at  the  dam,  and,  at  the  upper  end,  to  the  slope  of  the  water  surface  of  the  river  feed- 
ing into  the  reservoir. 

The  line  thus  formed  is  called  the  backwater  curve  and  its  exact  shape  cannot  be  calculated. 
However,  several  methods  have  been  devised  whereby  a  fairly  intelligent  guess  can  be  made. 


Sec.  17-1/] 


HYDRAULIC  STRUCTURES 


727 


If  the  dam  were  put  in  a  channel  with  vertical  sides  or  nearly  so,  the  shape  would  be  a  para- 
bola and  the  length  I  of  its  horizontal  projection 


where  h  is  the  height  of  the  new  water  level  above  the  natural  slope  S  of  the  water  surface  at 
the  dam  before  it  was  built  (Fig.  3). 

However,  as  the  shape  of  a  reservoir  basin  is  such  that  the  respective  cross-sections  are 
not  uniform,  the  best  method  to  apply  is  that  of  trial  and  error.  Therefore,  select  first  cross- 
sections  at  suitable  intervals,  h,  h,  h,  .  .  .  In,  and  determine  the  area  A,  the  wetted  perimeter 


Fig.  3. 


p,  the  hydraulic  radius  R  and  the  velocity  v  at  different  elevations  for  each  one  of  them.  Then 
assume  a  value  of  n  in  Kutter's  formula,  basing  it  on  the  prevailing  n  at  high  and  low  water 
in  the  river.  This  value  is  variable  because  the  frictional  resistance  is  greater  for  low  stages 
than  for  high,  not  only  because  of  the  increase  in  R  but  because  of  the  decrease  in  velocity  as 
well.  In  many  cases,  especially  if  the  dam  is  high,  it  is  advisable  to  make  a  curve  showing  the 
variation  in  n  and  extending  it  to  cover  stages  as  high  as  will  obtain  after  the  dam  is  built. 

As  the  water  level  at  the  dam  is  known,  the  computation  is  started  by  guessing  at  the 
slope  Si  in  the  first  section  Ix  (Fig.  4).  This  will  give  a  certain  elevation  at  the  first  cross-section 
so  that  A,      R  and  v  can  be  calculated  {v  =  Q/A,  Q  being  the  discharge).    Calculating  the 


Fig.  4. 


average  values  of  Am,  Pm,  Rm  and  Vm  for  the  section  and  inserting  them  in  the  Chezy  formula 

C  =  ^ 

'  Vrs 

a  value  of  Ci  is  determined. 

By  doing  the  same  in  the  Kutter  formula 

,  0.00281   ,  1.811 
41.65  H  ^  1  — - 


728 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-2 


a  value  of  C2  is  obtained.  Of  course,  if  *Si  were  correct,  both  values  would  have  been  the  same. 
By  guessing  at  *Si  and  correcting  Am,  Vm,  Rm,  and  Vm,  values  are  finrally  obtained  that  will  make 

Ci  =  C2 

This  is  the  correct  value  of  Si,  and  it  determines  the  height  of  the  backwater  curve  at  the 
cross-section  in  question. 

The  next  section  is  then  taken  and  dealt  with  in  the  same  way,  and  so  on  until  finally  a 
point  In  is  reached,  where  the  slope  coincides  with  the  natural  slope  S  of  the  water  surface. 

As  all  backwater  computations  are  based  on  a  given  volume  of  discharge  Q,  it  is  obvious 
that  in  order  to  find  the  limits  of  the  influence  of  the  water  backed  up,  at  least  two  sets  of  cal- 
culations must  be  made,  one  for  Qmaz  and  one  for  Qmin- 

The  inflow  in  a  reservoir  is 

I  =  D  +  E  +  S 

where  /  =  inflow ;  D,  outflow ;  E,  evaporation  and  seepage ;  and  S,  storage,  which  can  be  posi- 
tive, negative  or  zero. 

It  is  difficult  to  measure  the  inflow,  as  all  of  it  might  not  be  surface  water,  while  the  dis- 
charge D  can  be  measured  directly  and  E  calculated  from  evaporation  records  obtained  from 
pans  and  seepage  records  of  similar  reservoirs. 

2.  Design  of  Foundation. — When  designing  a  dam,  the  substructure  is  just  as  important 
as  the  superstructure,  as  a  structure  is  no  safer  than  its  weakest  part.  If  bedrock  of  good 
quality  is  available,  a  gravity-section  dam  can,  as  a  rule,  be  placed  directly  upon  it,  provided 
the  upper  strata  are  removed.  This  is  done  not  only  to  remove  disintegrated  portions,  but 
also  to  obtain  a  rugged  surface  with  which  concrete  will  give  a  good  bond. 

2a.  Grouting. — Should  the  rock  be  disintegrated  or  fissured,  it  is  often  neces- 
sary to  grout  it.  This  is  done  by  drilling  into  it  and  pressing  grout  into  the  fissures  through 
the  drill  holes.  The  consistency  of  such  grout  must  depend  upon  the  size  of  the  fissures,  which 
generally  are  so  thin  that  neat  cement  and  water  must  be  used.  Should  any  larger  fissure 
obtain,  sand  is  mixed  with  the  cement  in  various  proportions  and  the  grouting  pressure  is  reduced 
so  as  not  to  force  the  cement  out  of  the  mixture. 

26.  Cut-off  Walls. — In  fissured  rock,  cutoff  walls  of  concrete  are  often  used  instead 
of  grouting,  the  underlying  idea  being  to  establish  a  long  seam  offering  excessive  resistance  to 
seepage.  Of  course,  structures  placed  on  such  foundations  must  be  calculated  to  resist  a  con- 
siderable uplift. 

2c.  Caissons. — If  the  rock  is  so  disintegrated  that  it  consists  of  boulders  loosely 
cemented  together  between  which  a  rapid  percolation  takes  place,  it  might  be  found  necessary  to 
use  pneumatic  caissons,  as  was  done  at  Hale's  Bar,  near  Chattanooga,  Tenn.^.  Several  dams 
in  Europe  have  been  placed  on  such  foundations. 

In  soft  foundations  it  has  also  been  found  expedient  to  use  open  caissons  as  foundation 
for  the  core  wall  in  earthen  dams.  The  main  difficulty  in  using  caissons,  whether  pneumatic 
or  open,  lies  in  the  difficulty  in  making  water-tight  the  joints  between  them. 

2d.  Pilings. — In  soft  foundation,  piling  is  often  used  for  improving  the  ground. 
However,  a  portion  of  these  piles  must  be  placed  in  an  inclined  position  parallel  to  the  resultant 
of  all  the  forces  acting  on  the  structure  above  the  plane  of  loading  of  the  piles.  Otherwise, 
there  will  be  no  resistance  to  the  horizontal  component  of  the  hydrostatic  pressure  and  the  dam 
might  move  in  a  downstream  direction. 

2e.  Sheet  Piling. — In  soft  foundations,  where  it  is  impossible  to  reach  bedrock 
by  any  of  the  means  given  above,  sheet  pilings  are  often  used.  These  can  be  of  wood, 
steel  or  reinforced  concrete,  but  one  thing  applies  to  them  all:  they  must  be  strong  enough  to 
withstand  the  bending  moment  of  the  forces  acting  on  their  upstream  side  while  transmitting 
the  load  to  the  materials  on  the  downstream  side.    As  is  obvious  a  considerable  force  must  bci 

1  "Foundations  for  the  Hale's  Bar  Dam."    Eng.  Rec,  Feb.,  1913,  p.  178, 


Sec.  17-3] 


HYDRAULIC  STRUCTURES 


729 


resisted  on  the  downstream  side  at  the  top  of  such  sheet  piling,  and  it  is,  therefore,  customary 
to  imbed  the  top  firmly  in  the  masonry. 

One  thing  applies  to  all  details  appurtenant  to  the  improving  of  foundations,  whether 
firm  or  soft :  the  improved  portion  must  extend  deeply  enough  so  that  the  weight  of  the  materials 
including  the  weight  of  the  structure  itself  as  a  surcharge  on  the  downstream  side  more  than 
balances  the  forces  on  the  upstream  side  of  an  arbitrary  plane  generally  located  at  the  upstream 
side  of  the  dam  or  through  the  center  of  the  cutoff  wall,  if  such  is  made  use  of.  The  forces  on 
the  upstream  side  of  such  a  plane  are  due  to  the  full  hydrostatic  pressure  only,  if  the  foundation 
is  bedrock.  If  it  is  a  soft  foundation,  the  active  pressure  of  the  saturated  soil  must  be  added  to 
the  water  pressure,  while  on  the  downstream  side  the  weight  of  the  structure,  acting  as  a  sur- 
charge, naturally  increases  the  passive,  or  resisting,  earth  pressure. 

3.  Design  of  Dams  of  Gravity  Section. — This  type  of  dam  resists  the  hydrostatic  pressure 
through  its  great  weight,  which  is  sufficient  to  form,  with  the  horizontal  component  of  the  water 
pressure,  a  resultant  passing  the  plane  between  masonry  and  foundation  at  a  point  located  within 
the  middle  third.  As  masonry  cannot  be  depended  upon  to  resist  more  than  a  small  amount 
of  tension,  the  design  must  be  investigated  at  different  elevations  to  insure  against  tensile  stresses. 

3a.  Hydrostatic  Pressure. — In  the  analysis  it  is  customary  to  consider  a  strip 
of  the  structure  1  ft.  wide.  As  the 
weight  of  1  cu.  ft.  of  water  is  w — assumed 
at  62.5  lb.,  which  is  somewhat  too  high 
— the  intensity  of  pressure  per  square  foot 
at  any  depth  is 

p  —  wh  (lb.) 

where  h  =  depth  in  feet  below  surface  of 
water. 

The  total  pressure  P  on  a  vertical 
plane  extending  from  the  water  surface 
to  a  depth  H  increases  proportionally  from  zero  at  the  top  to  wH  at  the  bottom  (Fig.  5)  and 
is  expressed  by 

H  wIP_ 
2 


wHX-^  = 


(lb.) 


Should  the  plane  be  inclined  an  angle  a  with  the  horizontal  (Fig.  6),  the  maximum 


intensity  of  the  pressure  remains  the  same,  wH,  while  the  length  increases  to  H  X 


P  =  wH  X 


H 


so  that 


(lb.) 


2  sin  o;      2  sin  ot 

If  the  plane  is  submerged,  the  pressure  will  be  the  difference  of  the  total  pressure  P  minus 
the  pressure  -p  corresponding  to  the  upper  part  of  the  pressure  triangle  (Fig.  7),  or 

wH"^      wh^  _  w 
1 


Pi 


For  inclined  surfaces  multiply  by 


2  2^ 
as  shown  above. 


(lb.) 


sm  a 

The  resultant  force  of  the  hydrostatic  pressure  is  always  located  through  the  center  of 
gravity  of  the  pressure  diagram  and  normal  to  the  plane  in  question.    When  the  pressure 

diagram  is  a  triangle,  the  resultant  is  located  a  distance     above  the  lowest  point  (Figs.  5  and 


while  if  it  is  a  trapezoid  (Fig.  7),  the  distance  above  the  lower  side  is 

H 


^  H  -  h  wH  +  2wh 
y        3      ^  wH  +  wh 


h  ^  H  +  2h 
^  H  +  h 


(ft.) 


36.  Profiles  of  Dams. — The  simplest  form  of  a  dam  is  a  triangle  with  its  upstream 
side  vertical  (Fig.  8). 


730  .  CONCRETE  ENGINEERS'  HANDBOOK 

The  overturning  moment  is 


while  the  resisting  moment  is 


PH  ^  wH^  V  ^  =  ^ 
3  2         3  6 


2X  _  mHX  y  2X  _  mHX^ 
^  ^        "2^3  3 


[Sec.  17-36 

(ft.-lb.) 
(ft.-lb.) 


where  m  =  weight  of  1  eu.  ft.  of  masonry. 

Dams  are  designed  with  a  factor  of  safety  against  overturning  of  at  least  two :  Therefore 


Resisting  Moment  =  2{0veriurning  Moment) 


or 


and  the  length  of  base  will  be 


~3~  ~ 


X  =  H 


(ft. 


Fig.  10. 


Fig.  11. 


That  for  a  factor  of  safety  of  two  the  resultant  cuts  the  base  at  the  outer  edge  of  the 
middle  third  can  be  proved  as  follows  (Fig.  8) : 


P'.W  = 


XH 
3  '3' 


but  P=^,ndW  =  ^ 


so  that 


(ft.) 


The  triangular  shape  of  dam  as  an  economical  type  was  first  pointed  out  by  Edward 
Wegmann.i  He  recommended  that  the  water  level  for  safety  in  the  calculation  be  assumed  as 
extending  to  the  top  of  the  dam  and  that  the  superelevation  (s)  of  the  masonry  above  the 
actual  future  water  level  and  the  top  width  (a)  of  the  dam  crest,  each  be  made  one-tenth  of  the 
height  of  the  dam,  limiting  the  former  to  a  maximum  of  10  ft.  and  the  latter  to  a  minimum 
of  5  ft.  (Fig.  9). 

He  also  recommended  that  the  upstream  side  be  kept  vertical  until  the  unit  stresses  for 
"reservoir  empty"  approach  the  permissible  maximum.  Then  the  side  should  be  sloped, 
so  as  to  keep  the  stresses  at  or  somewhat  below  this  stress. 

As  the  limiting  pressure  will  be  reached  sooner  in  the  downstream  than  in  the  upstream 
face,  it  is  obvious  that  a  similar  slope  must  be  started  at  a  higher  elevation  on  that  side  (Fig.  10). 

Wm.  P.  Creager^  found  that  the  economical  top  width  of  a  dam  is  a  function  of  the  acting 
forces  (hydrostatic  pressure,  ice  pressure,  uplift,  etc.)  and  that  it  should  vary  from  10  to  17% 
of  the  height.  However,  as  the  height  varies  from  nothing  to  a  maximum  and  again  to  nothing 
along  the  length  of  a  dam,  Creager's  method  would  give  a  variable  top  width  in  addition  to 
irregularities  in  the  face  of  the  dam.  An  average  section  must,  therefore,  be  adopted  if  this 
method  is  used. 


1  Weqmann:  "The  Design  and  Construction  of  Dams,"  1st  Ed.,  1888. 

2  Creager:  "The  Economical  Top  Width  of  Non-overflow  Dams,"  Trans.,  Am.  Soc.  C.  E.,  vol.  61,  Nov.,  1915. 


Sec.  17-3c] 


HYDRAULIC  STRUCTURES 


731 


In  designing  a  dam  it  is  advisable  to  start  with  a  triangular  profile  and  in  that  way  obtain 
a  tentative  section.  The  top  width  is  then  determined  from  practical  considerations.  As  such 
added  weight  at  the  top  tends  to  place  the  resultant  of  the  structure  nearer  the  upstream  face, 
it  is  obvious  that  the  profile  can  be  somewhat  reduced,  and  its  downstream  face  given  a  slope 
asymptotic  to  the  face  of  the  triangular  profile  (Fig  11).  Thus  a  saving  is  effected  as  is 
shown  shaded  in  the  figure.    It  is  on  this  saving  in  material  Creager  has  based  his  theory. 

3c.  Uplift. — Should  a  dam  be  founded  on  pervious  material,  uplift  will  result. 
Its  magnitude  is  a  function  of  the  permeability  of  the  foundation  and  can  vary  from  full  hydro- 
static pressure  all  along  the  base  to  nothing.  Experiments  at  the  Oester  Dam  in  Germany 
showed  that  in  various  sections  the  following  pressures  existed: 

Section  I — fall  head  at  heel  to  one-half  at  toe. 

Section  II — full  head  at  heel  to  one-fourth  at  toe. 

Section  III — three-fourths  at  heel  to  one-fourth  at  toe. 

Section  IV — full  head  at  heel  to  zero  at  toe. 
At  the  Neye  Dam  in  Germany  similar  observations  were  made.    This  dam  has  its  founda- 
tion 26  ft.  below  the  surface  of  the 


rock,  or  about  twice  that  at  Oester. 
Here  57%  of  the  full  pressure  was 
observed  at  the  heel  and  32%  near 
the  toe. 

In  America  it  is  customary  to  as- 
sume two-thirds  of  the  full  hydro- 
static pressure  at  the  heel,  diminish- 
ing in  a  straight  line  to  zero  at  the 
toe  (Fig.  12a).  However,  a  more 
correct  way  would  be  to  assume  full 
pressure  at  the  heel  due  to  the  water 

on  the  upstream  side  and  full  pressure  at  the  toe  due  to  the  water  on  the  downstream  side 
(Fig.  126). 

A  still  better  way  is  to  provide  drainage  immediately  back  of  the  cutoff  wall  and  to  use  an 
uplift  corresponding  to  the  elevation  of  the  water  surface  below  the  dam  under  the  entire  base 
excepting  the  portion  in  front  of  the  drains  on  which  full  uplift  is  acting  (Fig.  12c). 

Depending  upon  which  of  the  above  assumptions  is  used,  the  pressures  and  moments 
referred  to  the  toe  of  the  section  will  be  as  follows: 

Force  in  pounds 
1 

l< 

Ui  +  U2  =  w{Ht  +  hv) 


Fig.  12. 


Fig.  12a 
Fig.  126 
Fig.  12c 


U 


U 


wHb 


XH  +  h)b 


U  = 


M 


M 


M 


Moment  in  foot-pounds 

=  1(^+2)^^ 
=  ^[Ht{b-l 


2 


Some  engineers  apply  the  uplift  theory  to  every  horizontal  joint  in  a  dam  and  use  then  the 
assumption  shown  in  Fig.  I2a  for  these  joints.    However,  if  care  is  taken  and  the  upstream 

side  made  as  water-tight  as  possible  and,  in  addition,  vertical 
drains,  or  weepers,  are  provided  a  few  feet  inside  the  face  and  con- 
nected to  a  drainage  gallery,  such  uplift  can  be  eliminated  entirely. 

In  order  to  get  as  impervious  a  surface  as  possible  and  at 
the  same  time  to  provide  as  ample  a  drainage  as  possible,  it  has 
been  proposed  to  build  in  front  of  gravity  section  dams  cellular 
facings  of  reinforced  concrete.    This  facing  is  anchored  to  the  masonry,  and  at  the  bottom 
the  cells  are  piped  through  the  base  of  the  dam.    The  cells  should  be  interconnected  at  certain 
intervals  from  the  bottom  up  (Fig.  13). 


Fig.  13. 


732 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  n-u 


Zd.  Wind  Pressure. — No  wind  pressure  needs  to  be  considered,  as  when  the 
reservoir  is  full  its  action  can  only  be  on  the  downstream  side,  thus  decreasing  the  unit  stresses 
in  the  masonry.  When  the  reservoir  is  empty,  such  pressure  on  the  upstream  side  will  be  con- 
siderably less  than  the  future  hydrostatic  pressure  and,  therefore,  need  not  be  considered. 
If  it  acts  on  the  downstream  side,  it  will  throw  the  line  of  pressure  backward  approximately 

SmH  +  6^ 

where  6  =  wind  pressure  in  pounds  per  square  foot;  p,  specific  gravity  of  masonry  (generally 
2.5);  m,  unit  weight  of  masonry  per  cubic  foot;  and  H,  height  of  structure  above  plane  in  con- 
sideration.   However,  the  influence  of  wind  on  the  stability  is  so  small  as  to  make  it  negligible. 

3e.  Ice  Thrust. — It  is  a  much  disputed  point  whether  ice  pressure  should  be 
considered  or  not.  Many  engineers  say  that,  as  the  dam  is  located  in  a  narrow  place,  arching 
stresses  between  the  banks  will  relieve  the  dam  of  the  ice  pressure.  However,  several  failures 
are  directly  traceable  to  such  pressure,  but  then,  as  in  the  case  of  Waldron,  111.,^  at  Minneapolis, ^ 
and  at  Thomaston,  Conn.,  ^  the  sheet  of  ice  was  cor.fined  and  the  fluctuations  in  water  level  intro- 
duced toggle  joint  effects  in  the  ice. 

Reputable  engineers,  acting  conservatively,  have  recommended  and  used  the  following 
ice  pressures:^ 

Pounds 
per  lin.  ft. 


St.  Maurice,  Que   50,000 

Wachusett,  Mass   47,000 

Olive  Bridge,  N.  Y   47,000 

Kensico,  N.  Y   47,000 

Croton  Falls,  N.  Y   30,000 

Cross  River,  N.  Y   24,000 

Keokuk,  Iowa,  on  piers  only   20,000 


Such  pressures  are,  as  a  rule,  applied  at  the  water  surface,  but  as  the  sheet  of  ice  is  as- 
sumed to  be  about  2  ft.  thick,  the  actual  point  of  application  is  about  1  ft.  below  the  surface. 
If,  therefore,  a  joint  is  considered  located  at  a  depth  h  below  the  water  surface  and  an  ice  pres- 
sure /  is  assumed  acting  at  a  depth  of  1  ft.  below  the  surface,  the  moment  will  be 

M  =  I{h  -  1)  (ft.-lb.) 

The  influence  of  the  ice  pressure  on  the  profile  of  the  dam  decreases  with  the  depth,  necessi- 
tating a  material  increase  of  the  upper  portions  only,  if  the  force  is  to  be  sustained  by  gravity 
action.  However,  because  of  this  decreasing  influence,  it  is  often  advisable  to  reinforce  the 
upstream  face,  so  as  to  enable  the  section  to  withstand  the  ice  pressure  by  cantilever  action. 

3/.  Initial  Stress. — As  the  construction  of  a  large  dam  covers  several  seasons, 
the  temperatures  under  which  masonry  is  laid  varies  considerably.  As  yet  no  rules  have  been 
laid  down  for  taking  into  account  in  the  design  the  effect  of  such  stresses. 

Zg.  Temperature  Stresses. — Seasonal  changes  in  the  temperature  and,  to  a  some- 
what smaller  extent,  daily  changes  will  cause  the  masonry  to  expand  or  contract.  It  is,  therefore, 
impossible  to  avoid  cracking,  especially  in  the  upper  and  thinner  portion.  In  order  to  limit 
this  cracking  to  a  minimum  and  to  locate  such  cracks  where  they  cannot  have  any  harmful 
influence,  it  is  customary  to  provide  cracks  or  expansion  joints  at  certain  intervals.  In  order 
to  make  them  water-tight  the  masonry  is  often  dovetailed  together,  or  strips  of  copper  flashing 
used. 

1  Eng.  News,  Apr.  23,  1908. 

2  Eng.  News,  May  11,  1899. 

3  Flinn:  "Water  Works  Handbook,"  p.  119. 
*  Smith:  "Construction  of  Dams,"  p.  117. 


Sec.  17-3/1 1 


HYDRAULIC  STRUCTURES 


738 


Such  expansion  joints  should  not  be  located  closer  than  20  ft.  and  not  more  than  50  ft. 
apart.  If  an  abrupt  change  in  the  foundation  occurs,  an  expansion  joint  should  be  located 
there  as  cracking  cannot  be  prevented  at  such  points. 

Zh.  Stresses  in  Masonry  and  on  Foundation. — After  the  resultant  of  all  the  forces 
acting  on  a  section  of  a  dam  located  above  a  certain  plane  has  been  determined  as  to  magnitude 
and  location,  it  is  necessary  to  calculate  the  unit  stresses  in  the  joint,  so  as  to  insure  against 
overloading.  If  in  Fig.  14,  the  resultant  R  (consisting  of  the  components  V  and  H)  cuts  the 
joint  a  distance  I  from  its  center,  it  is  possible,  without  changing  the  conditions,  to  imagine  two 
forces  equal  to  V  and  opposite  in  direction  placed  in  the  center  of  the  joint.  One  of  these 
forces  can  then  be  combined  with  the  component  V  to  form  a  couple  VI,  and  the  other  force  V 
gives  an  equal  loading  of  the  joint.  The  resultant  unit  pressures  will  then  be  a  combination 
of  the  corresponding  pressures  due  to  this  central  load  and  the  couple,  which  for  the  central 
load  V  is 

V 

Pi  =  —  (Ib.per  sq.  in.) 


where  a  is  the  area  of  the  joint  and  equal  to  bd,  or  b,  if  the  width  cZ  is  1  ft. 
For  the  couple  the  maximum  unit  stresses  are 


(Ib.per  sq.  in.) 


where  S  =  section  modulus  for  the  area  of  the  joint  referred  to  an  axis  through  its  center,  or 
^  if  the  joint  is  1  ft.  wide.  Therefore, 


P  -P  +P  -  ^  +  Vl  _V  6Vl  _V 
P  -  P,  ±  P,  -  -  ±       -  ~±        -  ~ 


V  ytjivr  pressurt 


(Ib.per  sq.  in.) 


Fig.  14. 


Fig.  15. 


Fig.  16. 


Of  course,  as  a  negative  stress  would  mean  tension  and,  as  such  stresses  are  not  permitted, 
such  outcome  of  the  calculation  proves  that  the  length  b  of  the  joint  is  too  short,  or,  in  other 
words,  the  resultant  falls  outside  the  middle  third. 

Prof.  Rankine  argued  that  the  pressures  near  the  faces  are  tangential  to  them  and  that, 
therefore,  in  considering  the  pressures  as  above — viz.^  normal  to  a  given  horizontal  joint — the 
maximums  are  not  obtained.  M.  Bouvier  recommended  that  the  pressure  be  calculated  on 
a  plane  normal  to  the  resultant  (Fig.  15).  If  the  resultant  R  cuts  the  horizontal  joint  at  a 
distance  I  from  its  center  and  under  an  angle  a.  with  the  vertical,  the  inclined  joint  will  also  make 
an  angle  <x  with  the  horizontal.  Consequently,  the  values  in  the  above  equations  will  be  R 
instead  of  F,  b  cos  a  instead  of  6,  and  I  cos  a.  instead  of  Z,  so  that 


6  cos  a  \        b  I 


(lb.  per  sq.  in.) 


In  Europe  it  is  customary  to  figure  the  stresses  on  joints  normal  to  both  faces  and  bent 
at  an  angle  inside  the  dam  (Fig.  16).  The  bend  is  located  at  a  point  where  the  unit  stresses  on 
the  projected  horizontal  joints  are  equal. 


734 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-3i 


Several  dam  profiles  (Rankine's,  etc.)  show  a  small  amount  of  tension  in  the  downstream 
face  when  horizontal  joints  in  the  upper  part  are  analyzed  for  the  condition  "reservoir  empty" 
and  using  the  formulas  given  above.  So  does  the  triangular  profile,  because  the  added  portion 
at  the  top  draws  the  pressure  line  upstream  of  the  middle  third.  It  is  extremely  doubtful  that 
tensional  stresses  actually  develop  in  the  joint,  so  long  as  the  resultant  remains  within  the 
limits  of  the  masonry.  If  the  joints  were  open,  tension  would  be  out  of  the  question  and  a 
corresponding  increase  in  the  maximum  compressive  stress  would  be  the  result.  In  view  of  the 
slight  ability  of  concrete  and  especially  cyclopean  masonry  to  resist  tensional  stresses,  it  is  ad- 
visable to  consider  the  joints  as  being  open.    If  then  the  resultant  R  (Fig.  16A)  cuts  a  joint 

at  a  point  located  a  distance  c  from  the  edge  of  the  masonry,  and  c  <      the  pressure  dia- 


gram would  be  a  triangle  with  the  base  3c. 
of  the  joint  is  1  ft. 


If,  furthermore,  the  width 


P  X3c 


P  = 


27 
3c 


(lb.  per  sq.  in.) 


Fig.  16A. 


where  V  is  the  vertical  component  of  the  resultant  R. 

The  maximum  permissible  compressive  unit  stress  should  not  exceed 
300  lb.  per  sq.  in.,  corresponding  to  21.6  tons  per  sq.  ft.  If  the  stress  is 
more,  it  will  be  necessary  to  increase  the  length  of  the  joint — that  is,  increase  the  area  and 
the  section  modulus,  thus  reducing  the  maximum  stress. 

3i.  Shearing  Stresses. — Each  joint  should  also  be  investigated  for  shearing 
stress.    As  the  horizontal  component  is  P,  the  unit  shear  s  in  the  horizontal  joint  would  be 

p 

s  =  -  (lb.  per  sq.  in.) 

where  a  is  the  area  in  square  inches. 

If  a  joint  such  as  d  (Fig.  17)  is  considered,  it  is  obvious  that  the  shearing  force  is  com- 
posed of  the  hydrostatic  pressure  P  cos  j3  and  a  portion  of  the  weight  of  the  masonry  = 
W  sin  (3,  so  that  the  total  shearing  force  is 

S  ^  P  con  (i  +  W  sin  ,3 

Several  joints  must  be  investigated  by  the  trial  and  error  method 
until  that  giving  the  maximum  stress  is  found. 

Two  dams  built  by  French  engineers  in  Africa  failed  at  points 
located  one- third  down  from  the  top  because  of  excessive  diagonal 
shear.  The  permissible  unit  shearing  stresses  should  not  exceed  100 
lb.  per  sq.  in.  and  many  engineers  do  not  like  to  exceed  70  lb. 
Often  the  joint  between  rock  and  masonry  is  investigated  for  fric- 
tion, neglecting  the  adhesion,  but  this  is  not  necessary,  as  (1)  such 
adhesion  exists,  and  (2)  the  roughness  of  the  rock  surface  gives  a 
good  mechanical  bond  with  the  concrete. 

Zj.  Final  Calculation. — After  it  has  been  decided  what  assumptions  are  to  be 
made  as  to  the  forces  acting  on  the  dam,  a  tentative  triangular  section  calculated,  and  the  top 
width  and  the  super  elevation  determined,  it  is  necessary  to  investigate  the  design  at  a  number 
of  different  elevations,  so  as  to  be  certain  that  the  unit  stresses  do  not  exceed  the  permissible 
adopted  for  the  design,  and  that,  on  the  other  hand,  the  actual  stresses  are  not  so  low  as  to  make 
the  design  uneconomical.  The  aim  is  to  keep  the  pressure  lines  inside  the  middle  third  in  such  a 
way  that  for  the  condition  "reservoir  empty"  the  line  falls  closely  to  the  upstream  limit  of  this 
middle  third  and  for  "reservoir  full"  as  closely  to  the  downstream  limit  as  possible.  The  ideal 
dam  would  have  these  pressure  lines  coinciding  with  the  middle  third  limits,  but  this  cannot,  for 
practical  reasons,  be  accomphshed  at  the  top  of  the  structure.  Often  the  pressure  line  for 
"reservoir  empty"  will  fall  slightly  outside  and  upstream  of  the  middle  third  limit,  thus  causing 


Fig.  17. 


Sec.  n-sj] 


HYDRAULIC  STRUCTURES 


735 


a  slight  tension  in  the  downstream  face.  In  one  case  a  dam  was  on  purpose  designed  so  as  to 
lean  upstream,  or  against  the  water  pressure  (Hauser  Lake,  Mont.)- 

As  a  rule,  both  sides  of  a  dam  are  kept  parallel  until  a  point  is  reached  where  the  resultant 
of  the  forces  passes  through  the  outer  limit  of  the  middle  third  (Fig.  18a)  or 


'  6*3 


If  now,  as  recommended  by  Wegmann,  the  water  surface  is  assumed  as  extending  to  the  top 
of  the  dam,  P  =         and  W  =  mad,  which  inserted  in  the 
equation  above  gives 


jvd^ 
2mad 


2d 


or  d 


(ft.) 


If  an  ice  pressure  /  is  to  be  taken  into  consideration,  it 
is  impossible  for  the  water  surface  to  reach  the  top  of  the 
dam.  In  this  case  moment  equations  are  the  more  con- 
venient to  use,  which,  established  in  respect  to  the  down- 
stream edge  (Fig.  186)  with  a  factor  of  safety  of  two,  would  read 


Fig.  18. 


mad  X 


mda^ 


In  this  equation  it  is  best  to  consider  the  top  width  a  as  the  variable,  unless  the  dam  is  rein- 
forced when  the  usual  reinforced-concrete  formula  for  cantilevers  can  be  added  to  the  right  side 
of  the  equation. 

If  uplift  of  %h  diminishing  to  zero  is  assumed  in  the  joint,  the  corresponding  moment  must 
be  added  to  the  left  side  of  the  equation  (see  Art.  3c). 


5425 
5405 
5385 
5365 
5345 
5325 
5305 
5285 
5265 


^5 


^dOOO 
74,600 
158^20 
Z80,00d 


634,690 
868,000  ^950 


1,138,630 
1,446,700 


RESEIRVOIR  EMPTY 


Cmv/fyline 


5.00  5.00 


7.53 

11.47 
16.00 


433,650  20.4842.85 


38.50 


16.00 
2520 
34.00 


25.005167 
60.50 
34.0069.33 


78.17 


Infensify 
of  pressure 


140.000  H9.50 


1192,200 


3,990,000  m.70 
9,520,000^ 
18,785,200 


32,784pO0m60 

52 ,500,000  mo 

78,934,300  fmo 
113,094,800 


mo 


+19.50 
-2.60 
-3.70 
■8090 -3.10 

mo 


-2.90 
-2.50 
■2.20 
-2.00 
■m-1.90 


RESEIRVOIR  FULL 


70^ 


34,530 
175,780 


282,030  31.67 
413/80 
56933045.00 
750.78051.67 
957,030  58.33 


If 


35,160 
446,000 
1732.730 


25.00  4M000 


15,841,000 
25,623,850 


55,823,6002.03 


Gmrihiine 


2.0559.25 
68Z0 
17.10 


Irrfensrfy 
of  pressure 


375 


14.27 
18.30' 
2250 


50.0026.67 
30.75 


3957 


+4.90  m.io 


10.00  mo 


neo 

^.20 


mio+m  17.90 


24.40 


■70.10 

■m  31.00 

+5.2O^109.8L  37.40 
e.40  (150.60  44.00 
35.13  +3.10  m.70 50.50 


+290  miO  57.00 


11.40 


Fig.  19. 


In  this  way  each  joint  is  analyzed  keeping  in  mind  that  all  the  forces  acting  on  the  dam  at 
or  above  the  joint  in  question  must  be  included. 

A  drawing  should  be  prepared  showing  the  profile  of  the  dam,  the  limits  of  the  middle  thirds 
and  the  pressure  Hues  of  "reservoir  empty"  and  "reservoir  full."  A  table  should  also  be  pro- 
vided giving  in  detail  the  various  weights,  moments,  stresses,  factors  of  safety,  etc.,  as  shown  in 
Fig.  19. 

Every  construction  joint  in  the  dam  offers  chances  for  defective  work.  Laitance,  dirt, 
etc.,  tend  to  establish  open  joints  through  which  water  might  percolate.    Such  joints,  of  course, 


! 


736  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  17-4 

do  not  offer  the  proper  resistance  to  shearing,  and  joints  should,  therefore,  never  be  made 
horizontal.  They  should  be  stepped  and  located  at  different  elevations  in  adjacent  sections. 
Rocks  should  be  left  projecting  halfway  up  to  enable  the  next  course  of  masonry  to  get  a 
good  hold.  Before  starting  this  next  course  the  surface  should  always  be  scrubbed  thoroughly 
with  steel  brushes  applying  water  and  neat  cement. 

In  Europe  it  is  customary  to  place  the  courses  in  such  a  way  that  the  top  surfaces  of  them 
are  always  normal  to  the  faces  of  the  dam  and,  in  many  cases,  the  courses  are  broken  and 
the  outer  part  placed  normal  to  the  pressure  line  "reservoir  full"  (Fig.  20). 

In  many  cases  dams  designed  as  gravity-section  structures  have  been  arched  in  plan 
(Roosevelt,  Arrowrock,  Tallulah  Falls).  The  reason  for  this  is  that  in  such  dams  temperature 
stresses  are  counteracted  by  arch  action  in  the  structure.  However,  at  Tallulah  Falls  when 
the  dam  contracts  it  pulls  away  from  the  rock  abutments,  proving  the  necessity  of  providing 

  sections  at  the  abutments  where  concrete  should  be  placed  in  cold 

weather  so  as  to  insure  a  tight  joint  under  maximum  contraction.  This 
course  was  followed  by  the  U.  S.  Reclamation  Service  when  building 
the  Arrowrock  Dam. 

4.  Design  of  Arched  Dams. — If  the  dam  site  is  narrow  and  good 
rock  abutments  are  available,  it  is  likely  that  an  arched  dam  will  prove 
economical.  Since,  however,  an  arch  is  longer  than  a  straight  line,  the 
economy  over  a  gravity-section  dam  depends  upon  whether  the  arch, 
with  its  smaller  cross-section,  greater  length,  more  expensive  formwork, 
greater  accuracy  in  instrument  work,  sometimes  richer  mix  of  con- 
crete and  possible  reinforcement  requirements,  will  prove  the  less; 
expensive. 

Arched  dams  can  be  divided  into  three  classes: 

Buttressed  AYches. — These  are  generally  built  of  reinforced  concrete  and  termed  multiple- 
arch  dams  (see  under  " Reinforced-concrete  Dams",  Art.  5/). 

Constant-radius  dams,  which  have  a  constant  length  of  radius  of  either  the  upstream 
side,  the  center,  or  the  downstream  side. 

Constant-angle  dams,  which  have  a  constant  subtended  angle,  but  a  variable  radius  being 
a  function  of  the  cord  lengths  at  the  different  elevations. 

4a.  Constant -radius  Dams. — Dams  of  this  type  are  also  called  "true  arches" 
as  they  are  built  mainly  on  the  principle  that  the  pressure  line  of  a  uniform  load  acting  on  the 
periphery  of  a  circle  has  a  circular  line  polygon.  Consequently,  as  soon  as  the  upstream 
radius  Ru  has  been  determined  upon,  the  stresses  in  the  arch  rings,  assumed  to  be  1  ft.  high, 
can  be  calculated  by  the  formula 

S  =  PRu  (lb.) 

where  P  —  water  pressure  in  pounds  per  square  foot  measured  to  the  center  of  the  height  o^ 
the  arch  ring  or  wH,  where  w  is  the  weight  of  water  per  cubic  foot  and  H  the  depth  in  feel 
of  the  center  of  the  arch  ring  below  the  water  surface. 

As  the  pressure  line  coincides  with  the  center  of  the  circular  arch,  a  correction  in  the 
value  of  S  in  the  above  formula  is  required. 

5,  :S  =  Ru:  ?^^±^  or      =  ^^^^  (lb.) 

where  Rd  is  the  radius  of  the  downstream  side  or  Rd  =  Ru  —  T,  where  T  is  the  thickness  o 
the  arch  ring  in  feet. 

If  the  arch  ring  is  h  in.  high  and  t  in.  wide,  its  area  is  ht  sq.  in.  The  permissible  com 
pressive  unit  stress  is  ^  lb.  per  sq.  in.,  so  that  the  total  resistance  is  ^ 

Q  =  qht  (lb. 


Sec.  17-4a] 


HYDRAULIC  STRUCTURES 


737 


As  now  Q  ^  Si,  obviously  Si  ^  qht 

or  the  required  thickness  t,  if  all  other  qualifications  are  given, 

^  qh 

A  correction  must  also  be  made  for  the  vertical  pressures  due  to  the  weight  of  the  dam, 
which  will  increase  the  stress      to  Si  +  AS. 

For  a  dam  with  a  vertical  downstream  face  and  a  battered  upstream  side  (Fig.  21a) 

Ru  \  7) 


AS  = 


1  + 


3/i    \    '  Ru  +  Rd/ 

and  for  a  dam  with  a  battered  downstream  face  and  a  vertical  up- 
stream side  (Fig.  216) 


AS 


3m  ( 


1  + 


R. 


Ru  +  Rc 


where  p  is  the  specific  weight  of  masonry  or 


weight 
"62^' 


and 


the  re- 


Rm 

m 

-f 

(o) 

Fig 


For  concrete  -  is  from  0.16  to  0.22  or  as 


ciprocal  of  Poisson's  ratio, 
an  average  n  =  5.^ 

An  arched  dam  is,  as  a  rule,  reinforced  in  both  faces,  in  the  upstream  face  so  as  to  take 
up  tensile  stresses  due  to  cantilever  action  and  in  the  downstream  face  so  as  to  insure  against 
cracks  due  to  tension  caused  by  vertical  beam  action.  The  action  of  the  dam,  because  of  its  re- 
sisting moment  when  considered  as  a  vertical  beam  1  ft.  wide,  and  because  of  the  support 
at  the  bottom,  which  is  fixed,  is  to  reduce  the  loading  of  the  intermediate  arch  rings  and  to 
increase  it  correspondingly  in  the  upper  rings. 

By  applying  these  formulas  the  thickness  of  the  arch  can  be  determined  at  as  many  ele- 
vations as  desired  and  the  cross-section  obtained.  However,  the  formula  is  correct  only  for 
an  arch  of  circular  form  with  fixed  ends,  while  an  arched  dam  is  also  fixed  along  its  bottom. 

Often  the  lower  part  is  so  short  and  the  cross-section  so  thick  that 
horizontal  beam  action  will  result.  It  is,  therefore,  necessary  to 
investigate  the  tentative  section  for  a  variety  of  different  condi- 
tions: First,  as  a  gravity  section,  until  tension  develops;  second, 
as  a  cantilever  section,  until  a  deformation  occurs  sufficient  to 
develop  arching  stresses;  third,  as  a  beam  tending  to  equalize 
such  arching  stresses,  decreasing  them  at  the  bottom  and  in 
creasing  them  at  the  top;  and  fourth  as  an  arch.^ 

Approximate  methods  for  finding  what  proportion  of  the 
TO'  80°  90'  iQSi^  is  taken  by  the  arch  and  by  the  cantilever  respectively  have 
been  discussed  by  Harrison  and  Woodard.^    Shirreffs  in  his  dis- 
cussion of  that  paper  develops  the  following  formula  for  the 


0    10°  £0"  30°  40°  50°  60° 

Values  of  ^ 
Fig.  22. 


crown  deflection  of  an  arch  dam: 


Dc  = 


C  +  PiRu"" 


Et 


where 


and, 


Pi  =PX 


2  sin 


(1  —  cos  (p)  +  ^(cos  2(p  —  1) 


Zip 


+  (1  —  cos  <p) 


-h  cos  (p  —  4i 
sin  (p 

1  Bellet:  "Barrages  en  Marconnerie." 

2  "For  a  full  discussion  of  these  stresses  see  Morrison  and  Brodie:  "  Masonry  Dam  Design," 

3  Lake  Cheesmau  Dam  and  Reservoir,"  Trans.  Am.  Soc.  C.  E.,  vol.  53,  p.  89. 
47 


738 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-46 


and  is  a  factor  which  takes  the  curved  beam  action  into  consideration  and  can  be  found  directly 
from  Fig.  22.    E  is  the  modulus  of  elasticity  and  t,  the  thickness  of  the  arch  ring. 

This  formula  and  curve,  however,  do  not  take  the  initial  stresses  in  the  dam  structure  into 
consideration,  and,  therefore,  before  applying  it  for  finding  arch  deflections  it  is  necessary  to 
determine  how  much  of  this  load  is  carried  by  the  arch  due  to  initial  stresses,  because  only 
after  deducting  this  part  of  the  load  does  the  remainder  divide  up  between  arch  and  cantilever 
action. 

By  initial  stresses  are  meant  stresses  principally  due  to  the  weight  of  the  structure  and 
to  the  water  pressure.  Therefore,  -these  stresses  reach  their  maximum  values  at  or  near  the 
foundation,  and  are  zero  at  the  crest. 

A  number  of  arched  dams  of  very  slender  dimensions  have  been  built  in  Australia  by  the 
English  engineer  Wade.  The  following  table  has  been  taken  from  Wegmann,  "The  Design 
and  Construction  of  Dams." 


Max. 

Top 

Base 

Radius  of 

Max.  pressure, 

Top  above 

Locality 

height, 

width, 

width. 

curve. 

tons  per  square 

water  surface, 

feet 

feet 

feet 

feet 

foot 

feet 

Parramatta  

52 

0 

4 

8 

15 

0 

160 

15 

2.0 

Lithgow  No.  1  

35 

0 

3 

5 

10 

9 

100 

10 

3.5 

Parkes  

33 

5 

3 

0 

13 

5 

300 

24 

5.0 

Cootamundra  

.46 

0 

3 

0 

13 

0 

250 

25 

1.0 

Picton  

28 

0 

7 

0 

13 

6 

120 

12 

10.0 

Tam  worth  

61 

0 

3 

0 

21 

5 

250 

20 

2.0 

Wellington  

48 

0 

3 

0 

10 

0 

150 

20 

2.0 

Mudgee  

50 

0 

3 

0 

18 

0 

253 

20 

1.0 

WoUongong  

42 

0 

3 

5 

11 

6 

200 

20 

1.0 

Katcomba  

25 

0 

3 

0 

20 

3 

220 

15 

1.0 

Lithgow  No.  2  

87 

0 

3 

0 

24 

0 

100 

10 

3.0 

Medlow  

65 

0 

3 

5 

9 

0 

60 

12 

3.0 

Queen  Charlotte  Vale  

32 

0 

3 

0 

8 

6 

90 

10 

2.0 

Most  of  these  dams  are  reinforced  to  take  care  of  cantilever  and  temperature  stresses. 

The  largest  arched  dams  in  the  United  States  are  located  at  Pathfinder  and  Shoshone,  both 
in  Wyoming.  They  are  of  almost  identical  design,  with  a  radius  of  150  ft.  figured  to  the  center 
of  the  top  width.  The  upstream  slope  is  0.15  :1  and  the  downstream  0.25  :1  in  both  cases. 
The  former  has  a  top  width  of  14  ft.,  a  bottom  width  of  94  ft.  and  a  total  height  of  210  ft.; 
the  latter  a  top  width  of  10  ft.,  a  bottom  width  of  108  ft.  and  a  total  height  of  328.4  ft.  The 
lower  85  ft.  do  not  taper  but  are  of  a  uniform  thickness  of  108  ft.  Both  dams  are  built  by  the 
U.  S.  Reclamation  Service. 

46.  Constant-angle  Dams. — If  a  circular  arch  of  given  chord  length  is  investi- 
gated for  economy,  it  will  be  found  that  the  most  economical  shape  has  a  subtended  angle 
2(p  =  133.5  deg.  It  can  also  be  shown  that  for  variations  between  120  and  150  deg.  the  increase 
in  area  is  negligible.^  As  for  any  elevation  the  chord  C  is  known,  the  corresponding  mean 
radius  is  (Fig.  23).  i 

Rm   -        ^  i 

2  sin  ^  I 

The  volume  in  a  given  section  is  equal  to  the  area  multiplied  by  the  length  of  the  mean  arc, 

V  =  area  X  Rm  X  2(p 

where  ip  is  given  in  terms  of  tt. 

1  Lars  Jorgensen:  "The  Constant  Angle  Arch  Dam,"  Trans.  Am.  Soc.  C.  E.,  vol.  78,  p.  685,  1914. 


Sec.  17-5] 


HYDRAULIC  STRUCTURES 


739 


Poisson's  ratio  for  lateral  strains  is  taken  into  consideration  in  determining  the  relative 
arch  action  in  a  dam  of  this  type,  a  value  of  one-fifth  being  adopted,  and  the  initial  stresses 
induced  axially  by  the  weight  of  the  dam  on  the  foundation,  together  with  the  water  load,  being 
utilized  to  help  support  the  latter.  (See  above  under  "Constant-radius  Dams.")  However, 
dams  designated  in  accordance  with  this  method  are  liable  to  have  an  overhang,  necessitating 
a  thickening  of  its  lower  part.  This  is,  as  a  rule,  accomplished  by  increasing  the  downstream 
radius  Ra  for  these  lower  arch  rings,  while  keeping  the 
former  radius  Ru.  The  result  is  an  arch  thicker  at  the 
crown  than  at  the  haunches. 

When  the  tentative  cross-section  has  been  deter- 
mined it  must  be  analyzed  in  the  same  way  as  that 
of  a  constant-radius  dam. 

Several  dams  of  this  type  have  been  built  in  the 
West  and  in  Alaska.  One  constructed  for  the  Alaska- 
Gastineau  Mining  Co.  near  Juneau,  Alaska,  is  168  ft. 
high.  Another  dam,  which*  ultimately  will  be  305  ft. 
high,  has  been  built  for  the  Pacific  Gas  &  Electric  Co. 
at  Lake  Spaulding,  Cal.  The  maximum  stress  in  this 
dam  is  23.8  tons  per  sq.  ft. 

5.  Design  of  Reinforced-concrete  Dams. — Rein- 
forced-concrete  dams  possess  many  theoretical  advan- 
tages and  they  are  by  far  the  most  satisfactory  dam,  so  far  as  the  type  goes.  The  few 
failures  on  record  of  such  dams  have  never  been  due  to  fault  of  the  dam  proper;  they  have 
always  been  traced  to  faulty  foundation.  Overconfidence  in  this  type  has  led  engineers  to 
neglect  the  facts  that  a  secure  foundation,  sufficiently  deep  cut-off  walls,  adequate  resistance 
against  sliding  in  soft  ground,  etc.,  are  just  as  important  details  as  the  design  and  construc- 
tion of  the  superstructure  itself. 

Because  of  the  comparatively  light  weight  of  the  structure,  it  is  customary  to  support  the 
apron  or  water-tight  membrane  on  a  series  of  triangular  buttresses  in  such  a  way  that  its  inclina- 


FiG.  2c 


Fig.  24. 


Fid.  25. 


tion  is  about  45  deg.  (Figs.  24  and  25).  Obviously,  the  horizontal  component  of  the  water 
pressure  thus  equals  the  vertical  and  the  resultant  has  an  inclination  of  approximately  45  deg. 
From  Fig.  26  it  is  evident  that  if  the  buttresses  are  of  the  shape  indicated,  the  resultant  of  the 
water  pressure  cuts  the  base  in  the  outer  edge  of  the  middle  third.  The  weight  of  the  structure 
draws  the  resultant  somewhat  inside  this  point.  The  corresponding  unit  pressures  on  the 
foundation  are  thus  greater  at  the  downstream  edge  than  at  the  upstream. 

If  soft  foundation  prevails,  it  is  desirable  that  it  be  loaded  as  uniformly  as  possible.  The 
buttresses  are  then  increased  in  length  so  that  the  resultant  will  cut  it  near  the  center  of  the 
base.     If  the  upstream  slope  of  a  bulkhead  dam  is  1  : 1  and  the  downstream  batter  of  the 


740 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  n-5a 


IVater  surface 


buttresses  4  : 1,  or,  in  other  words,  the  length  of  the  base  is  Y^E,  where  E  is  the  height  of  the 
dam,  experience  has  shown  that  the  resultant  of  water  and  concrete  cuts  the  base  almost  exactly 
in  the  center.  n  addition,  the  buttresses  are  placed  on  spread  footings  on  a  continuous  founda- 
tion mattress,  so  that  the  load  will  be  distributed  evenly  over  the  whole  base. 

A  dam  of  this  type  can  be  bulkhead  (Fig.  24)  or  spillway  section  (Fig.  25).  It  can  be 
placed  on  any  kind  of  foundation,  and  in  1909  a  dam  22  ft.  high  was  built  on  baled  hay  at 
Anadarko,  Okla.  The  top  strata  consisted  of  a  pecuhar  waxy  clay  or  marl  under  which  a 
pocket  of  floating  quicksand  was  found.  To  control  the  quicksand  baled  hay  was  laid  down 
on  the  surface  of  the  sand  pocket  and  on  this  was  distributed  a  number  of  perforated  pipes, 
which  were  again  covered  with  more  hay.    The  pipes  led  to  a  sump  outside  the  dam,  from 

which,  during  construction,  the  water  was  constantly 
pumped.  On  the  sand  and  hay  foundation  a  contin- 
uous foundation  mattress  was  bull!;  and  the  dam  and 
power  house  placed  upon  it.  Although  several  severe 
floods  have  passed  over  this  structure,  so  far  no  de- 
fects have  developed. 

In  1908  a  dam  was  constructed  near  Douglas, 
Wyo.,  135  ft.  high  above  the  water  hne,  of  which  80 
ft.  in  the  center  are  founded  on  clay  and  hard-pan. 
The  unit  load  under  the  mattress  is  5.2  tons  per  sq.  ft. 

5a.  Cut-off  Walls. — When  built  on 
soft  foundations,  cutoff  walls  of  reinforced  concrete 
(sometimes  extended  by  sheet  pilings  of  steel,  wood, 
or  reinforced  concrete)  are  built  at  the  upstream  heel  of  the  dam.  The  required  depth  of 
such  cutoffs  can  be  calculated  by  means  of  the  usual  earth  and  hydrostatic  pressure  theories 
after  the  necessary  data  have  been  obtained  through  test  pits  or  borings.  However,  as  a 
rule,  if  such  cutoffs  extend  below  the  ground  level  or  bottom  of  the  superstructure  to  a  depth 
one-half  the  height  of  the  superstructure,  they  are  safe. 

As  such  cutoffs  must  be  strong  enough  to  resist  the  unequal  pressures  acting  on  them,  they 
must  be  reinforced  and  the  superstructures  designed  for  taking  up  a  considerable  reaction  from 
them. 

56.  Foundation  Mattress. — In  soft  ground  the  buttresses  are  placed  on  a  con- 
tinuous foundation  mattress,  which  must  be  reinforced  in  order  to  distribute  the  load  from  the 
buttresses  uniformly  over  the  foundation.    Weep  holes  are  often 
provided  so  as  to  prevent  uplift  from  leakage,  which  possibly  might        jfr  jfr 

I  I 


fiTMltlllifl^ 


Fig.  26. 


Spread 
■  footing 


Fig.  27. 


find  its  way  around  the  cutoff. 

When  the  buttresses  are  placed  on  this  mattress  on  widely  , 
spread  footings,  a  certain  amount  of  inverted  arch  action  will  take         J  y^nl^^ 
place,  thus  reducing  the  reinforcement  materially.    The  concrete  ^  ^ 
mixture  in  the  mattresses  is  as  a  rule  1:3:5.    The  pressures  on  the 
foundation  are  calculated  by  the  formulas  used  for  figuring  the 
stresses  in  a  gravity-section  dam  (see  Art.  3). 

6c.  Buttresses. — On  top  of  the  mattress  or  placed  directly  on  the  rock,  if 
such  can  be  reached,  are  the  buttresses.  If  built  on  a  mattress  or  soft  rock,  such  buttresses 
are  given  a  wide  base  by  stepping  them.  Such  widening  should,  if  not  reinforced,  be  made  in 
such  a  way  that  lines  drawn  at  45  deg.  and  intersecting  between  the  buttresses  at  the  underside 
of  the  mattress  will  lie  entirely  within  the  steps  (Fig.  27).  If  this  is  not  done,  the  steps  must 
be  reinforced. 

Because  of  the  reinforcement,  the  buttresses  in  some  dams  have  been  designed  to  take 
tensile  stresses  in  their  upper  parts  (acting  as  cantilevers).  In  such  cases  the  usual  reinforced- 
concrete  beam  formulas  are  used.  Further  down,  where  the  buttresses  are  longer,  no  tensile 
stresses  are  permitted  and  at  the  base  the  resultant  must  be  well  within  the  middle  third. 


Sec.  17-5(1] 


HYDRAULIC  STRUCTURES 


741 


iforcemenf 


■-Reinforcement 


6' to  £4" 


Vis- 


Fig.  28. 


The  most  dangerous  stresses  in  a  buttress  are  due  to  shear.  As  the  apron  or  water-tight 
membrane  placed  on  the  upstream  side  carries  the  load  to  the  buttresses,  it  is  obvious  that 
each  buttress  must  withstand  the  load  on  one  entire  span.  As  the  spacing,  as  a  rule,  is  about 
18  ft.  these  forces  are  considerable.  So  far  no  satisfactory  method  has  been  developed  whereby 
the  exact  lines  of  shear  can  be  determined,  and  the  designer,  therefore,  must  be  satisfied  by 
figuring  the  shearing  stresses  on  horizontal  joints,  checking  himself  roughly  to  be  certain  that 
the  areas  parallel  to  the  water  pressure  are  large  enough. 

As  the  shear  increases  with  the  depth,  the  buttresses  become  thicker.    In  many  cases  the 
top  portions  have  been  made  12  in.  thick,  but 
this  is  somewhat  too  small  and  16  in.  should 
be  adopted  as  the  minimum. 

In  high  dams  the  bottom  thickness  has 
been  as  great  as  72  in.,  but  this,  of  course,  is 
,a  function  of  the  length  of  the  buttress. 

In  no  case  should  the  permissible  unit 
shear  exfceed  100  lb.  per  sq.  in.  and  even  then, 
some  reinforcement  should  be  used.  In  walls 
not  reinforced  the  stress  should  be  limited  to 
70  lb.  per  sq.  in. 

Sometimes  when  the  buttresses  are  very  long,  as  for  instance  in  high  overflow  dams,  their 
weight  will  draw  the  resultant  downstream  of  the  center.  There. is  no  objection  to  this,  pro- 
vided the  foundation  is  good  and  able  to  resist  the  unbalanced  pressure.  However,  if  the 
foundation  is  soft  and  an  equal  loading  is  desired  under  the  entire  base,  the  portions  of  the 
buttresses  next  to  the  apron  are  thickened  sufficiently  to  place  the  resultant  in  the  center. 

In  order  to  form  a  seat  for  the  slabs  of  the  apron,  the  buttresses  at  their  upstream  edge  are 
shaped  as  shown  in  Figs  28  and  29.    The  width  of  this  seat  varies  from  6  to  24  in.,  depending 
upon  the  thickness  t  of  the  slab.    At  the  buttress  the  thickness  of  the 
haunch  must  at  least  be  t  in  order  to  develop  the  same  resistance  to  shear- 
ing as  the  slab  itself. 

The  concrete  mix  in  buttresses  is  generally  1:3:5,  but  sometimes  a 
richer  mix  is  used. 

hd.  Bracing. — As  buttresses  are  very  high  as  compared 
with  their  width,  it  is  often  necessary  to  brace  one  against  the  other.  This  is  done  by  means 
of  rectangular  beams  as  shown  in  Fig.  24. 

5e.  Apron. — The  apron  consists  of  slabs  (Ambursen  type)  or  arches  (multiple- 
arch  type).  Its  sole  function  is  to  act  as  a  water-tight  membrane  and  to  transfer  the  hydro- 
static pressure  to  the  buttresses.  Slabs  are  designed  as  uniformly  loaded  and  the  usual  formulas 
apply.    As  a  rule  the  moment  is 

M  =-^^  (ft.-lb.) 

where  W  is  the  load  in  pounds  on  a  strip  1  ft.  wide.  As  the  unit  load  is  wh  lb.  per  sq.  ft.  and 
the  length  of  the  loaded  strip  I  ft.,  W  =  whl  and 


M  =         =  7.8125  hl^ 

■  o 


M  =  93.75  hl^ 


(ft.-lb.) 
(in.-lb.) 


The  reason  for  using  this  formula  is  that  the  buttresses  are  built  first  and  the  slabs 
afterward  and  in  such  a  way  that  no  continuity  of  action  can  be  depended  upon  (Fig.  28). 

As  these  slabs  are  submerged,  and  as  it  is  difficult  to  make  them  absolutely  water-tight, 
some  engineers  believe  there  is  danger  that  in  time  the  reinforcement  will  corrode.    In  order  to 


742 


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[Sec.  17-5e 


Sec.  17-5/] 


HYDRAULIC  STRUCTURES 


743 


overcome  this  objection,  slabs  have  sometimes  been  built  as  semi-arches,  as  shown  in  Fig.  29, 
but  the  haunches  must  be  designed  for  arch  action  and  not  like  those  shown  in  the  figure.  As 
a  rule,  the  concrete  mix  for  these  slabs  or  arches  is  1  :  2 : 4. 

After  the  proper  slab  thickness,  the  buttresses,  etc.,  have  been  calculated,  one  entire  panel 
of  the  dam  is  analyzed  for  safety  of  design  and 
the  corresponding  unit  stresses  determined  (Fig. 
30). 

Some  practical  details  of  design  are  shown  in 
Fig.  31.  It  is  also  customary  to  provide  a  ser- 
vice bridge  inside  the  dam,  as  shown  in  Fig.  30,  so 
that  the  underside  of  the  slabs  and  their  joints 
with  the  buttresses  can  be  inspected  without 
difficulty  as  often  as  desired. 

The  advantages  of  the  hollow  reinforced  ^ 
dam  have  led  a  number  of  designers  to  develop 
various  types.  Many  of  them  have  never  been 
built  like  those  developed  by  Ransome  (Fig.  32) 
and  Morton  (Fig.  33).  The  Ransome  dam  con- 
sists of  buttresses  placed  at  a  certain  angle  so  that 
they  intersect.  The  slabs  are  thus  of  a  variable 
span.  This  is  a  very  strong  structure,  but  the  cost 
of  forms  excessive.  In  the  Morton  dam  the  apron 
is  supported  on  inclined  columns  braced  by  inter- 
mediate beams.  The  disadvantages  are  that  these 
columns  are  liable  to  bend,  that  the  load  is  con- 
centrated on  the  column  foundations,  that  the 
form  cost  is  high  and  that  the  placing  of  re- 
inforcement and  concrete  difficult.  Fig. 

The  Edge  dam,  used  in  a  somewhat  modi- 
fied form  in  the  reconstruction  of  the  Austin  Dam  in  Texas,  offers  several  structural  advan- 
tages (Fig.  34).  The  apron  is  divided  into  square  panels  reinforced  both  ways,  which  gives 
it  great  structural  strength  and  the  buttresses  are  thoroughly  braced  by  intermediate  walls 
supporting  the  deck.  However,  it  is  not  always  possible  to  take  advantage  of  the  structur- 
ally slender  thickness  of  the  apron,  as  a  certain  thickness  against  leakage  is  required.  Further- 
more, the  form  cost  is  excessive  and  the  saving  in  concrete  slight. 


Plan 
32. — Ransome  dam. 


Fig.  33.— Morton  dam.  Fig.  34.— Edge  dam. 


5/.  Multiple -arch  Dams. — To  overcome  what  he  considered  objectional  features 
of  the  Ambursen  dam — viz.,  the  reinforced-concrete  slabs  and  the  many  buttresses — Eastwood 
developed  a  type  consisting  of  a  series  of  circular  arches  of  long  spans.    The  first  dam  built 


744 


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[Sec.  17-5/ 


Sec.  17-6] 


HYDRAULIC  STRUCTURES 


745 


of  this  type  was  for  the  Hume-Bennett  Lumber  Co.  in  CaUfornia  in  1908.  It  consists  of  12 
circular  arches  of  50-ft.  span  supported  on  13  buttresses.^ 

A  later  dam  of  this  type  was  condemned  by  the  California  Railroad  Commission  because 
of  insufficient  bracing  of  the  buttresses.  The  advantage  of  the  slab  type  is,  that  should  one 
series  of  slabs  collapse,  the  adjacent  buttresses  will  prevent  further  damage  to  the  structure, 
while  if  a  series  of  arches  collapses  the  whole  structure  will  fall  because  of  the  absence  of  a 
counterforce  at  the  buttress. 

In  some  recent  dams  designed  by  Jorgensen^  the  buttresses  have  been  braced  so  that  they 
can,  by  cantilever  action,  sustain  the  arch  reaction  should  the  arches  in  the  adjacent  panel  be 
missing  (Fig.  35).  Quoting  Jorgensen,  the  most  economical  spacing  of  the  buttresses  lies 
between  30  and  50  ft.  For  low  dams  the  lower  limit  would  be  the  best  and  for  high  dams  the 
upper. 


It  should  be  noted  that  for  arches  with  a  large  subtended  angle  and  placed  in  an  inclined 
position,  the  crown  lies  at  a  considerably  higher  elevation  than  the  haunches  and  that  the  load 
varies  due  to  the  variation  in  hydrostatic  pressure. 

For  designing  the  thickness  of  the  arches,  the  methods  given  under  ''Arched  Dams"  (Art.  4) 
can  be  used.  However,  if  the  subtended  angle  is  large  and  the  inclination  considerable,  it  is  more 
convenient  to  use  graphic  statics,  drawing  one  pressure  line  for  the  weight  and  another  for  the 
hydrostatic  pressure  and  then  combining  them  (Fig.  36). 

6.  Earthen  Dams  With  Concrete  Core  Wall. — The  design  of  earthen  dams  is  purely  a 
matter  of  experience.  The  ruling  factor  is  preventing  water  from  traversing  the  dam.  This 
is  effected  by  providing  an  impermeable  core  of  clay,  puddle,  concrete,  masonry,  steel  plates 
protected  with  concrete  or  asphalt  coatings,  and,  especially  in  smaller  dams,  sheet  pilings  of 
lumber.  It  is  absolutely  necessary  if  an  earthen  dam  is  decided  upon,  that  the  necessary 
materials  are  available  at  or  near  the  site,  as  the  quantities  are  so  voluminous  that  it  is  impos- 
sible to  haul  them  any  great  distance. 

1  Wegmann:  "The  Design  and  Construction  of  Dams,"  1911  Ed.,  p.  436. 

2  Labs  Jorgensen:  "  Multiple-aroh  Dams  on  Rush  Creek,  CaUfornia."  Trans.  Am.  Sbe.  C.  E.,  March,  1917. 


746 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-6 


An  earthen  dam  may  consist  of : 

1.  A  homogeneous  bank  of  earth. 

2.  A  bank  of  earth  having  a  puddle  core. 

3.  A  bank  of  earth  having  a  masonry  core  wail. 

4.  A  bank  of  earth  having  a  puddle  placed  on  the  water  slope. 

The  first  method  can  be- used  only  when  the  required  quantity  of  earth  or  gravel,  containing 
enough  clay  to  make  it  water-tight,  can  be  obtained  at  a  reasonable  cost. 

In  cases  where  this  would  prove  too  expensive,  a  central  core  is  provided  of  clayey  earth 
or  gravel,  ordinary  earth  being  used  in  the  other  portions  of  the  dam.  In  order  to  prevent  leak- 
age under  the  dam  this  core  should  be  extended  down  in  a  trench  to  an  impervious  stratum, 
or  at  least  far  enough  down  to  make  the  path  of  such  leakage  as  long  as  possible. 

In  the  third  plan,  masonry  is  substituted  for  the  puddle  core.  This  plan  is  adopted  when 
no  claye}''  earth  can  be  obtained  at  a  reasonable  cost.  As  a  rule  it  is  more  expensive  than  plans 
1  and  2,  but  has  great  advantages  as  regards  safety. 

As  regards  plan  4,  it  is  open  to  two  objections:  The  puddle  is  injured  if  the  slope  settles, 
which  nearly  always  happens,  and  cracks  will  occur  in  the  water  line  due  to  alternate  wetting 
and  drying. 

In  some  cases  concrete  paving,  plain  or  reinforced,  has  been  used  on  the  upstream  side 
of  an  earthern  dam  for  making  the  dam  water-tight  However,  such  paving  is  apt  to  slide 
and  should  be  heavily  anchored  down.  Even  then,  settlements  in  the  slope  will  cause  cracking, 
and  leakage  is  bound  to  take  place. 

The  theory  of  earth-dam  design  is  very  simple:  The  upstream  portion  and  the  core  wall 
serve  to  reduce  the  leakage  to  such  an  extent  that  the  hydraulic  gradient  falls  inside  the  dam 
body,  and  the  downstream  portion,  through  its  weight,  will  hold  the  saturated  mass  in  position 
and  prevent  it  from  sliding  in  a  downstream  direction.  It  has  often  been  noted  that  earthen 
dams  have  a  tendency  to  fail  through  the  caving  of  the  downstream  slope,  which  proves  that  the 
hydraulic  gradient  did  not  fall  inside  the  dam  but  intersected  the  slope  some  distance  above 
the  foundation. 

In  order  to  broaden  the  base  and  to  bring  the  downstream  slope  out  as  far  as  possible  on 
high  dams,  it  is  customary  to  step  the  slope  (so-called  berms)  at  elevations  20  to  30  ft.  apart, 
which  obviously  means  a  saving  in  materials.  Such  berms  are  usually  paved  and  provided 
with  gutters  on  the  inside. 

In  order  to  confine  the  hydraulic  gradient  to  the  embankment,  the  Pierson  Engineering 
Corporation,  when  building  a  series  of  earthen  dams  in  Spain,  ^  placed  drainage  dykes  of  broken 
rock  near  the  downstream  side  of  each  dam  at  the  toe  of  a  somewhat  pervious  section,  and  pro- 
vided outlets  for  any  leakage  collected  by  these  dykes. 

When  sheet  pilings  are  used  below  a  core  wall  and  the  foundation  is  very  soft,  it  is  often 
necessary  to  increase  the  downstream  portion  of  the  dam,  in  order  to  create  a  surcharge  suffi- 
cient to  counterbalance  any  unbalanced  forces  on  the  sheet  piling  due  to  hydrostatic  pressure. 

Experience  has  shown  what  general  dimensions  are  most  suitable  for  earthen  dams.  They 
are,  of  course,  to  a  certain  extent  a  function  of  the  materials  used  and  the  height  of  the  struc- 
ture, additional  strength  being  given  to  high  dams:^ 


The  upper  portion  of  the  upstream  slope  should  be  protected  against  erosion  by  waves 
and  burrowing  animals  by  a  riprap,  15  to  20  in.  thick,  or  concrete  paving,  5  to  8  in.  thick,  ex, 

1  Eng.  Rec,  Aug.  29,  1914,  p.  250. 

2  Wegmann:  "The  Design  and  Construction  of  Dams." 


Top  width  

Superelevation  above  high  water 

Upstream  slope  

Downstream  slope  


.10  to  30  ft. 
. .  5  to  25  ft. 
..l:2:tol:3 
l:lHto  1:2K 


Sec.  17-6] 


HYDRAULIC  STRUCTURES 


747 


tending  some  distance  below  and  5  to  15  ft.  above  the  water  line.  The  top  of  the  dam,  the 
downstream  slope  and  the  upstream  slope  above  the  paving  are  generally  covered  with  good 
soil  and  sodded. 

A  fairly  satisfactory  formula  for  the  top  thickness  is  given  by  Lyndon:^ 

r  =  5+0.2i/  (ft.) 

where    H  =  height  of  dam  in  feet. 

As  the  earth  fill  is  bound  to  settle  it  is  customary  to  increase  the  profile  from  one-fifteenth 
to  one-twentieth  of  its  height  (Fig.  36A).  This  shrinkage  is,  of  course,  a  function  of  the  quahty 
of  the  materials  and  the  degree  to  which  they  have  been  rammed.  As  the  height  varies  from 
zero  to  a  maximum,  this  method  will  make  the  crest  of  the  dam  arched  in  the  longitudinal 
section. 


; ,  Surcharge^ H  to^H 


Fig.  36^. 


Core  walls  are  never  designed  to  resist  the  whole  water  pressure  as  they  serve  merely  as  a 
water-tight  membrane  and  are  backed  by  the  downstream  portion  of  the  dam.  They  should 
extend  from  1  to  2  ft.  above  the  highest  water  level  in  the  reservoir  and  have  a  top  width  of 
from  2.5  to  6  ft.  The  sides  are  battered  from  16: 1  to  20: 1,  so  that  the  thickness  at  the  natural 
ground  surface  is  from  one-sixth  to  one-seventh  of  the  height.  Instead  of  battering  the  faces, 
the  increase  in  thickness  can  be  obtained  by  offsets. 

Parker^  gives  a  method,  whereby  the  stability  of  core  walls  can  be  determined:  Draw 
in  Fig.  37  on  the  water  side  a  line  ah  making  with  the  horizontal  an  angle  </>  equal  to  the  angle  of 


Fig.  37. 


repose  of  the  saturated  earth  (usually  =  20  to  23  deg.).  Then  draw  on  the  downstream  side 
a  line  cd,  making  with  the  horizontal  an  angle  O  equal  to  the  angle  of  repose  of  the  rammed 
earth  (generally  9  =  45  to  55  deg.). 

Calculate  the  areas  located  above  these  lines.  For  0  =  20  deg.  and  a  1:3  slope  of  the 
upstream  side,  the  area  ahc  becomes  very  nearly  Y/^h})  and  with  6  =  45  deg.  and  a  1:2  slope 
of  the  downstream  side  the  area  cde  is  J-^/i^.  The  weight  of  rammed  earth  can  be  taken  at 
132  lb.  per  cu.  ft.  and  that  of  saturated  at  160.    The  thrust  on  the  core  wall  would  thus  be 

y^h}  (160)  -         (132)  =  76/i2  (lb.  per  lin.  ft.) 

If  the  thickness  of  the  core  wall  is  x  ft.,  its  ultimate  resistance  to  shear,  when  of  concrete, 
is  about  30,000  x  lb.  per  lin.  ft.    If  a  factor  of  safety  /  (usually  /  =  2)  is  used, 

30,000  X  =  7QhH  or  x  =  about  ^  •  (ft.) 

1  Lamar  Lyndon:  "Hydro-electric  Power,"  vol.  I,  p.  279. 
'Philip  A.  Morley  Parker:  "The  Control  of  Water,"  p.  318. 


748 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-7 


Unless  h  is  great  this  formula  will  give  results  somewhat  smaller  than  experience  has  shown 
as  requisite  to  stop  percolation  through  an  ordinary  mix  of  concrete.  Especially  for  reinforced 
concrete,  it  is  necessary  to  use  a  very  dense  mix  or  to  coat  the  upstream  surface  with  an  imper- 
vious material. 

HerscheP  gives  the  following  practical  rules  for  first-class  work:  4  to  5  ft.  thick  at  bottom 
of  trench  enlarged  to  8  ft.  at  natural  surface  and  tapering  to  4  ft.  at  top  of  core  wall.  However, 
for  smaller  dams  these  dimensions  are  entirely  too  clumsy.  Herschel  states  also  that  a  wall 
2  ft.  thick  throughout  is  sufficient  to  stop  percolation. 

When  building  earthen  dams  the  materials  should  be  deposited  in  layers  from  8  to  12  in. 
thick  and  each  course  should  be  well  packed.  This  is  best  accomplished  by  steam  rollers,  of 
which  the  first  one  has  grooved  rollers  and  the  other  smooth  ones.  Especially  in  dams  without 
core  walls,  every  layer  should  be  somewhat  inclined  toward  the  water  side  of  the  dam  and 
arched  upward,  so  that,  later  on,  when  the  materials  settle,  no  pockets  are  formed.  Such 
pockets,  if  impervious,  will  retain  water  and  the  hydrostatic  pressure  will  be  carried  out  to  the 
downstream  slope,  which  then  will  cave.  It  has  happened  that  dams,  saturated  in  this  way, 
after  having  been  in  successful  operation  for  several  years  have  failed  in  an  upstream  direction, 
because  of  the  outer  hydrostatic  pressure  being  removed  through  a  lowering  of  the  water  surface. 

Hollow,  cellular  core  walls  of  reinforced  concrete  extending  to  the  top  of  the  dam  have 
been  proposed  because  they  offer  a  convenient  way  of  providing  a  continuous  overflow  along 
the  crest  of  the  dam,  thus  preventing  overtopping. 

7.  Passing  the  Discharge.— Openings  must  be  provided  in,  at,  or  near  a  dam  at  such  an 
elevation,  that  when  the  water  in  the  reservoir  rises  above  a  certain  level,  it  will  escape  through 
one  or  more  of  these  openings,  thus  preventing  the  bulkhead  portion  from  being  overtopped. 
Such  relief  must  be  designed  to  discharge  the  maximum  flood  observed  or  anticipated  at  the  dam 
site.  If  the  reservoir  has  a  large  surface,  the  rise  in  water  level  to  an  elevation  required  to 
give  the  necessary  head  on  the  spillway  is  sometimes  considerable,  and,  if  in  addition  the 
floods  are  of  short  duration,  a  reduction  can  be  made  in  the  spillway  requirements. 

7a.  Form  of  Spillway. — There  are  several  ways  of  passing  floods  at  dams. 
Pipes  laid  at  or  near  the  base  of  the  structure,  thus  acting  under  a  great  hydraulic  head,  are 
sometimes  used,  but,  as  a  rule,  in  conjunction  with  other  types  of  spillways.  Overflow  spillways 
are  of  many  designs.  Sometimes  they  are  located  apart  from  the  main  dam  and  the  water 
discharged  into  a  gulley,  canal,  or  channel  conveying  it  back  into  the  river  a  safe  distance  below 
the  dam;  in  other  cases  they  are  located  in  the  dam  itself,  part  of  which  has  been  lowered  for  the 
purpose. 

When  spillways  are  located  in  places  where  attendance  is  possible,  such  as  for  power 
plants  with  the  station  at  the  dam,  they  are  often  outfitted  with  some  type  of  movable  dam, 
generally  gates,  as  it  provides  means  for  keeping  the  water  level  at  a  higher  elevation,  thus 
increasing  not  only  the  storage  but  also  the  head.  Another  advantage  of  this  system  is  that 
the  spillway  can  be  shortened  materially  as  the  discharge  openings  can  be  made  very  deep,  with- 
out necessitating  a  sacrifice  in  the  storage  capacity.  Consequently,  such  dams,  as  built  at 
McCalls  Ferry  and  for  the  Ozark  Power  Company  on  the  White  River  in  Missouri,  are  not 
suitable.  They  are  designed  to  resist  and  to  pass  the  maximum  floods,  16  and  12,5  ft.,  respec- 
tively, and,  because  of  the  lack  of  movable  dams  or  gates,  the  water  level,  after  the  flood  has 
passed,  soon  falls  to  the  crest  of  the  dam.  Flashboards  about  5  ft.  high  are  now  used  at  both 
places,  but  such  provisions  are  more  or  less  to  be  considered  as  makeshifts. 

When  spillways  are  located  in  places  where  they  cannot  be  under  constant  surveillance, 
they  must  be  given  ample  length,  so  that  when  the  water  level  rises  a  comparatively  large 
discharge  can  be  accommodated,  thus  preventing  a  rapid  rise  which  might  endanger  the  main 
structure.  In  order  to  obtain  a  great  length  of  spillway  in  as  short  a  distance  as  possible,  they 
are  sometimes  arched  or  zig-zagged  in  plan.  However,  because  of  the  interference  at  the  cor- 
ners of  such  broken  lines  the  effective  length  is  shorter  than  the  actual  total  length.  Sometimes, 

1  Proc.  I.  C.  E.,  vol.  132,  p.  255. 


Sec.  17-76] 


HYDRAULIC  STRUCTURES 


749 


for  high  heads  the  water  flows  over  the  whole  structure  in  such  a  way  that  the  effective  length 
is  the  straight  line  between  the  end  points. 

76.  Discharge  Capacity. — The  discharging  capacity  of  a  spillway  depends  upon 
its  shape.    The  general  formula  used  reads: 

Q  =  Vs  tMlhV2gh  or  Q  =  H  l^lV^g  (hf  (sec.-ft.) 

where  Q  =  discharge  in  second-feet;  I,  length  of  the  spillway;  h,  head  acting  on  it;  g  =  32.16; 
and  fi  an  empirical  coefficient  depending  upon  the  shape  of  the  spillway,  and  giver,  in  Fig.  38. 
If  the  velocity  of  approach  Vo  is  considerable,  its  influence  on  the  discharge  must  be  taken 

Vo' 

into  account.    This  is  done  by  transforming  it  into  the  corresponding  velocity  head  k  = 


and  introducing  it  in  the  equation,  which  thus  becomes: 

Q  =  y3f^lV2g[{h  +kf^ 


2sf 
(sec.-ft.) 


fj.'0.75-085 


u,=a80-685 
1^=060-0.65 


0.75-0.65 


Fig.  38. 


Should  the  crest  of  the  dam  be  very  wide  d>  h  (Fig.  39)  with  sharp  corners,  the  discharge  is: 

Q  =  0.351  V2g  (h  +  kf'     or  fx  =  0.525 
and 

e  =mh  +  k) 

and  for  rounded  corners 

Q  =  0A0lV2g(h  +  k)^^     or  ^  =  0.60 


Francis  found  that  for  vertical,  sharp-crested,  rectangular  weirs  with  complete  contractions 
and  free  overfall 


Q  =  3.33 


where  n  =  number  of  lateral  contractions,  0,  1,  or  2.    His  constant  3.33  corresponds  to  /x  = 
0.62  in  the  above  given  general  formula.    As  a  rule  the  end  contractions  can  be  neglected 
when  a  spillway  is  considered  so  that  the  formula  becomes: 

Q  =  3.33Z/i'^ 

and  the  influence  of  the  velocity  of  approach  Vo  is  introduced  as  given  above. 

Because  of  the  lack  of  experimental  data  on  weirs  with  h  <2  ft.,  engineers  are  using  for 
higher  heads,  formulas  developed  for  smaller  heads.  However,  it  has  been  shown  that  the 
Francis  formula  gives  reasonably  accurate  results  for  heads  up  to  5  ft. 

7c. — Profiles  of  Spillways. — Furthermore,  spillways  are  seldom  built  in  the 
shape  of  sharp-crested  weirs.  They  are,  as  a  rule,  given  an  ogee  shape,  so  as  to  prevent  a 
vacuum  below  the  falling  sheet  of  water,  the  so-called  nappe. 

It  is,  therefore,  customary  to  design  the  shape  of  the  nappe  for  the  maximum  head  acting 


750 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-7c 


on  the  spillway  using  the  general  form  as  found  by  Bazin  for  sharp-crested  weirs,  and  then  to 
form  the  concrete  work  accordingly.  It  is  d,dvisable  to  let  the  concrete  on  the  downstream 
side  of  the  apex  of  the  curve  for  the  lowex  nappe  encroach  somewhat  on  the  water,  so  as  to  be 
certain  that  a  vacuum  cannot  form  (Fig.  40A).   If  the  abscissae  are  x,  the  ordinates  for  the  upper 


+Y 


+x 


-0.1 
-0.2 


Nappe  for  slope  oo  I  ( Vertical  mir)- 
Nappe  for  slope  I  Z  


06-0.5-0.4-0.3-0,2-0,1    -I  0.1    0.2  0.3  04  Q5  06  0.7  0.3  0,9    LO   I.I    1.2    1.3  1,4 


Fig.  40. 


nappe  ?/„  and  for  the  lower  yi  and  the  head  Bazin  found  the  following  values  for  verticle  sharp- 
crested  weirs: 


X 

u 

yi 

h 

h 

h 

-3.00 

0.997 

-1.00 

0.963 

0.00 

0.851 

0.000 

0.05 

0.059 

0.10 

0.826 

0.085 

0.15 

0.101 

0  20 

0.795 

0.109 

0.25 

0.782 

0.112 

0.30 

0.762 

0.111 

0.35 

0.106 

0.40 

0.724 

0.097 

0.45 

0.085 

0.50 

0.680 

0.071 

0  55 

0.054 

0.60 

0.627 

0.035 

0.65 

0.013 

0.70 

0.569 

-0.009 

1.40 

-0.020 

Consequently,  if  the  head  is  10  ft.,      =  -  3.00 or    =  -  30ft.  and  ~^  =  0.997  or      =  9.97 

ft.,  etc.  It  is  obvious  that  the  lower  nappe  rises  from  origin  to  a  height  0.1 12A  in  the  distance 
0.25/1  and  that  the  shape  is  approximately  an  ellipse  with  the  major  axis  horizontal  and  equal 
to  }y^h  and  the  minor  axis  vertical  and  equal  to  }-^h. 


^     Sec.  17-7c]  HYDRAULIC  STRUCTURES  751 

Boussinesque  found  that  on  the  ordinate  0.25h  the  flow  was  practically  horizontal.  ^  From 
f     this  observation  can  be  deducted  the  velocity  in  the  upper  film  of  the  nappe  Vu  =  0.475  \/ 2gh 
and  that  in  the  lower  film  vi  =  0.946  \/ 2gh.    Assuming  that  the  pressure  increase  on  this 
ordinate  is  in  a  direct  proportion  to  the  depth,  the  average  velocity  takes  place  one-third  from 
I     the  bottom  of  the  nappe. 

For  a  sharp-crested  weir  the  discharge  per  linear  foot  is 

Q  =  VsfJ^h  V2^  with  /X  =  0.62 

On  the  ordinate  0.25/i  the  thickness  t  of  the  nappe  is 

t  =  (0.782 -0.112)/i  =  0.67/i  (see  Bazin's  table) 

so  that  the  mean  velocity  is 


and 


Fig.  40A. 


If  it  is  assumed  that  the  water  jet  on  the  downstream  side  of  the  ordinate  0.25/i  follows 
the  laws  for  a  heavy  body  thrown  horizontally  in  a  vacuum,  then 

X  =  Vmt  and  V  =  2' 

or 

^  Comptes  rendus  de  L' Academie  des  Sciences,  July-Oct.,  1887. 


752 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  n-7c 


Introducing  in  this  parabolic  expression  the  value  found  above,  or 


2v„ 


=  1.54/i  it  becomes  y 


1.54/1 


and      =  {1.54:h)y 


By  plotting  this  parabola  the  thickness  of  the  nappe  at  any  point  can  be  found  by  con- 
structing graphically  the  tangential  velocity  Vx,  keeping  in  mind  that  the  horizontal  velocity 
remains  constant  Vm  =  O.Q2\/2gh  (Fig.  40 A).  As  the  discharge  Q  also  remains  constant, 
the  thickness  tx  of  the  nappe  is  expressed  by 

Q 


Of  this  thickness  ~  is  plotted  downward  on  the  normal  to  the  parabola  in  the  point  in 


By  combining  the  upper  and  the  lower  points  respectively,  the 


2tx 

question  and  upward. 
o 

shape  of  the  nappe  is  found. 

A  parabola  can  be  calculated,  which  approximates  the  shape  of  the  underside  of  the  nappe. 
As  the  stability  of  overflow  dams  is  calculated  in  the  same  manner  as  that  for  gravity-section 

dams,  reinforced-concrete  dams,  etc.,  it  is  not  always  possible  to 
keep  this  parabolic  shape  of  the  spillway  all  the  way  to  the  toe. 
Generally  a  tangent  is  drawn  to  the  parabola  at  such  an  angle 
that  its  intersection  with  the  base  provides  the  required  width 
(Fig.  41). 

From  the  above  it  is  obvious  that  the  true  head  for  figuring 
the  discharge  is  larger  than  the  head  on  the  crest  of  the  spill- 
way. This  true  head  can  always  be  found  if  the  elevation  of 
the  crest  of  the  spillway  and  the  surface  of  the  water  perpen- 
dicularly above  it  are  known.  If  this  thickness  t  of  the  nappe  is 
known,  the  true  head  h  is 

h  =  ^  =  — ^ 

0.7.82  -  0.112  0.67 


Fig.  41. 


1.49^ 


which  is  the  head  to  be  used  in  the  discharge  formula.  If  the  discharge  is  very  small  in  com- 
parison with  that  for  which  the  spillway  was  figured,  the  Francis  formula  must  be  used  with  t 
instead  of  h. 

It  sometimes  happens,  especially  when  ogee  curves  are  fitted  to  spillways  in  arched  dams, 
that  the  crest  thickness  is  insufficient  to  accommodate  the  curvature. 
In  such  cases  the  crest  of  the  spillway  is  cantilevered  over  the  upstream 
face  as  shown  in  Fig.  42. 

Reinforced-concrete  dams  have  decks  sloping  about  1  : 1,  so  that  the 
velocity  of  approach  is  increased  gradually.  Therefore,  the  oblique  pres- 
sure on  the  nappe,  due  to  the  part  of  the  discharge  coming  from  the  body 
of  water  located  below  the  elevation  of  the  crest,  is  at  a  smaller  angle  with 
the  horizontal,  than  for  a  vertical  face  of  the  dam.  In  consequence,  the 
curvature  of  the  underside  of  the  nappe  is  not  so  pronounced. 

Bazin  observed  the  flow  over  a  sharp-crested  weir  inclined  down- 
stream on  a  slope  of  1  :2  (Fig.  40).  The  coordinates  observed  are  as 
follows: 


Fig.  4  2— Canti- 
levered spillway. 


Sec.  ll-7d] 


HYDRAULIC  STRUCTURES 


753 


X 

l/u 

yi 

h' 

h 

h 

0.00 

0.730 

0.000 

0. 10 

0.700 

0.011 

0.20 

0.666 

0.005 

0.30 

0.630 

—  0.014 

0.40 

0.585 

—  0.044 

0.50 

0.535 

—  0.083 

0.60 

0.480 

—  0. 130 

0. 70 

0.418 

0.80 

0.350 

0.90 

0.276 

1.00 

0.196 

1.10 

0.109 

1.20 

0.009 

1.30 

-0.098 

For  the  same  head  h  Bazin  found  that  the  indined  weir  gave  nearly  13%  greater  discharge. 

Knowing  that  for  a  slope  1  :  co ,  or  the  horizontal,  the  water  flows  horizontally  until  the 
crest  (or  in  this  case  the  end  of  the  channel)  has  been  reached  and  that  then  the  shape  of  the 
nappe  follows  the  laws  for  a  heavy  body  thrown  horizontally  (see  under  Boussinesque)  that 
for  slopes  of  1  : 2  and  oo  :  1,  or  the  vertical,  the  shapes  are  as  given  above,  it  is  comparatively 
easy  to  determine  approximately  by  interpolation  the  shape  of  the  nappe  for  any  slope. 
However,  in  order  to  be  safe,  the  concrete  lines  should  be  designed  so  as  to  encroach  upon  the 
lower  nappe  for  the  maximum  head  on  the  spillway,  as  otherwise  a  vacuum  will  form 

Horton^  in  figuring  the  discharge  over  ogee  curves  uses  the  formula 

Q  =  Clh}'' 

where  h  is  measured  from  the  crest  of  the  curve.  A  correction  is  introduced  in  C,  which  is 
expressed 

C=  [3.62  -  0.16(*S  -  1)]  /i''"" 

where  S  is  the  slope  of  the  approach  to  the  crest,  or 

^  _  horizontal  run 
vertical  rise 

This  is  obviously  the  best  formula  to  use  for  dams  with  inclined  water  surface  like  re- 
inforced-con  Crete  structures. 

If  thus  ^  is  1  vertical  to  2  horizontal  and  h  =  4.0  ft.,  C  =  3.71. 

Actual  experiments  have  shown  that  C  is  3.74  which  proves  that  the  formula  gives  some- 
what conservative  values.  It  is  to  be  noted  that  the  portion  upstream  of  the  ordinate  0.25/i 
(see  Bazin's  method)  must  be  at  least  3  ft.  in  width  for  this  increase  in  C  to  take  place. 

7<i.  Overflow  Dams. — ^When  a  dam  acts  as  an  overflow  and  its  height  is  com- 
paratively large,  the  energy  of  the  water  when  reaching  its  toe  is  sometimes  considerable. 
The  force  P. on  a  plane  normal  to  the  nappe  is: 

where  v  is  the  velocity  ;  Q,  the  quantity;  w,  the  unit  weight  per  cubic  foot  of  water  =  62.5; 
and  g,  gravity  =  32.16. 

1  Water  Supply  Paper  200,  p.  131. 
48 


754 


CONCRETE  ENGINEERS'  HANDBOOK 


(Sec.  Vt-le 


If  the  water  below  the  dam  is  of  sufficient  depth  to  act  as  a  shock  absorber,  it  is  customary 
to  provide  the  spillway  at  its  bottom  with  a  sweep,  so  that  the  water  is  discharged  from  it  in 
a  horizontal  direction  against  the  water  below  the  dam  (Fig.  41). 

Should  the  water  level  below  the  dam  be  too  low  to  act  as  a  cushion,  it  is  sometimes  nec- 
essary, as  was  done  at  Gatun,  Panama  Canal,  to  place  concrete  blocks  in  the  path  of  the 
water,  thus  breaking  up  its  force  by  eddie  formations. 

Another  method  is  by  providing  stilling  pools,  which  often  are  formed  by  a  low  secondary 
dam  placed  some  distance  below  the  main  dam. 

Often  aprons  are  constructed  to  protect  the  river  bed  from  erosion.  Wegmann  recom- 
mends that  if  L  is  the  length  of  such  an  apron  in  the  downstream  direction  and  the  height 
of  the  crest  of  the  spillway  above  the  top  of  the  apron 

L  =2H 

with  the  intention  that  the  standing  wave  will  occur  in  this  distance.  However,  in  many 
instances  this  is  not  the  case  and  in  India  L  is  made  much  longer.  Often 

L  =  3  to  4// 

and  sometimes  extended  by  a  riprap  1.5H  in  length. 

Rehbocki  suggests  that  for  the  maximum  head  on  the  spillway  hmax  the  length  be  made 

L  =  1.5H  +  6hma.  to  2H  +  Shma. 

7e.  Sluices. — Dams  are  generally  provided  with  pipes  laid  through  their  base, 
so-called  sluices,  to  enable  the  drawing  down  of  the  water  level  below  the  spillway  crest.  Often 
such  sluices  are  designed  with  the  intention  of  removing  possible  silt  deposits,  but  their  efficiency 
is  doubtful.  Should  a  flood  occur,  greater  than  that  for  which  the  spillway  is  designed,  such 
sluices  are  very  useful  as  their  discharge  capacity  is  great. 

Such  sluices  should  have  their  valves  or  gates  placed  in  an  open  shaft,  and  stop  logs  should 
be  provided  at  their  upstream  side,  so  that  the  valves  can  be  inspected  or  removed  for  repairs. 
Coarse  screens  are  sometimes  placed  in  the  conduit  to  prevent  water-logged  timbers  or  other 
large  objects  from  entering.  Bell  mouths  should  be  formed  in  the  concrete  in  order  to  make 
the  losses  due  to  entry  as  small  as  possible.  If  h  is  the  head  measured  from  the  center  of  the 
opening  to  the  water  surface,  or  the  difference  in  elevation  between  the  upstream  and  down- 
stream water  surfaces,  if  the  downstream  opening  of  the  conduit  is  submerged,  and  if  I  is  the 
length  of  the  conduit  the  losses  in  the  conduit  are 

?;2  y2         p       ,.2      ,.2  p 

2g         2g         a        2g     2g  ^  a  ' 

where  the  first  term  is  the  losses  due  to  the  velocity  of  the  flow;  the  second,  due  to  entry;  and 
the  third,  the  frictional  resistance  in  the  conduit. 
The  entry  coefficient 

so  that  fx  varies  from  0.06  for  a  pipe  with  a  bell-mouthed  entry  to  0.50  for  a  pipe  projecting  into 
the  reservoir. 

The  coefficient  C  depends  upon  the  frictional  resistance  in  the  conduit,  p  is  the  wetted 
perimeter  and  a  is  the  net  area  of  the  conduit.    For  round  pipes 

P  ^  wd  X  4c  _4 
a         ird^  d 


1  "Handbuch  der  Igenieurwissenschaften. "    "Der  Wasserbau,"  p.  37. 


Sec.  17-7/] 


HYDRAULIC  STRUCTURES 


755 


and  for  rectangular  conduits  t  ft.  high  and  6  ft.  wide 

P  _2(t  +  b) 
a  tb 

A  good  trial  value  of  C  is  0.0075. 

Generally  the  quantity  Q  is  given  and  it  is  desired  to  find  the  area  of  the  conduit  or  the 
diameter  d  of  a  pipe  sufficiently  large  to  discharge  this  quantity  under  a  given  head ;  thus 

introducing 

At  =  0.5,  C  =  0.0075,  and  v  = —,  where  a  =  ^ 

a  4 

and  solving 

=      /  iM  +  omi] 

hw^g  \  / 

In  this  equation  the  only  variable  is  d  which  is  easiest  found  by  trial.  A  good  first  trial 
value  is 


(r)  (9)  (h) 

Area  A  in  each  case  measured  on  section  "A- A" 
Ka)  Standard  rnouttjpiec€-  ir=0.82li^-.-Q=Av=Q82AiEgh.<,e)  Re-entrant  tube-ir'012iEgh-  Q'^Av=0.7EAi^. 

(b)  Sharp  edged  orFios  --v-^037^h  -  Q-0MAv-=d.6ZAiZgPi.  (f)  Conical  diverging  tube  -  Q-0  95AifFqh. 

(c)  Streamline  contour-\H)96iMi--Q= Av  =036 A IZgh.     (g)  ^nturi  adjutage  Angle  0=  5°to  8°  Q= I.SAllEgh 

(d)  Borda'5  mouthpiece-vO$9/^--Q'054Av=0.53AiEgh.   (h)  Conical  converging  tube  - Angle  Q^S'tolO'-  Q-OSSA^Egh. 

Fig.  43. 

In  reinforced-concrete  dams  the  conduit  is,  as  a  rule,  very  short  and  serves  merely  as  a 
setting  for  the  sluice  gate.  It  is  continued  through  the  dam  in  the  open  channel  formed  by  the 
buttresses.  In  such  a  case  the  conduit  can  be  considered  as  a  mouthpiece  and  the  velocity 
determined  directly  from  Fig.  43.  ^ 

7/.  Siphonic  Spillways. — In  places  where  the  discharge  to  be  handled  is  com- 
paratively small,  siphonic  spillways  can  be  used  to  advantage.^  As  such  devices  generally  are 
designed  for  automatic  operation,  it  is  obvious  that  a  close  regulation  of  the  water  surface 
will  be  obtained.  As,  furthermore,  the  operating  head  is  the  difference  in  elevation  between  the 
water  surfaces  above  and  below  less  the  hydraulic  losses  in  the  siphon,  the  discharging  ca- 
pacity per  linear  foot  is  considerably  in  excess  of  that  of  an  overflow  spillway. 

1  Slocum:  "Elements  of  Hydraulics,"  Ed.  II,  p.  69. 

2  Hillberg:  "Spillways  of  the  Siphonic  Type,"  Eng.  Rec,  May  3,  1913,  p.  488. 


756 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-7/ 


In  the  design  three  details  are  of  importance: 

1.  The  upper  part  must  be  so  made  that  as  soon  as  the  water  rises  above  the  level  to  be 
maintained,  the  siphon  intake  is  sealed  to  the  air  and  is  kept  sealed  until  the  water  level  has 
been  drawn  down  again  to  normal.  The  air  openings  must  then  be  large  enough  to  admit 
quickly  sufficient  air  to  break  the  siphonic  action.  Both  of  these  features  can  be  secured  by 
having  long  and  sharp  edges  on  the  intake  to  the  siphon  at  the  normal  water  level. 

2.  The  lower  end  of  the  siphon  must  be  submerged  deeply  enough  to  secure  a  constant 
seal  from  the  beginning  of  the  siphonic  action.  The  upper  edge  of  this  opening  must  be  as 
sharp  as  possible  to  permit  an  easy  escape  of  any  air  carried  out  by  the  water. 

3.  The  cross-sectional  area  should  be  as  large  as  possible  at  the  intake  to  reduce  losses  due 
to  entry.    Back  of  the  intake  provisions  should  be  made  for  an  efficient  absorption  of  the 
enclosed  air.    This  is  obtained  by  building  a  channel  around  the  opening,  so  that  in  the  be-  || 
ginning  water  will  flow  into  it  from  all  sides  forming  a  spray.    The  neck  of  the  siphon  is  gen- 
erally curved,  so  that  the  water  pressure  on  any  entrained  pocket  of  air  will  move  it  down- 
ward flattening  it  so  that  the  friction  at  the  contact  surface  will  tear  off  layers  of  air  until  i| 
all  of  it  has  been  carried  out.    A  gradual  narrowing  of  the  cross-sectional  area  up  to  this  point  ' 
is  desirable  because  the  increase  in  velocity  head  will  lessen  the  static  pressure  thus  creating 
an  overpressure  on  the  upper  part  of  such  air  pockets.    Below  this  point  no  enlargement  of 
the  area  is  permissible  as  the  corresponding  decrease  in  velocity  will  release  a  certain  portion 

of  the  entrained  air,  which,  especially  if  the  siphon  is  curved,  will  collect  and  cause  interrup- 
tion of  the  siphonic  action  taking  the  form  of  pulsations.  From  this  it  is  obvious  that  the 
best  practice  is  to  incline  the  lower  leg,  as  released  air  would  thus  quicker  reach  the  concrete 
wall  and  be  again  entrained  in  the  water. 

In  a  siphon  the  sum  of  all  losses  must  equal  the  difference  in  elevation  E  between  the 
water  surfaces  or 

£  =  |(l  +     +  ^ 

where  v  =  velocity;  g,  32.16  or  gravity;  /j.,  coefficient  for  loss  due  to  entry  (probable  maximum 
0.50);  X,  coefficient  for  loss  due  to  friction  in  upstream  leg  (probable  maximum  0.10);  C  = 
coefficient  for  loss  due  to  friction  in  downstream  leg  (varies  from  0.005  to  0.009);  p,  its  wetted 
perimeter;  a,  its  area;  I,  its  length;  and  k,  coefficient  for  loss  due  to  bends  or  curves  (probable 
maximum  0.25). 

This  equation  is  applicable  for  all  conditions  up  to  E  =  33.9  ft.,  which  is  the  suction  limit. 
Should  E  be  greater  than  this,  the  losses  must  be  kept  equal  to  or  smaller  than  33.9  ft.  by  taper- 
ing the  downstream  leg  in  such  a  way  that  its  smallest  cross-section  is  at  or  near  the  lowest 
point.  As  the  maximum  velocity  will  take  place  at  this  section,  it  is  obvious  that  a  certain 
amount  of  head  is  still  in  the  form  of  pressure  in  the  sections  above.  This  can  be  formulated 
in  the  following:  Calculate  a  conduit  with  a  hydraulic  gradient  so  that  the  sum  of  all  losses  is 
33.9  ft.  or  less.  One  siphon  at  Gibswil,  Switzerland  (Fig.  44)  operates  under  an  elevation 
difference  of  52.48  ft. 

Experiments  made  in  Switzerland  on  the  operation  of  siphons  shows  that  the  general 
formula 

Q  =  av  ^  afx\^2gh  (sec. -ft.) 

can  be  used  with  a  coefficient  /x  varying  from  0.55  for  smaller  heads  to  0.70  for  higher.  It  is 
always  convenient  to  use  this  formula  for  trial  computations,  but  to  check  the  final  design  with 
the  more  correct  theoretical  formula.    It  is  to  be  remembered,  however,  that  hmax  =  33.9  ft. 

K  the  discharge  is  too  voluminous  to  be  handled  in  one  conduit,  several  are  used  and 
placed  side  by  side. 

The  materials  used  for  building  smaller  siphons  are  steel  pipes  with  reinforced-concrete 
hoods  or  reinforced  concrete  is  used  throughout.    Larger  siphons  are  always  built  of  concrete 


Sec.  17-7/1 


HYDRAULIC  STRUCTURES 


757 


328'  High  wQferTivel-^ 


758 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-8 


which  can  be  either  mass  or  reinforced.  One  siphon  built  of  reinforced  concrete  in  Switzerland 
is  shown  in  Fig.  45. 

Because  of  the  suction  the  exterior  load  on  the  siphon  walls  equals  the  full  atmospheric 
pressure  of  14.7  lb.  per  sq.  in.  or  2120  lb.  per  sq.  ft.  On  the  underside  this  load  can  be  reduced 
because  of  the  weight  of  the  water  and  the  structure  itself. 

The  biggest  siphon  so  far  proposed  is  designed  for  the  Dunning's  Dam  of  the  Scranton,  Pa. 
water  supply  (Figs.  46 A  and  465).    It  consists  of  five  conduits  4  ft.  high  and  6  ft.  wide  and 


Requinsd.  SH  6'/6'xf-6'-e'fa 




'    ill      jll  ,  i  

•     "Twisted  ban  ffchc.  '^i//'     Section  "B-B"        --f  Twisted  bars  8"cfoc 


pBars,  twisted  4'chc. 
every  other  bar  benf 
as  shown. 


•'»[  li'Mi"/7r  •  J  J  '^t':<M'" Twisted 
.'♦c^Hi  Twiltfd.  %^Mbars4'Joc.  Pgi 
tars  6  c  toe  L    every  other  bm  \^"\ 
L  fbentasshom.f'J 


Section  "B- 

i'° Twisted  bars  S'ctoc.   

bars.: 


Section''C-C" 

Fig.  4G5. — Details  of  siphon  for  Dunning's  dam,  Scranton  Gas  &  Water  Co. 


its  total  discharge  capacity  is  3750  sec. -ft.  Its  overall  width  is  38  ft.  and  the  length  90  ft.  The 
maximum  stress  in  the  concrete  is  543  lb.  and  in  the  steel  13,750  lb.  per  sq.  in. 

8.  Movable  Dams.^ — Movable  dams  are  used  in  places  where  a  wide  opening  is  required 
to  accommodate  the  flood  discharge.  Where  such  dams  are  used  for  river  regulation  they 
are  generally  placed  straight  across  the  channel  and  erected  on  a  substructure  which  is  nothing 
more  than  a  low  sill.    The  movable  parts  are  so  made  that  they  can  be  laid  down  on  this  sill, 


1  The  best  textbook  on  movable  dams  is  "  Handbuch  der  Ingenieurwissenschaften,  Part  III' 
bau,"  Chapter  III  "Die  Beweglichen  Wehre,"  by  Prof.  K.  E.  Hilgard, 


'  'der  Wasser- 


Sec.  n-Sa] 


HYDRAULIC  STRUCTURES 


759 


removed  entirely  to  the  shore  or  hoisted  between  piers,  so  as  to  leave  an  unobstructed  channel 
of  practically  the  same  width  as  that  before  the  placing  of  the  dam. 

Movable  crests  are  often  used  in  combination  with  spillways  for  dams  in  places  where  it 
is  desired  to  maintain  as  nearly  constant  as  possible  the  elevation  of  the  water  surface  above 
the  dam. 

All  types  of  movable  dams  can  be  divided  into  three  groups:  (1)  Requiring  operating 
machinery;  (2)  operating  under  hydrostatic  pressure  differences;  and  (3)  automatically 
operating. 

8a.  Requiring  Operating  Machinery. — These  dams  can  be  operated  manually, 
electrically,  hydraulically,  or  in  any  other  mechanical  way.  The  operating  machinery  is  often 
mounted  on  a  traveler  or  a  barge  so  that  it  can  be  moved  along  the  dam  and  used  at  any  desired 
point.  The  principal  types  are:  Stop  logs,  needle  dams,  A-frame  dams,  curtains,  flashboards, 
gates,  wicket  gates,  bridge  dams,  taintor  gates  and  rolling  dams. 

86.  Operating  under  Hydrostatic  Pressure  Differences. — These  dams  are 
generally  so  designed  that  they  are  operated  by  the  opening  or  closing  of  valves  in  conduits 
connecting  an  inclosed  chamber  under  the  gate  with  the  high  water  above  and  the  low  water 
below  the  dam.    The  usual  types  are:    Bear  traps,  drum  dams  and  butterfly  dams. 

8c.  Automatically  Operating. — For  close  regulation  of  water  levels,  automati- 
cally operating  devices  have  come  to  the  front  during  the  past  10  years.  The  first  to  be  built 
was  in  Connecticut  as  early  as  in  1902.^  They  were  made  of  oak  and  about  3.5  ft.  high  and 
6  ft.  wide.  Each  gate  operated  on  the  principle,  that  when  the  water  level  reached  its  top, 
the  resultant  of  the  hydrostatic  pressure  fell  above  the  point  of  support.  In  order  to  prevent 
the  gate  from  opening  with  an  accelerated  speed,  the  shaft  was  provided  with  toothed  cams  at 
the  ends,  shifting  the  point  of  support  upward  on  the  gate  when  opening.  In  1914  gates  of 
similar  design  and  from  5  to  15  ft.  high  and  18.5  ft.  wide  were  installed  at  Austin,  Tex.^  They 
consist  of  steel  frames  with  wooden  covering.  Their  lower  part  is  filled  with  concrete  to  place 
the  center  of  gravity  below  the  point  of  support.  However,  such  gates  have  not  been  a  success 
because  of  the  difficulty  of  designing  a  cam  or  a  bascule  which  will  prevent  the  gate  from  gaining 
in  speed  when  opening.  Because  of  this  the  impact,  when  the  gate  reaches  the  open  position, 
is,  by  larger  gates,  sufficient  to  destroy  them.  Practically  the  only  effective  way  of  making 
gates  automatically  operating  is  by  providing  them  with  counterweights,  so  designed  that  their 
moments  increase  in  proportion  to  the  increase  in  moment  due  to  hydrostatic  and  impact  pres- 
sures on  the  gate  leaf.  Among  such  balanced  gates  are  those  with  overhead  rolling  counter- 
weight, underhung  counterweight,  counterweights  suspended  at  ends  of  levers,  and  those  with 
variable  counterweights. 

9.  Fish  Ladders. — To  permit  fish  to  pass  dams  in  search  of  spawning  grounds  and  of  food, 
the  laws  of  many  States  require  that  fishways  be  provided.  Such  ways  or  ladders  consist  of 
a  number  of  compartments  arranged  in  steps  and  separated  by  cross-partitions  or  baffles. 
The  construction  varies  depending  upon  the  habits  of  the  fish  living  in  the  stream  in  question, 
but  they  can  be  divided  into  two  main  groups:  Jump  ladders  and  swim  ladders.  Combina- 
tions of  both  are  sometimes  built  if  the  prevailing  conditions  should  so  require.  All  fishways 
must  be  so  designed  that  the  outlet  is  below  low  water  level  and  so  located  as  to  have  an  unob- 
structed discharge  of  water  in  order  to  attract  the  fish.  The  intake  or  upstream  end  should  be 
not  less  than  1  ft.  lower  than  the  crest  of  the  dam.  The  slope  of  the  bottom  should  never  be 
more  than  1:4  and  if  possible  be  1: 10  or  even  less.  The  width  should  not  be  less  than  4  ft. 
and  often  it  is  up  to  10  ft.  No  compartment  should  be  shorter  than  4  ft.  or  in  depth  less  than 
2.5  ft.  Plenty  of  light  should  be  admitted  or  the  fish  will  not  use  it.  However,  to  protect  the 
fish  from  birds  and  human  beings,  fishways  should  be  covered  by  gratings  so  built  as  to  facili- 
tate inspection  and  cleaning.  There  should  be  no  regulating  gates  at  the  intake,  necessitating 
attendance.    Fishways  are  built  of  wood,  steel,  masonry,  or  reinforced  concrete. 

1  Eng.  Rec,  Mar.  8,  1902,  p.  222. 

2  Lamar  Lyndon:  "Hydro-electric  Power,"  vol.  1,  p.  285. 


760 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-10 


RESERVOIRS 

10.  General  Types. — There  are  two  general  types  of  reservoirs — open  reservoirs  and  covered 
reservoirs.  Open  reservoirs  vary  in  size  from  great  catchment  basins  closed  by  dams  or  em- 
bankments, either  of  earth,  or  of  masonry,  or  both,  to  smaller  containers  constructed  largely 
or  wholly  of  masonry,  such  as  sewage  treatment  basins.  Fig.  47  shows  a  5,000,000-gal.  open 
circular  basin  constructed  by  the  city  of  Duluth,  Minn. 


Fig.  47. — Duluth  circular  reservoir.  Hoop  rein-  Fig.  48. — Covered  equalizing  and  storage  reservoir 
forcement  for  wall  was  supported  by  notched  steel  for  Hibbing  water-works, 

plate  brackets  riveted  to  vertical  channels. 


Covered  reservoirs  are  of  relatively  limited  size  and  usually  are  constructed  of  concrete 
masonry  in  floors,  roof,  and  walls,  with  earth  covering  on  roof  and  against  walls  (see  Figs.  48 
and  49).  Covered  reservoirs  prevent  freezing  or  disagreeable  warming  of  water,  as  well  as 
pollution  from  outside  sources  and  organic  growths  which. require  sunlight.^ 

11.  Quality  of  Concrete  for  Reservoir  Masonry. — Concrete  for  reservoirs  has  density  and 
correlatively,  impermeability  as  basic  requisites.    To  this  end,  the  selection  of  materials,  the 

1  For  discussion  see  Ellms:  "Water  Supply;"  Flinn,  Weston  and  Bogert:  "Water  Works  Handbook;" 
Hazbn:  "  American  Civil  Engineers  Pocket  Book;"  and  others. 


Sec.  17-12] 


HYDRAULIC  STRUCTURES 


761 


proportioning,  the  mixing,  the  placing  and,  particularly,  the  quantity  of  water  employed 
should  be  subject  to  rigid  regulation.  Percolating  and  entrant  water  is  the  most  active  disinte- 
grating agent  to  which  concrete  is  normally  subject.  The  use  of  arbitrary  proportions  and 
careless  methods  of  manipulation  in  such  concretes  is  therefore  not  only  poor  engineering,  but 
a  direct  courting  of  trouble.  The  number  of  specifications  and  textbooks  permitting  and  ad- 
vocating such  practices  is  at  present  regrettably  large,  either  in  ignorance  of,  or  regardless  of, 
the  definite  authoritative  and  generally  available  knowledge  as  to  their  danger  and  incorrectness. 

12.  Open  Basins  with  Embankment  Walls. — With  soil  of  proper  character,  open  reser- 
voirs may  be  constructed  without  masonry.  It  is  usually  preferable,  however,  after  forming 
dense  banks  from  excavated  or  other  materials,  to  cast  upon  them  and  upon  the  bottom, 


Section  thru  secondary  beams 


\lf.5-0'lg-'"^ 


f/£"c.fo<y 


Elighfh  Ave^ 
18'  SuDcly  Pipe       .14  'Scour  and OT pipe 


IS 

la  H  H  — 

B  IS 
SI  SI 


—  H 

—  H 


B  SI 
IS  SI 


B  SI  la  El  B  s  - 

Reservoir 
B     H    SI    H    H  B- 
capacify  Z000,000qal5  ■ 
H    H    Sf    H    H    M  - 


,)^.„...4'-IO"-  ^■'■■■3'-9" 

Fig.  49. — Covered  water-works  reservoir  at  Regina,  Sask. 


slabs  of  concrete,  reinforced  or  not,  according  to  the  stability  and  uniformity  of  the  foundation 
and  embankments. 

For  embankment  walls,  concrete  of  rather  stiff  consistency  is  cast  directly  on  a  sand  coat 
over  a  layer  of  puddled  clay.  This  clay  layer  should  be  from  10  to  24  in.  in  thickness;  and  the 
slope  about  3  :  1  and  never  steeper  than  2:1.  Reinforcing  mesh  or  rods  may  be  embedded 
in  embankment  slabs  if  individual  circumstances  of  location  or  material  indicate  this  procedure 
as  advisable.!  Concrete  core  walls  may  be  used  with  earth  embankment,  with  or  without 
masonry  facing.  In  all  cases,  whether  or  not  concrete  facings  are  used,  embankments  should 
be  well  settled  and  compacted  and  well  worked  into  a  thoroughly  stripped  and  scarified  subsoil. 

13.  Concrete  Floors  for  Reservoirs. — Concrete  floors  for  reservoirs  are  laid  in  one  or  more 
separate  layers,  either  as  a  continuous  slab  or  superposed  slabs,  or  in  rectangular  blocks  with 

1  See  Eng.  News,  vol.  74,  p.  267,  1915. 


762 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-14 


closely  abutting  joints.  As  before  stated,  the  concrete  should  be  as  impervious  as  possible; 
and  to  prevent  leakage,  continuous  construction  of  a  monolithic  slab  is  advantageous,  inasmuch 
as  the  often  considerable  leakage  at  joints  is  thereby  prevented.  The  strength  of  the  concrete 
should  be  such  as  to  support  the  weight  of  water  over  slight  inequalities  of  bottom  when  the 

reservoir  is  full;  and  at  least  sufficient  to 
withstand  upward  pressure  of  ground  water 
with  the  reservoir  empty.  A  thickness  of 
from  6  to  12  in.,  depending  upon  subsoil  con- 
ditions, is  usually  sufficient. 

When  concrete  floors  are  divided  into 
panels,  the  blocks  of  from  15  to  60  ft.  square 
are  connected  at  the  edges  by  some  sort  of 
lock-joint.  This  is  to  provide  for  flexibility 
during  settlement,  and  for  contracton. 
There  is  usually  a  beam  of  concrete  laid 
along  and  below  the  joint.  Details  of  such 
joints  are  shown  in  Fig.  50.  If  a  tongue- 
and-groove  joint  is  used,  the  tongue  should 
be  V-shaped,  otherwise  it  will  be  broken 
off. 

Pipes  and  other  fixtures  passing  through 
the  bottom  should  be  flanged  and  well 
water-proofed. 

14.  Groined  and  Flat  Floors. — Inverted  groins  have  become  a  familiar  type  of  reservoir 
bottom  in  view  of  the  advantages  offered  by  footings  adapted  to  distribute  column  pressures 
formed  by  the  thicker  portions,  with  channels  for  water  flow  and  cleansing  offered  by  the  con- 
tinuous inverts.    This  type  of  floor  is  generally  used  with  covered  reservoirs,  and  it  may  be 


Fig.  51. — Construction  view  of  groined  reservoir  floor  being  placed  in  two  layers. 


laid  in  one  or  two  layers,  as  desired.  In  Fig,  51  is  shown  in  process  of  construction  such  a  floor, 
placed  in  two  layers,  the  lower  layer  being  run  flat. 

A  modification  of  the  groined  floor  is  shown  in  Fig.  52.  This  type  offers  the  additional 
constructional  advantage  of  permitting  continuous  placing  of  plastic  concrete.    This  design  was 


Sec.  17-151 


HYDRAULIC  STRUCTURES 


763 


Groined  floor  

Modrfied  fkri-  floor 


Fig.  52. — Modification  of  groined  floor. 


developed  by  the  John  F.  Casey  Co.  in  their  repairs  to  the  Filtered  Water  Reservoir  at  the  Divi- 
sion Pumping  Station,  Cleveland,  Ohio.^ 

Flat  floors  may  be  used  in  either  open  or  covered  reservoirs.    In  large  open  reservoirs  they 
are  customary  as  groined  slabs  are  more  difficult  of  construction  and  not  advantageous 
where  no  piers  are  to  be  supported,  all  necessary  water  channels  being  readily  formed  by  sloping 
slabs.    A  notable  example  of  large,  open  concrete 
reservoir  construction  of  this  type  is  the  Hillview 
Reservoir  of  the  Catskill  Water  Supply  for  the 
City  of  New  York.^ 

15.  Concrete  Walls  for  Open  Reservoirs. — 
Concrete  walls  for  reservoir  sides  are  designed  as 
retaining  walls,  except  that  reservoir  walls  must 
withstand  earth  thrust  from  outside  when  the 

reservoir  is  empty,  and  water  pressure  from  within  when  the  reservoir  is  full.  The  resistance 
of  outside  earth  embankments  against  water  pressure  is  sometimes  deducted,  but  this  procedure 
requires  that  to  bear  upon  the  earth,  the  wall  may  undergo  no  deflection;  i.e.,  the  earth  does  not 
shrink  away  from  the  outer  face  of  the  wall  but  is  constant  in  bearing.  Various  means  are 
used  to  prevent  such  loss  of  contact  between  wall  and  bank.  The  wall  may  be  battered,  or 
better,  stepped  slightly.  The  portion  of  the  fill  next  to  the  wall  is  sometimes  puddled,  but 
where  this  is  done,  provision  against  excessive  thrust  must  be  made  in  the  design,  or  the  wall 
must  be  braced. 

When  the  embankment  on  one  side  of  a  wall  is  caused  to  resist  pressure  from  the  opposite 
side  of  the  wall,  there  is  a  tendency  to  force  out  a  prism  of  earth.  The  largest  thrust  which  the 
earth  will  resist  is  called  the  -passive  thrust. 

In  Fig.  53  let  AB  be  a  given  wall  with  an  embankment  whose  earth  surface  is  Abfn  tending 

to  resist  a  pressure  acting  against  the  wall 
from  the  left.  The  friction  between  wall  and 
earth  will  act  downward,  since  the  earth  will 
tend  to  move  upward.  The  reaction  of  the 
earth  P  will  thus  be  directed  upward  making 
an  angle  above  the  normal  to  the  wall  of  Z, 
but  never  greater  than  4>  (see  Art.  16,  Sect. 
13) .  Lay  off  on  the  surface  line  points  a,  b,  c, 
etc.  arbitrarily.  Draw  lines  from  these  points 
to  B,  thus  bounding  a  series  of  prisms  of 
length  1  ft.  perpendicular  to  the  drawing. 
Compute  the  weights  of  these  prisms  and  to 
any  convenient  scale  lay  them  off  in  order, 
on  the  line  BW  which  makes  an  angle  </>  with 
Draw  through  one  of  these  points  a  line,  as  twd,  which  makes  an 
angle  Z  to  the  right  of  a  normal  to  BW.  Then  through  each  point  on  BW  draw  a  line  parallel 
to  this  direction  tWd,  to  an  intersection  with  corresponding  ray  through  B,  as  We  to  Be  at  Se', 
Wf  to  Bf  at  Sf',  etc.  Through  the  points  S  draw  a  smooth  curve.  (This  curve  will  have 
breaks  at  rays  connecting  B  with  points  of  change  of  slope.)  Draw  a  tangent  v  to  the  curve 
parallel  to  BW,  and  through  the  point  of  tangency  draw  a  ray  from  B,  as  BSgg.  This  line  will 
represent  the  plane  of  rupture  of  the  embankment  if  the  passive  thrust  is  exceeded.  The 
distance  WgSg  between  BW  and  the  tangent  v,  measured  parallel  to  the  direction  tWd  and  to 
the  same  scale  as  that  used  in  laying  off  the  weights  on  BW,  is  the  magnitude  of  the  passive 
thrust. 


the  horizontal  as  Wa,  Wb,  Wc,  etc. 


1  See  Eng.  Rec,  Dec.  9.  1916,  p.  702. 

2  See  Proc.  Am.  Cone.  Inst.,  1915.  See  also  Taylor  and  Lyndon  on  pavement  of  circular  reservoir  at 
Austin,  Tex.,  Proc.  Am.  Cone.  Inst.,  1916,  p.  143. 


764 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-16 


The  point  of  application  of  P,  the  reaction  of  the  earth  against  the  wall,  will  be  one-third 
of  AB  above  B. 

Proof  of  the  construction  may  be  at  once  seen  by  revolving  the  force  triangle  BSgWg  to 
such  a  position  that  BWg  lies  on  AB.  Bwg  is  then  seen  to  be  the  weight  of  the  block  of  earth 
AbfgB  lying  above  the  plane  of  rupture  Bg;  BSg  is  the  resultant  pressure  on  the  plane  Bg  and 
making  the  internal  friction  angle  <^  thereto ;  and  as  previously  noted,  WgSg  denotes  the  passive 
thrust,  at  an  angle  (90  deg.  +  Z)  to  the  wall. 

The  moment  of  the  passive  thrust  is  added  to  the  moment  of  resistance,  taken  about  the 
third  point  toward  the  earth,  when  the  reservoir  is  full;  and  the  moment  of  the  active  thrust  is 
taken  as  the  attacking  moment  about  the  third  point  toward  the  water,  when  the  reservoir  is 
empty. 

16.  Partition  and  Outside  "Walls. — Walls  subdividing  the  basin  for  purposes  of  filhng  or 
emptying  are  usually  of  concrete.  They  consist  either  of  a  cantilever  wall  or  a  double-counter- 
forted  wall  with  the  stem  at  the  center  of  the  base.  In  the  latter  type  the  double-counter- 
fort acts  as  a  wedge-shaped  beam  with  both  faces  inclined,  and  is  reinforced  to  act  in  either  direc- 
tion. The  stem  of  the  cantilever  wall  may  be  designed  in  the  same  manner.  The  base  slab 
is  designed  to  take  the  resultant  pressure  from  either  side. 

Vertical  joints  in  concrete  walls  and  partitions  should  be  made  at  intervals  not  to  exceed 
60  ft.  The  tongue-and-groove  type  of  keyway  with  a  folded  metal  strip,  as  in  slabs,  makes 
a  satisfactory  joint.    It  should  be  thoroughly  waterproofed. 

Concrete  in  such  walls  should  be  well  spaded  next  to  the  forms  to  obtain  a  smooth  surface. 
The  whole  material  should  be  well  tamped.    The  thinner  the  wall,  the  more  essential  is  proper 
selection  and  proportioning  of  materials,  adequate  mixing,  and  careful 
placing, 

17.  Provision  for  Ice. — All  walls  for  reservoirs  in  which  ice  is 
likely  to  form,  should  be  battered  at  the  water  line  to  heave  the  ice 

,  as  it  expands.    Paved  embankments  usually  give  little  trouble  in  this 
respect. 

18.  Covers  or  Roofs  for  Reservoirs  and  Basins. — The  purpose  of 
a  roof  may  be  (1)  to  prevent  contamination  or  organic  growths,  (2)  to 
prevent  freezing,  or  (3)  to  maintain  lower  water  temperature  in  warm 
climates.  Three  types  of  construction  are  used:  beam-and-slab,  flat- 
slab,  and  groined- (elliptical)  arch  construction,  support  being  afforded 
by  walls,  by  columns,  or  piers  extending  to  the  floor.  The  first  two 
types  are  the  same  as  those  for  floors.  The  last  requires  separate 
analysis. 

19.  Groined-arch  Construction. — Experience  shows  that  due 
either  to  temperature  or  to  settlement,  cracks  are  likely  to  form  at  construction  joints  at  the 
crown  a  —  a'  (Fig.  54);  and  when  such  cracks  have  formed,  little  or  no  arch  action  prevails. 
The  nature  of  failures  indicates  that  arch  action  is  not  sufficient  to  be  considered  in  the  design. 
The  design,  therefore,  should  be  made  for  shear  and  cantilever  moment,  and  may  be  made  as 
for  footing  slabs.  It  is  advisable  to  reinforce  the  ''umbrella"  at  the  upper  face  over  the 
column,  and  at  the  lower  face  of  the  crown.  Due  to  the  increased  cost  of  formwork  and 
difficulty  of  construction,  this  type  of  roof  is  not  often  as  economical  as  the  usual  flat-slab,  or 
other  types  of  floor  construction. 

.20.  Construction  Details  of  Columns  and  Roof. — Footings  for  walls  and  columns  are  laid 
below  the  pavement  or  else  the  pavement  is  thickened  at  bearing  points.  To  prevent  undue 
settlement  pressures  on  footings  should  closely  approximate  those  on  floors  of  basins.  If 
separate  footings  are  provided,  expansion  joints  should  be  made  in  the  pavement  about  the 
column.  Roof  slab  should  be  reinforced  against  temperature  changes  and  shrinkage  by  adding 
0.4%  of  steel.    Many  reservoir  roofs  have  been  built  continuous  with  the  side  walls,  but  if 


Fig.  54. 


Sec.  17-21] 


HYDRAULIC  STRUCTURES 


765 


the  width  of  structure  is  considerable,  or  if  material  temperature  change  is  anticipated,  expansion 
joints  should  be  provided  between  roof  and  walls. 

STANDPIPES  AND  SMALL  TANKS 

A  standpipe  is  a  cylindrical  tank  resting  directly  upon  its  foundation,  and  usually,  though 
not  always,  having  a  height  greater  than  its  diameter.  It  may  be  used  for  the  storage  of  fluids 
other  than  water,  though  the  latter  use  is  the  most  common. 

Standpipes  of  concrete  require  particular  care  in  construction.  Not  only  must  the  con- 
crete be  of  sufficient  strength  to  withstand,  without  outside  support,  bursting  from  pressure 
of  water  or  cracking  from  temperature  changes,  but  further  the  concrete  must  be  so  continuous 
and  of  such  strength,  density,  and  finish  that  percolation  at  work  planes  or  other  points  will 
not  take  place. 

21.  Analysis  of  Stresses  in  Standpipes. — Since  the  pressure  of  a  fluid  varies  in  intensity 
with  the  depth,  the  unit  pressure  at  a  depth  y  is 

Py  =  wy 

Suppose  a  circumferential  strip  1  ft.  wide  to  be  cut  from  the  shell  at  a  depth  y  (Fig.  55). 
The  total  tension  on  any  diameter  is 

T  =  wr 

where  py  is  in  pounds  per  square  foot;  r  is  the  inner  radius  of  the  tank  in  feet;  and  T  the  pull 
on  one  side  of  the  tank  per  foot  of  height. 


.Y 

Fig.  55. 


Fig.  53. 


In  a  standpipe  of  concrete  the  tensile  resistance  is  necessarily  low,  since  at  a  given  tensile 
unit  stress  the  concrete  will  crack,  permitting  seepage  under  high  heads.  Tests  indicate  that 
concrete  of  good  quality  will  crack  minutely  at  an  elongation  of  0.00016  to  0.0006  inches  per  inch. 
The  value  0.00010  corresponds  to  a  unit  stress  of  200  lb.  per  sq.  in.  in  the  concrete,  and  (when 
bars  are  present)  3000  lb.  per  sq.  in.  in  the  steel.  Stresses  above  these  values  require  full  tensile 
resistance  of  the  steel.  Where  high  heads  are  used,  low  stresses  should  be  employed;  but  in 
tanks  having  a  head  of  30  ft.  or  less,  steel  stresses  of  8000  to  10,000  lb.  per  sq.  in.  have  proven 
successful,  since  the  cracks  do  not  open  enough  to  cause  appreciable  seepage  at  these  low  heads. 

European  practice  employs  a  very  rich  mix  for  use  in  standpipes,  varying  from  1  cement: 

graded  aggregate,  to  1  cement:  23^^  graded  aggregate,  these  values  varying  for  tanks  from 
100  ft.  high  to  30  ft.  or  less  in  height. 

22.  Restraint  at  Base. — The  deformation  of  a  standpipe  is  not  wholly  due  to  the  elon- 
gation of  the  hoops  under  stress.  At  the  base  the  rigidity  of  the  bottom  prevents  hoop  expansions 
and  introduces  a  restraining  moment  on  a  vertical  element.  If  the  side  of  the  tank  were  of 
uniform  thickness  and  a  hemogeneous  material  were  employed,  the  deformation  of  the  rings 
would  vary  as  the  depth  of  water.  But  in  the  design  of  a  concrete  standpipe  with  steel  rein- 
forcement, the  hoop  elongation  will  be  limited  to  that  elongation  which  corresponds  to  the 
adopted  working  unit  stress  in  the  steel.    Thus  in  Fig.  56,  the  portion  BC  of  the  exaggerated 


766 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-22 


deformation  is  a  constant  for  any  depth  between  B  and  C.  The  deformation  to  AB  may  be 
a  straight  Une  or  not;  however,  it  is  the  gradual  increase  of  deformation  up  to  that  correspond- 
ing to  the  working  hoop  stress. 

The  restraint  of  the  bottom  is  such  that  at  D  no  hoop  stress  exists,  but  rather  a  fixity, 
similar  to  a  vertical  beam  fixed  at  the  lower  end.    This  restraint  decreases  so  that  at  some  point] 
C  only  hoop  stress,  and  likewise  hoop  deformation,  prevails.    It  is  evident  that  at  this  point] 
C,  the  tangent  to  the  deformation  curve  is  again  vertical,  thus  parallel  to  the  tangent  to  the] 
curve  at  the  bottom. 

Suppose  the  lower  portion  of  the  shell  of  the  tank  or  standpipe  to  be  made  up  of  vertical' 
beams  restrained  at  their  lower  end,  and  having  a  length  sufficient  to  include  the  deformation 

CD,  Fig.  56.  Then  (Fig.  57)  the  water  pressure  varies  from  its 
upper  end  with  w{h  —  I)  to  its  lower  end  with  wh.  Let  the  beam 
be  acted  upon  at  its  upper  end  by  a  moment  M',  sufficient  to 
maintain  the  slope  at  that  end  parallel  to  that  at  the  base.  Then 
the  slope  at  C  is  zero  with  respect  to  that  at  D.  The  deforma- 
tion A  at  C  must  be  equal  to  that  caused  by  ring  working  stress 
only. 

Now  imagine  the  elastic  hoops  existing  between  the  levels  C 
and  D  to  restrain  the  deformation  of  the  beam  somewhat.  Let 
the  deformation  of  the  beam  thus  modified  be  that  shown  by 
CD,  Fig.  57.  The  hoops  stresses  between  the  levels  C  and  D  will 
thus  vary  as  abscissas  to  the  deformation  curve  CD.  Before  we  may  again  consider  the  ver- 
tical beams  separately,  the  effect  produced  by  these  hoop  stresses  should  be  used  to  modify 
the  water  pressure  on  this  beam.  The  deformation  area  DcC  may  be  converted  to  a  cor- 
responding stress  area,  and  subtracted  from  the  pressure  trapezoid  obDc  by  placing  cD  upon 
ah.  The  loading  left  to  the  restrained  cantilever  beam  to  be  resisted  by  beam  action  is 
therefore  represented  by  the  area  hfecD. 

Since  the  actual  form  of  the  curve  hfec  is  still  unknown,  the  resultant  loading  is  likewise 
unknown.  So  far  as  concerns  the  deflection  A  of  the  end  C  a  very  close  approximation  is  ap- 
parent by  using  the  triangular  loading  bcD.  It  should  be  noted  that  this  triangle  exceeds  the 
actual  loading  at  e  (curve  hfce)  but  is  less  than  that  at  f;  but  since  the  upper  portion  of  the  beam 
contributes  more  than  half  of  the  deflection  A,  the  approximation  becomes,  if  anything,  slightly 
on  the  safe  side.    For  the  loading  adopted,  and  for  a  homogenous  beam. 


M  = 


24 


A  = 


SOEI 


(1) 


From  the  theory  of  deflections  of  reinforced-concrete  beams ^  the  deflection  A  of  the  beam 
CD  becomes,  instead  of  that  just  given  for  a  homogeneous  beam, 

1      62.5  W     n  ^       1      hP  n 
SOEs  '   24  hd^  '  a      368.8£/.       '  a 


A  = 


(2) 


in  which 


h  =  depth  of  water  at  bottom  of  tank,  in  inches. 
/  =  length  of  beam  element  CD,  in  inches. 
d  =  effective  depth  of  beam  element  CD,  in  inches. 
Es  =  modulus  of  elasticity  of  steel,  pounds  per  square  inch. 
n/a  =  numerical  coefficient  dependent  upon  p  and  n,  in  which  n  is  recommended  by 
Turneaure  and  Maurer  to  be  8  or  10  (see  Fig.  58). 
A  =  deflection  of  end  C,  in  inches. 


I 


Referring  again  to  Figs.  56  and  57,  it  will  be  noted  that  A  must  equal  the  deflection,  or 
change  in  radius  due  to  hoop  tension.  This  may  be  expressed  in  terms  of  the  steel  working 
stress  fa,  the  radius  r  in  inches,  and  E^. 


1  See  Art.  28,  Sect.  7. 


Sec.  17-23] 


HYDRAULIC  STRUCTURES 


767 


Since  this  must  equal  the  beam  deflection,  equating  (2)  and  (3)  gives 

^4  ^  4425/'.rd3 


(3) 


whence 


I  =  8.16 


(in.) 


(4) 


This  is  the  value  of  I  which  will  give  the  desired  deflection  A.  Having  thus  found  I,  the  moments 
of  its  loading  may  be  determined.  Thus,  with  all  linear  dimensions  in  inches,  M  in  inch- 
pounds  is  from  (1)  and  (4), 


M  =  3.612 


fsrd% 


In  using  this  formula  it  should  be  noted  that/^  is  the  unit  stress  in  the  hoops.  M' 
the  relation 


(5) 

is  given  by 
(6) 


qbilO 

5  100 
u 

f  90 

8  80 

3  60 


The  point  of  inflection  is  at  0.37Z  above  the  bottom.    At  this  point  the  reinforcement 
may  swing  from  the  inner  to  the  outer  face.    Although  only  a 
third  of  the  steel  is  needed  at  the  outer  face,  the  remaining 
steel  should  be  carried  up  sufficiently  to  provide  ample  bond. 

The  moment  above  the  point  C  may  be  assumed  to  vary 
as  a  straight  line  from  the  value  M'  at  C  to  zero  at  the  top. 
This  is  not  strictly  true  but  is  sufficiently  close  to  provide  a 
means  of  cutting  some  of  the  steel  near  the  outer  face  if 
desired. 

23.  Shear  at  Base. — The  shear  at  the  base  may  be  seen 
from  Fig.  57  to  be  equal  to  the  triangular  loading  on  the 
beam.    Thus,  the  shear  per  foot  of  circumference  becomes 

V  =  0.2l7hl 

where  h  and  I  are  in  inches. 


05 


Percentage  of  remforcemeni 
Fig.  58. 


Illustrative  Problem. — Let  h  =  40  ft.,  diameter  =  20  ft.,  thickness  of  shell  =  10  in.  U 
per  sq.  in.  for  hoop  stress.    Assume  7i  =  10  and  p  =  1.5%. 

From  formulas  (2)  and  (3)  in  Art.  286,  Sect.  7,  or  Fig.  58,  page  7G7,  -  =  86.    At  the  base 


A  =  8000  lb. 


M 


3  pOOO  +  120  X  (8.5)3  x  480 


207,000  in.-lb. 


Assuming  i  =  0.83  (now  n  =  15)  and  noting  from  Diagram  2  on  page  360  that  when  p 
fc  =  650,  the  moment  value  of  1  sq.  in.  of  steel  thus  stressed  is,  for  d  =  8.5  in., 
M  =  fsjd  =  (10,500)  (0.83)  (8.5)  =  74,100  in.-lb. 
207,000 


1.5%,  f,  =  10,500  when 


Checking, 


74,100 
As  _  2.8 
bd 


2.81  sq.  in.  steel 

=  0.028,  nearly  3  % 


It  will  be  necessary  to  taper  the  wall  at  the  base. 

207,000 
d^  =   =  131.7 


(8.5) (12) 

Solving  for  the  effective  depth  required  for  p  =  1.5%  (/C  =  131) 
d  =  11.5  in.  or  14  in.  total 


(131) (12) 

As  =  12  X  11.5  X  0.015  =  2.07  s^.  in.  per  ft.  of  shell. 
Use  ^i-in.  sq.  bars  spaced  4>'2  in.  on  centers. 


768 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec,  17-24 


The  point  of  reversed  moment  is  I  above  the  base,  or 
I 


=  8.16^. 


8000  X  120  X  8.5^ 


480  X  86 


=  109.4  in. 


Point  of  inflection  is  at  0.37Z  =  40.5  in.  above  the  base.    The  moment  at  the  distance  I  is 


V   y  Y 


M'  =  -  ■  207,000  in.-lb. 
3 

69,000 


69,000  in.-lb. 


K  = 


12  X  8.52 


This  will  require  0.6%  of  steel,  or 

As  =  12  X  8.5  X  0.006  =  0.61  sq.  in. 

Every  third  bar  of  those  needed  at  the  bottom  will  suflBce. 
The  unit  shear  at  the  base  is 


0.217;iZ      (0.217)  (480)  (109.4) 


12  jd 


(12)  (0.83)  (11.5) 


=  99.5  lb.  per  sq.  in. 


..>|/^"1<.   Stirrups  are  thus  required,  for  a  distance  of  I  —  x  from  the  bottom  where 


Fig,  59. 


109.4 
99.5 


X  =  43.9  in. 


65.5  in. 


The  stirrups  should  be  anchored  to  vertical 


Inclined  rods,  figured  as  inclined  stirrups  in  a  beam,  may  be  used, 
rods  near  the  outer  face  (see  Fig.  59). 

24.  Small  Tanks. — Tanks  and  reservoirs  of  small  size  are  very  readily  constructed  of 
concrete,  particularly  when  they  may  be  built  as  monoliths.  Their  uses  are  manifold  and 
encouraging,  in  so  far  as  the  use  of  concrete  in  larger  constructions  to  meet  difficult  situations 
is  concerned.  In  paper  mills,  concrete  tanks  for  sulphite  processing  have  proven  satisfactory, 
with  a  useful  life  of  from  4  to  10  years.  With  proper  grading 
and  choosing  of  aggregates,  concrete  resistant  to  acids  and  acid 
fumes  has  been  produced,  this  resistance  being  directly  propor- 
tional to  the  proportion  of  silicious  materials  and  inversely  pro- 
portional to  the  cement  exposed  to  contact  with  the  attacking 
fluid  or  gas.  Concrete  tanks  are  in  successful  use  for  various  oils, 
even  including  those  of  organic  derivation;  for  tanning  solutions; 
for  various  fermenting  substances,  such  as  sauerkraut;  and  when 
coated  with  mastic,  for  solutions  incident  to  the  refining  of  copper. 
Among  these  latter  may  be  mentioned  those  erected  in  Chile  by 

the  Chile  Exploration  Co.,  which  have  successfully  withstood  earthquakes  as  well  as  chemical 
attack. 

The  sides  of  small  circular  tanks  are  designed  for  hoop  stress  in  the  same  manner  as  are 
the  sides  of  standpipes.  In  tanks  under  15  ft.  deep  the  restraint  of  the  base  is  somewhat 
different  than  for  the  foregoing  case  of  deeper  tanks.  The  two  cases  following  give  the  statical 
limitations  of  the  secondary  stresses  caused  by  restraint. 

(a)  Walls  Continuous  with  Base. — The  moment  at  the  base  (Fig.  60a)  is 

M  =  0.0QQ7wh^ 
M'  =  0.029Swh^ 
V  =  0.4rf 

y  =  0.553/i 

(6)  When  the  Base  Is  Separated  by  a  Joint  or  hy  Cracking  (Fig.  606).- 

M'  =  0.0M2wh^ 
V  =  0.333w;/i2 

y  =  0.423/1 


Sec.  17-25] 


HYDRAULIC  STRUCTURES 


769 


In  the  above  formulas,  w  is  the  weight  per  cubic  foot  of  the  hquid,  and  h  is  the  height  of 
the  tank  in  feet.    All  moments  are  in  foot-pounds. 

Tanks  not  circular  in  cross-section  should  be  designed  to  resist  moment  in  a  horizontal 
plane  (see  chapter  on  ''Deep  Grain  Bins,"  Sect.  18). 

25.  Construction  Details  of  Tanks  and  Standpipes. — The  piping  for  these  structures 
should  be  so  placed  that  they  will  not  interfere  with  expansion  and  contraction.  Pipes  should 
be  protected  from  frost. 

It  is  held^  that  thick  walls  are  an  advantage  over  thin  walls  because  of  the  expense  of  the 
taper  of  the  latter;  that  some  seepage  is  likely  to  occur;  and  that  in  cold  climates  little  ice  will 
be  formed,  and  no  protective  housing  will  be  necessary  if  the  structure  is  properly  covered. 


)<--■  j't>"  >f  s'^o"--   -  t--o'  -  -■■■>! 

Fig.  61. — Standpipe  at  Fulton,  N.  Y.,  having  disconnected  base  and  flexible  seal. 


Care  should  be  taken  to  thoroughly  splice  the  joints  in  the  steel  hooping.  Mechanical 
bond  should  be  provided,  preferably  by  bolted  clamps. 

Fig.  6P  shows  the  detail  of  a  tank  at  Fulton,  N.  Y.,  having  a  sliding  joint  at  the  junction 
of  the  base  and  sides.  This  was  patented  by  Wm.  Mueser.  It  is  claimed  that  there  is  no 
lateral  restraint  of  the  sides  at  their  base,  and  that  therefore  the  secondary  stresses  at  that 
section  are  eliminated.  This  can  be  true  only  when  the  joint  is  perfectly  frictionless.  Some 
friction  does  exist,  though  not  large;  and  the  moment  in  the  sides  due  to  this  restraint  should 
be  provided  for  by  vertical  rods  near  the  outer  face. 

Fig.  623  shows  the  details  of  a  low  standpipe  at  Penetanguishene,  Ont.  Its  capacity  is 
300,000  gal.  The  wall  is  thicker  than  required  for  strength,  to  prevent  the  formation  of  a 
heavy  ice  crust.  The  connection  between  wall  and  bottom  was  analyzed  for  restraint  by  an 
application  of  Grashof's  theory. 

1  W.  J.  Douglas:  Trans.  Am.  Soc.  C.  E.,  vol.  74,  p.  394,  1911. 

2  Eng.  Rec,  Jan.  10,  1914,  p.  43. 

8  Eng.  &  Cont'g.,  Jan.  22,  1913,  p.  110. 
49 


770 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17 


Sec.  17-26] 


HYDRAULIC  STRUCTURES 


771 


Fig.  63^  shows  the  details  of  a  small  standpipe  of  143^^  ft.  inside  diameter  and  40  ft.  high, 
built  at  Merrimack,  N.  H.  The  standpipe  has  a  capacity  of  50,000  gal.  The  concrete  was 
poured  in  one  continuous  operation  which  lasted  393^  hr, 

26.  Precautions  in  Construction. — The  construction  of  standpipes  of  concrete  has  not 
been  thus  far  wholly  satisfactory.  It  is  a  relatively  simple  matter  to  design  against  water 
pressure  alone,  but  true  monolithic  construction,  without  leaks  at  junction  of  base  and  walls 
or  at  work  planes,  or  cracks  from  secondary  stresses,  is  less  easy. 

In  addition  to  the  procedures  for  producing  dense  concrete  before  referred  to  and  treated 
in  detail  in  Sect.  2,  care  should  be  taken  to  so  place  the  concrete  as  to  secure  thorough  com- 
pacting in  the  forms  and  close  contacting  with  forms  and  with  steel.  To  this  end,  forms  in 
relatively  shallow  lifts  are  advantageous  for  puddling  and  compacting,  together  with  ex- 
pulsion of  entrained  air,  which  can  be  further  facilitated  by  tapping  forms  with  mauls  or 
mallets,  or  better  yet,  with  air  hammers. 

Although  shallow  lifts  are  advantageous,  provision  must  be  made  in  their  design  for  rapid 
addition  of  higher  lifts,  since  the  best  construction,  with  avoidance  of  work  planes,  requires 
continuous  deposition,  even  though  day  and  night  work  is  entailed,  preferably  without  per- 
mitting any  portion  to  take  even  initial  set  before  new  concrete  is  placed  upon  it.  Excess 
water  is  a  potent  source  of  trouble  in  constructions  of  this  character,  as  through  its  use,  laitance 
in  bands  and  pockets  is  encouraged. 

Where  continuous  placement  of  concrete  is  impossible  for  one  reason  or  another,  vertical 
diaphragms  of  sheet  metal  may  be  embedded  in  the  concrete  as  work  joints.  Sheet  copper, 
with  asphalt  or  asphalt  mastic  filler,  can  be  made  to  give  water-tight  construction,  but  the 
sightliness  of  the  standpipe  is  usually  impaired  by  the  irregular  belt  of  friable  and  easily  weath- 
ered material  at  each  division. 

ELEVATED  TANKS 

Elevated  tanks  may  be  classed  in  groups  according  to  the  type  of  floor  employed:  (a) 
suspended,  (h)  flat,  (c)  beam-and-slab,  (d)  dam,  or  (e)  double-dome. 

The  suspended  bottpm  was  employed  in  the  Middleboro  tank^  (see  Fig,  64).  It  was 
designed  in  a  manner  similar  to  the  same  type  of  steel  tank.  For  the  anal3^sis  of  such  a  bottom, 
see  Ketchum's  "Structural  Engineers'  Handbook,"  page  366. 

Only  small  tanks  have  been  constructed  with  flat  circular  floors.  Such  construction  follows 
that  for  flat  slab  floors.    Floors  of  beams  and  slab  are  also  designed  after  similar  building  floors. 

When  the  floors  restrain  the  sides  of  the  tank,  the  negative  moment  at  the  base  of  the  wall 
may  be  provided  for  in  a  manner  similar  to  that  emploj^ed  for  standpipes. 

Dome  floors  are  common  in  Europe,  and  some  have  been  built  in  this  country.  The 
analysis  of  the  double-dome  floor  follows.  Tanks  with  only  the  curved  dome  have  been  built. 
It  is  reported  that  trouble  has  been  experienced  due  to  restraint  between  walls  and  dome, 
and  to  the  lateral  thrust  of  the  dome.  This  difficulty  may  be  eliminated  by  using  the  same 
unit  stress  in  the  steel  in  the  ring  of  the  dome  that  is  used  in  the  hoops  of  the  sides.  Then 
the  dome  ring  will  expand  under  load  an  amount  equal  to  that  of  the  sides  and  there  will  be 
no  restraint  between  the  two.  The  analysis  of  a  single  dome  will  be  that  for  a  similar  portion 
in  the  following  analysis. 

27.  Analysis  of  Stresses. — The  roof  A  (Fig.  65)  is  a  simple  dome,  and  may  be  designed 
as  a  thin  spherical  segment.  In  this  case,  all  stresses  are  assumed  to  be  tangential  to  the 
spherical  surface. 

Assuming  a  uniformly  distributed  load  of  w  lb.  per  sq.  ft.  on  a  horizontal  projection,  which 
will  include  the  weight  of  the  dome  since  it  is  relatively  flat,  the  vertical  component  per  foot  of 

rim  is  w        If  the  tangent  to  the  shell  at  a  vertical  diameter  makes  the  angle    with  the  horizon- 

1  Eng.  News,  Dec.  23,  1915. 

2  Eng.  &  Contg.,  vol.  44,  p.  473,  Dec.  22,  1915. 


772 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-27 


1,     3-i"Rodl5  wif-h  iurnhuckles-^  .w 


 '^1 


Lighi  weight  manhole  with  perforafed 
cover  and  ^4" clear  opening 


These  rods  extend  fo  El  S6I. 

These  rods  iv  El  e65;. 
These  rods  fa  EIS69-1; 

These  rodstoEI.E73 


Plan  of  Radial  Refnf.  in  bottom  of  Tank 


w-'z^io"--^  m 

Elevatfon  of  Balcony 
Developed  on"  21-8"  Radius 

^"°15"c.  fo  c.  108  in  circunrtfrence 


f^lZ''c.foc:4^Hc 


Junction  of  Roof  &  Wall 


aM\  J  -45^^ 

''■■24  Circular  opening 

Sectional  Elevation 


Belting  Zoi^rs^ 


I yy         j"<>o"c.  to  c  £64  in  circumfrence . 
Base  of  Tov^er 


Fig.  64. — Details  of  tower  tank  at  Middleboro,  Mass. 


Sec.  17-27] 


HYDRAULIC  STRUCTURES 


773 


tal,  the  outward  pressure  Ti  per  foot  of  rim  is  j 


WD 


7  (since  Vi      Ti  =  tan  <t>').    The  thrust 


4  tan  0 

tangent  to  the  dome  at  its  rim  will  be  the  resultant  of  these  two  forces,  or  \/T^^  +1^1^. 
Taking  a  value  of  fc  in  pounds  per  square  inch  and  letting  t  —  thickness  of  shell, 


12  tfc 


1 


t  =  j^Vt.^  +  v.^ 

It  will  be  found  that  for  diameters  D  less  than  20  ft.  the  controlling  factors  in  determining  the 
thickness  will  be  practicability  of  building  the  thin  shell,  and  provision  for  accidental  punching 
shear.  Fairly  satisfactory  proportions  for  large  diameters,  remember- 
ing these  limitations,  will  be  obtainable  by  assuming  a  low  concrete 
unit  stress,  say  100  lb.  per  sq.  in.  Metal  fabric  or  lath  should  be 
used  as  an  added  provision  against  possible  concentrations.  Vertical 
shear  at  the  base  ring  should  be  computed. 

The  thrust  Ti  should  be  resisted  by  a  ring  of  reinforcement  at 
the  top  of  the  wall.    The  tension  S  in  this  ring  will  be 


S  = 


TiD 


Tan  <(>'  may  be  found  from  the  relation 

tan  -  = 


FiQ.  65. 


The  steel  required  for  the  hoop  will  be 


As 


TiD 


The  tensile  unit  stress  in  the  steel  should  not  exceed  about  8000  lb.  per  sq.  in. 

4  ft.    Adopted  load  of  150  lb.  per  sq.  ft.  on  horizontal  projection. 


Illustrative  Problem. — D  =  40  ft.,  r' 
including  dead  load.    Let  fs  =  5000. 

y   _  '^^  _  ^ 


1500  lb.  per  ft. 


Tan 


-  )  whence —  =  11"18' 
5  2 


22''36' 

tan  <p' 
1 


tan 
1500  _ 
0.416  ~ 


/  =  0.416. 
3600  lb.  per  ft. 
1 


12/c 
3600  X  40 


As  = 


2 

72,000 
5000 


1  12  X  100 
72,000  lb. 


(3920)  =  3.3,  say  3>^  in. 


14.5  sq.  in.,  say  14  1-in.  sq.  rods. 


A  beam  may  be  cast  around  the  top  of  the  tank  in  which  half  of  the  steel  may  be  encased.  The  remainder  may 
be  put  in  the  dome  itself  near  the  rim. 

The  shell  of  the  tank  B  (Fig.  65)  is  designed  like  the  sides  of  a  standpipe.  Reinforcement 
consists  of  rings,  and  sufficient  vertical  steel  to  support  them. 

The  conical  portion  C  carries  a  vertical  load  of  V2  per  foot  of  upper  rim,  which  is  equal 
to  the  dead  weight  of  the  tank  shell  and  the  roof.  In  addition  it  carries  a  normal  water 
pressure  of  wh  lb.  per  sq.  ft.  at  the  upper  rim,  and  one  of  w  {h  +  a)  lb.  per  sq.  ft.  at  its 


774 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-28 


lower  rim.  The  sides  of  the  cone  are  assumed  to  slope  at  45  deg.  The  shear  per  lineal  foot 
of  the  bottom  rim  is  equal  to  the  weight  of  the  structure  above  this  level  plus  the  weight 
of  water  above  the  conical  portion,  divided  by  the  perimeter  of  the  rim.  Since  the  slope  of 
the  cone  is  45  deg.,  the  thrust  has  the  same  value  per  lineal  foot  as  F3.  Likewise  the  thrust 
at  the  upper  rim,  T3,  is  equal  to  the  shear  V2  at  that  level,  or  the  weight  of  structure  above  it. 
Two  rings  may  be  used,  one  to  resist  Tz,  and  one  to  resist  T^,  with  reinforcement  in  the  slab  to 
span  between  these  rings;  or,  rings  of  steel  rods  may  be  distributed  somewhat,  through  the  coni- 
cal side,  to  aid^the  resistance  of  the  sloping  rods  spanning  between  rings.  This  will  be  modified 
with  respect  to  the  action  of  T4  when  the  dome  thrust  T4  is  determined.  Vertical  shear  at 
the  base  should  be  computed  and  provided  for. 

The  dome  of  the  floor  has  a  vertical  shear  at  its  perimeter  equal  to  its  weight  plus  the  weight 
of  water  directly  above  it.  This  shear  is  the  vertical  component  of  the  thrust  at  the  base  ring 
acting  tangent  to  the  same  surface,  or  at  the  angle  </>.  Hence, 

T5  =  F4  cot  (t> 

This  is  the  ring  thrust  acting  at  the  base  of  the  dome. 


Fig.  66.  Fig.  67. 


Now  the  ring  stress  actually  to  be  resisted  is  that  produced  by  the  difference  between 
Ti  and  T5.  If  they  are  made  equal,  then  the  reaction  of  the  tank  is  vertical  only  at  this  point, 
and  no  reinforcement  need  be  placed  for  ring  tension. 

Fig.  66  gives  the  proportions  of  this  type  of  floor  when  the  thrust  Ti  balances  the  thrust  T^. 

28.  Supporting  Tower. — The  tower  carrying  an  elevated  tank  may  be  either  a  cylindrical 
shell  or  a  group  of  columns.  For  stresses  due  to  vertical  load  and  wind  see  the  design  of  deep 
grain  bins  or  silos,  Art.  4,  Sect.  18. 

A  tower  formed  of  a  group  of  columns  is  shown  in  Fig.  67,  acted  upon  by  a  total  wind  pres- 
sure of  W  lb.  at  a  height  of  a  in.  Let  the  distance  from  the  axis  of  the  group  to  the  column  far- 
thest out  be  X  in.    Then  the  unit  stress  at  this  distarce  x  due  to  W  will  be 

^  Wax 
'      Ic  +  cA 

assuming  little  or  no  tension  to  exist  on  the  section  under  the  action  of  W  and  G.  The  number 
of  columns  is  denoted  by  c.  This  unit  stress  must  be  multiplied  by  the  area  A  of  the  column 
to  obtain  its  load.  Other  columns  will  carry  a  similar  stress  when  the  wind  is  in  another 
direction. 

Investigation  of  compressive  stress  due  to  wind  should  be  made  on  the  leeward  side  of  the 
tank  at  its  base  and  at  other  sections  when  shear  is  vital. 


Sec.  17-29] 


HYDRAULIC  STRUCTURES 


775 


Bracing  in  reinforced-concrete  towers  consists  usually  of  horizontal  struts  only,  designed 
to  resist  moment.  The  analysis  of  stresses  in  a  bent  of  the  tower  may  be  made  by  the  use  of 
the  method  of  slope-deflections  (see  Sect.  10). 

Fig.  68^  shows  an  elevated  tank  with  double-dome  bottom,  built  at  Kitchener,  Ont.  It 
forms  an  excellent  example  of  this  type  of  structure. 


Fia.  68. — Tank  for  water-works  at  Kitchener,  Ont. 
CULVERTS 

29.  General  Considerations. — The  term  culvert  is  usually  applied  to  structures  built  to 
carry  surface  water  or  small  streams  through  highway  or  railroad  embankments.  When  the 
area  of  waterway  required  is  comparatively  small,  a  pipe  culvert  is  usually  the  most  economical. 
For  the  larger  openings  either  the  box  or  arch  form  should  be  employed  depending  upon  the  avail- 

1  Eng.  News,  vol.  69,  p.  309,  Feb.  13,  1913. 


776 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-30 


able  headroom,  the  depth  of  fill,  the  condition  of  the  foundation,  and  whether  or  not  an  artistic 
arch  design  is  especially  desirable. 

The  ordinary  type  of  arch  culvert  and  the  box  culvert  without  a  load-supporting  floor 
(called  open-box  culvert)  are  in  reality  small  bridges,  and  it  is  sometimes  a  question  of  how  large 
such  structures  may  become  before  they  should  be  considered  strictly  in  the  bridge  class.  No 
arbitrary  division  is  adhered  to  in  the  following  articles  except  that  a  culvert  is  considered  a 
structure  which  can  be  completely  and  economically  standardized,  based  on  a  given  area  of 
waterway  and  height  of  embankment. 

30.  Factors  in  Culvert  Design. 

30a.  Culvert  Efficiency. — A  culvert  to  be  efficient  in  the  amount  of  water  it 
can  discharge  should  have  its  headwalls  or  wings  arranged  so  as  to  facilitate  the  flow,  and  its 
bed  should  be  considerably  inclined  for  those  cases  where  the  channel  below  the  culvert  will 
permit  the  water  to  flow  away  freely.  If  any  well-defined  stream  bed  exists,  the  bed  of  the 
culvert  should  have  the  same  inclination  as  that  of  the  stream,  as  otherwise  either  the  outlet 
or  inlet  end  will  clog  depending  upon  whether  the  slope  of  the  culvert  is  greater  or  less  respec- 
tively than  the  slope  of  the  stream  bed. 

Any  projections  in  the  culvert  bed  should  be  avoided  as  they  will  retard  the  water  and 
diminish  efficiency.  It  is  also  important  that  culverts  be  placed  across  roadways  in  the  di- 
rection of  the  stream  flow  since,  if  this  is  not  done,  clogging  and  subsequently  washouts  will  be 
likely  to  occur. 

A  culvert  will  discharge  twice  as  much  under  a  head  of  4  ft.  as  under  a  head  of  1  ft.,  but 
water  should  not  be  allowed  to  dam  up  in  this  manner  unless  the  culvert  is  well  constructed 
through  a  water-tight  embankment. 

306.  Waterway  Required. — Assuming  an  efficient  culvert  design,  the  area  of 
waterway  required  depends  principally  upon  the  maximum  rate  of  rainfall,  the  area  and  shape 
of  the  watershed,  the  kind  and  condition  of  the  soil  throughout  this  watershed  area,  and  the 
character  and  inclination  of  both  drainage  surface  and  stream  bed.  A  number  of  empirical 
formulas  have  been  proposed  by  which  to  calculate  the  required  culvert  opening,  but  obviously 
a  problem  of  this  kind  does  not  admit  of  an  exact  mathematical  solution  and  the  desired  size 
of  culvert  should  be  determined  by  direct  observation  whenever  that  is  possible. 

In  a  new  country  an  empirical  formula  is  often  the  only  method  by  which  the  required 
area  of  waterway  can  be  determined.  Talbot's  formula  is  the  one  most  generally  employed 
and  is  as  follows : 

A  =  C^V' 

where  A  =  area  of  waterway  in  square  feet,  a  =  drainage  area  in  acres,  and  C  is  a  coefficient 
which  varies  from  1  to  ^■i  in  the  following  manner : 

For  steep  and  rocky  ground,  C  varies  from  %tol.  For  rolling  agricultural  country  subject  to  floods  at  times  of 
melting  of  snow,  and  with  the  length  of  valley  three  or  four  items  its  width,  C  is  about  ys;  and  if  the  stream  is  longer 
in  proportion  to  the  area,  decrease  C.  In  districts  not  affected  by  accumulated  snow,  and  where  the  length  of  the 
valley  is  several  times  the  width,  H,  M.  or  even  less,  may  be  used.  C  should  be  increased  for  steep  side  slopes, 
especially  if  the  upper  part  of  the  valley  has  a  much  greater  fall  than  the  channel  at  the  culvert,  i 

The  proper  area  of  waterway  can  best  be  determined  by  knowing  the  dimensions  of 
existing  openings  on  the  same  stream  and  by  careful  observation  of  the  stream  and  the  amount 
of  water  which  it  carries  at  flood  times.  This  amount  of  water  can  be  determined  by  measuring 
a  cross-section  of  the  stream  at  some  narrow  place  near  the  culvert  site. 

30c.  Length  of  Culverts. — The  length  of  a  culvert  should  depend  upon  the  width 
of  roadway  and  the  depth  of  fill  on  top  of  the  culvert.  The  slope  of  an  earth  fill  can  generally  be 
taken  as  1^  :1 — that  is,  for  every  1  ft.  in  height,  the  horizontal  distance  is  1}^  ft. 

In  highway  construction  the  roadway  should  never  be  narrowed  at  a  culvert  since  such  a 
practice  is  dangerous  and  the  construction  unsightly. 

1  Selected  papers  of  the  Civil  Engineers'  Club  of  the  University  of  Illinois,  No.  2,  p.  14. 


Sec.  17-30fil 


HYDRAULIC  STRUCTURES 


777 


SOd.  Design  of  Ends. — The  arrangement  of  the  headwalls  or  wings  may  be 
substantially  the  same  for  all  arch  and  box  culverts.  The  arrangement  should  be  such  that 
the  embankment  is  protected  and  the  flow  of  water  facihtated.  Wing  walls  may  be  built 
parallel  with  or  at  right  angles  to  the  axis  of  the  culvert,  or  they  may  be  so  placed  as  to  make 
an  angle  (usually  30  or  45  deg.)  with  this  axis. 

For  the  shorter  spans  (including  spans  for  pipe  culverts),  wings  parallel  with  the  roadway 
are  generally  used  for  low  fills  and,  in  highway  construction  at  least,  these  headwalls  are  carried 
up  above  the  grade  line  to  provide  a  low  guard  rail.  This  type  of  end,  however,  is  not  eco- 
nomical for  the  larger  spans  since  the  straight  wings  under  such  conditions  need  to  be  made  of 
considerable  length  and  height  to  retain  the  fill  efficiently.  A  low  guard  rail  may  be  formed  with 
flared  wings  by  raising  and  coping  both  head  and  wingwalls.  The  top  of  the  wings,  of  course, 
should  have  a  slope  consistent  with  the  slope  of  the  earth  fill. 

Flared  wings,  especially  at  the  upstream  end,  are  the  best  for  hydraulic  reasons  and, 
when  used,  the  culvert  is  less  likely  to  become  choked  than  when  either  of  the  other  two  forms 
of  wingwalls  are  employed.  Straight  wings — namely,  wings  parallel  to  the  axis  of  the  culvert — 
are  of  advantage  in  railroad  construction  when  an  extension  of  the  culvert  is  likely  to  be  made 
in  the  near  future  to  accommodate  another  track. 

It  is  common  practice  to  design  wing  and  headwalls  of  sufficient  length  to  keep  the  culvert 
opening  clear  when  the  earth  is  assumed  to  fall  around  the  ends  on  a  13^^  :  1  slope.  In  some 
cases  a  steeper  slope  could  be  assumed,  but  some  soils  take  even  flatter  slopes  than  the  standard. 


S^-  8"   -> 


Fig.  69. — Reinforced-concrete  pipe. 

Box  and  arch  culverts  are  built  both  with  and  without  a  floor,  but  in  almost  every  case 
the  smooth  waterway  that  can  be  obtained  by  using  a  concrete  floor  will  greatly  increase  the 
capacity  of  the  culvert.  A  floor,  if  properly  constructed,  will  also  prevent  any  danger  from 
erosion  of  the  stream  bed  and  undermining  of  the  foundation.  The  floor  at  the  ends  of  the 
culvert  should  be  provided  with  an  apron  or  baffle  wall  at  its  outer  edge,  and  this  wall  should 
in  all  cases  be  carried  as  low  as  the  bottom  of  the  footings.  If  especially  desirable,  the  floor 
should  extend  out  to  the  end  of  the  wingwalls. 

31.  Pipe  Culverts. — One  or  more  lines  of  pipe  with  suitable  headwalls  to  protect  the  em- 
bankment is  the  simplest  form  of  culvert.  The  pipe  may  be  of  burned  clay,  cast  iron,  plain 
concrete,  or  reinforced  concrete;  but,  oji  account  of  frequent  breakages,  there  seems  to  be  a 
tendency  at  the  present  time  to  discontinue  the  use  of  vitrified  and  cast-iron  pipe  and  also 
pipes  of  plain  concrete.  All  kinds  of  pipe  culverts  have  the  same  type  of  concrete  headwalls, 
consequently  the  following  articles  treat  only  of  pipe  culverts  of  reinforced  concrete. 

Since  it  is  desirable  to  make  as  few  openings  as  possible  through  an  embankment,  water 
is  usually  conducted  along  the  side  of  the  roadway  until  at  least  a  15-in.  diameter  of  pipe  is 
required.    In  the  following  articles  a  pipe  of  at  least  this  size  is  assumed. 

Reinforced  culvert  pipes  are  usually  made  in  from  4-  to  8-ft.  lengths,  and  with  bell  and 


778 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-31a 


spigot  joints.  The  largest  diameter  of  pipe  yet  made  is  72  in.  The  pipes  usually  have  a 
hoop  reinforcement  which  is  near  the  interior  surface  at  the  top  and  bottom  of  the  pipe,  and 
near  the  exterior  surface  at  the  sides  (Fig.  69),  Pipe  with  a  double  line  of  reinforcing  is  also 
used,  as  shown  in  Fig.  70.  Longitudinal  reinforcement  is  provided  in  pipes  of  the  longer 
lengths  due  to  the  likelihood  of  beam  action  if  settlement  takes  place. 

31a.  Pressure  in  Trenches. — The  most  elaborate  and  thorough  investigation 
of  the  subject  of  pressure  on  pipes  in  ditches  was  made  a  few  years  ago  at  the  Iowa  State  College 
of  Agriculture  and  Mechanic  Arts,  the  results  of  which  were  published  in  Bulletin  No.  Sl^ 


f°B'ars 
/z'c.toc.     EncI  yiew 


for  diameters  be/ow 
»  30"-36" 


'37-42" ,  X=JB" 


Double  //ne 

of  Peinforcement. 


Section 


^re  MesTr 

or 

:  Expanded 
Metal 
equfya/enffo 
^.S.&lY.Co's 
4-Mest7  shoyyn 
'//7  t^b/e 


£4", 
42  ".F^ 


Table  of  Dimensions 
for  Circular  Pipe 


Diameter 

TTiickness  of 

Required  Steel 

Shell  =  T 

/Area -for  each  Jine 

IS" 
/d" 
84" 

30" 
36" 
42" 

2.^5" 
2.50" 
3.00" 
3.50" 
4.00" 
4.50" 

A5.&  yV-Gy.  Sq. in.  7 

Sfy/e6*.058perJB 
"     5-.077  "  " 
0     4'.I02  "  " 
42 '.f  5/   "  " 
"   23:170  "  " 
«   32-.225  "  " 

Fig.  70. — Standard  dimensions  for  concrete  pipe  culverts  with  concrete  head-walls,  Iowa  Highway  Commission. 


of  the  Engineering  Experiment  Station.  The  investigation  was  made  with  special  reference 
to  drain  tile  and  sewer  pipe,  but  the  results  apply  equally  well  to  culverts  laid  in  trenches. 
The  following  tables  and  other  data  were  taken  from  the  bulletin  above  mentioned.  The 
correctness  and  reliability  of  the  theory  which  was  developed  by  reason  of  this  investigation 
were  demonstrated  with  remarkable  closeness  by  actual  weighings  of  loads  on  pipes,  the  pipes 
ranging  from  12  to  36  in.  in  internal  diameter  placed  in  ditches  from  0  to  19  ft.  in  depth. 

1  Written  by  Prop.  Anson  Marston  and  Mr.  A.  O.  Anderson. 


Sec.  17-31a] 


HYDRAULIC  STRUCTURES 


779 


Table  i.— Approximate  Maximum  Loads  in  Pouni>6  Per  Linear  Foot,  on  Pipes  in 
Ditches  from  Common  Ditch-Fillinq  Materials 


H  =  height  of 
fill  above  top 
of  pipe 


B  =  breadth  of  ditch  a  little  below  top  of  pipe 


1  ft. 


1     2  ft. 

3  ft. 

4  ft. 

5  ft. 

1  ft. 

2  ft. 

3  ft. 

4  ft. 

5  ft. 


Partly  compacted  damp  top  soil  90  lb.  per  ou.  ft. 


Saturated  top  soil  110  lb.  per  cu.  ft. 


2  ft. 

130 

310 

490 

670 

830 

170 

380 

600 

820 

1,020 

4  ft. 

200 

530 

880 

1,230 

1,580 

260 

670 

1,090 

1,510 

1,950 

6  ft. 

230 

690 

1,190 

1,700 

2,230 

310 

870 

1,500 

2,140 

2,780 

8  ft. 

250 

800 

1,430 

2,120 

2,790 

340 

1,030 

1,830 

2,660 

3,510 

10  ft. 

260 

880 

1,640 

2,450 

3,290 

350 

1,150 

2,100 

3,120 

4,150 

Dry  sand,  100  lb.  per  cu.  ft. 

Saturated  sand,  120  lb.  per  cu. 

ft. 

2  ft. 

150 

340 

550 

740 

930 

180 

410 

650 

890 

1,110 

4  ft. 

220 

590 

970 

1,360 

1,750 

270 

710 

1,170 

1,640 

2,100 

6  ft. 

260 

760 

1,320 

1,890 

2,480 

310 

910 

1,590 

2,270 

2,970 

8  ft. 

280 

890 

1,590 

2,350 

3,100 

340 

1,070 

1,910 

2,820 

3,720 

10  ft. 

290 

980 

1,820 

2,720 

3,650 

350 

1,180 

2,180 

3,260 

4,380 

12  ft. 

300 

1,040 

2,000 

3,050 

4,150 

360 

1,250 

2,400 

3,650 

4,980 

14  ft. 

300 

1,090 

2,140 

3,320 

4,580 

360 

1,310 

2,570 

3,990 

5,490 

16  ft. 

300 

1,130 

2,260 

3,550 

4,950 

360 

1,350 

2,710 

4,260 

5,940 

18  ft. 

300 

1,150 

2,350 

3,740 

5,280 

360 

1,380 

2,820 

4,490 

6,330 

20  ft. 

300 

1,170 

2,420 

3,920 

5,550 

360 

1,400 

2,910 

4,700 

6,660 

22  ft. 

300 

1,180 

2,480 

4,060 

5,800 

360 

1,420 

2,980 

4,880 

6,960 

24  ft. 

300 

1,190 

2,540 

4,180 

6,030 

360 

1,430 

3,050 

5,010 

7,230 

26  ft. 

300 

1,200 

2,570 

4,290 

6,210 

360 

1,440 

3,090 

5,150 

7,460 

28  ft. 

300 

1,200 

2,600 

4,370 

6,390 

360 

1,440 

3,120 

5,240 

7,670 

30  ft. 

300 

1,200 

2,630 

4,450 

6,530 

360 

1,440 

3,150 

5,340 

7,830 

Infinity 

300 

1,210 

2,730 

4,850 

7,580 

360 

1,450 

3,270 

5,820 

9,090 

Partly  compacted  damp  yellow  clay,  100  lb.  per  cu.  ft. 

Saturated  yellow  clay,  130  lb.  per  cu.  ft. 

2  ft. 

160 

350 

550 

750 

930 

210 

470 

730 

1,000 

1,240 

4  ft. 

250 

620 

1,010 

1,400 

1,800 

340 

840 

1,330 

1,870 

2,370 

6  ft. 

300 

830 

1,400 

1,990 

2,580 

430 

1,140 

1,900 

2,630 

3,410 

8  ft. 

330 

990 

1,720 

2,500 

3,250 

490 

1,380 

2,360 

3,360 

4,400 

10  ft. 

350 

1,110 

2,000 

2,920 

3,880 

520 

1,570 

2,760 

3,980 

5,270 

12  ft. 

360 

1,200 

2,220 

3,320 

4,450 

540 

1,730 

3,100 

4,560 

6,050 

14  ft. 

370 

1,280 

2,410 

3,650 

4,950 

560 

1,850 

3,410 

5,050 

6,760 

16  ft. 

370 

1,330 

2,570 

3,950 

5,400 

570 

1,940 

3,660 

5,510 

7,440 

18  ft. 

380 

1,390 

2,710 

4,210 

5,810 

570 

2,020 

3,880 

5,930 

8,060 

20  ft. 

380 

1,410 

2,830 

4,450 

6,180 

580 

2,090 

4,070 

6,280 

8,610 

22  ft. 

380 

1,430 

2,920 

4,640 

6,500 

580 

2,140 

4,240 

6,610 

9,130 

24  ft. 

380 

1,450 

3,000 

4,820 

6,800 

580 

2,180 

4,380 

6,910 

9,590 

26  ft. 

380 

1,470 

3,060 

4,980 

7,080 

580 

2,210 

4,500 

7,160 

10,010 

28  ft. 

380 

1,480 

3,120 

5,100 

7,310 

580 

2,240 

4,610 

7,380 

10,430 

30  ft. 

380 

1,490 

3,170 

5,230 

7,530 

580 

2,260 

4,700 

7,590 

10,780 

Infinity 

380 

1,520 

3,410 

6,060 

9.480 

580 

2,340 

5,270 

9,360 

14,620 

The  width  of  the  ditch  above  the  pipe  makes  practically  no  difference  in  the  load  on  the  pipe,  which  is  just  as 
great  for  a  vertical  ditch  as  for  one  several  times  as  wide  at  the  top  but  of  the  same  width  a  little  below  the  top'of 
the  pipe. 

In  ditches  of  proportions  customary  in  actual  work,  the  diameter  of  the  pipe  used  in  any  particular  ditch  of  a 
fixed  given  width  makes  practically  no  difference  in  the  load  on  the  pipe.  A  12-in.  pipe  will  have  to  carry  the  same 
load  as  an  18-in.  pipe,  if  both  are  placed  in  ditches  2  ft.  wide  under  other  similar  conditions. 


780 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-31a 


In  case  a  wide  ditch  is  necessary  for  constructive  reasons,  the  load  on  the  pipe  can  be  diminished  greatly,  in 
firm  soil,  by  stopping  the  wide  ditch  a  few  inches  above  the  top  of  the  pipe  and  digging  in  the  bottom  the  narrowest 
ditch  practicable  to  receive  the  pipe,  making  bell  holes  at  the  side  for  the  sewer  pipe,  if  necessary. 

Grades  or  fills  built  over  the  surfaces  of  completed  ditches,  and  piles  of  sand,  gravel,  and  other  materials  having 
internal  friction,  operate  to  increase  the  loads  on  pipes  in  ditches  to  the  same  extent  as  an  equal  added  height  of 
ditch  filling,  for  a  breadth  of  ditch  equal  to  that  at  a  little  below  the  top  of  the  pipe. 

A  superload  is  any  load  applied  to  the  upper  surface  of  the  ditch  filling,  except  loads  from  fills  or  heaps  of 
granular  materials.  A  long  superload  is  one  extending  a  considerable  length  along  a  ditch,  as  compared  with  its 
depth  and  breadth,  and  may  be  caused  by  piles  of  paving  brick,  lumber,  etc.,  over  the  ditch.  Long  superloads 
on  completed  ditches  cause  increases  in  the  loads  on  pipes  in  ditches  by  percentages  of  the  superload  which  decrease 
as  depth  increases,  and  safe  values  for  which  can  be  computed  by  Table  2.  Table  2  has  been  closely  checked  by 
actual  weighings  of  the  increase  in  loads  on  pipes  in  ditches  due  to  super  loads. 

Table  2. — Approximate  Safe  Values  of  C  to  Use  in  Formula  L 


CLi 


L  =  loads  per  unit  of  length,  on  pipes  in  ditches,  due  to  Li. 
Li  =  long  superloads  on  ditches,  per  unit  of  length. 


H 
B 

Sand  and  damp  top 
soil 

Saturated  top  soil 

Damp  yellow  clay 

Saturated  yellow 
clay 

0.0 

1.00 

1.00 

1.00 

1.00 

0.5 

0.85 

0.86 

0.88 

0.89 

1.0 

0.72 

t).75 

0.77 

0.80 

1.5 

0.61 

0.64 

0.67 

0.72 

2.0 

0.52 

0.55 

0.59 

0.64 

2.5 

0.44 

0.48 

0.52 

0.57 

3.0 

0.37 

0.41 

0.45 

0.51 

4.0 

0.27 

0.31 

0.35 

0.41 

5.0 

0.19 

0.23 

0.27 

0.33 

6.0 

0.14 

0.17 

0.20 

0.26 

8.0 

0.07 

0.09 

0.12 

0.17 

10.0 

0.04 

0.05 

0.07 

0.11 

A  short  superload  is  one  extending  a  short  distance  along  a  ditch  as  compared  with  the  breadth  and  depth, 
and  may  come  from  the  wheels  of  wagons,  traction  engines,  steam  road  rollers,  etc.    Short  superloads,  on  com- 
pleted ditches,  cause  increases  in  the  loads  on  pipes  in  ditches  by  percentages  of  the  superload  which  decrease 
as  the  depth  increases,  and  safe  values  which  can  be  estimated,  but  not  very  reliably,  by  Table  3.    Table  3  has 
not  been  checked  by  actual  weighings  of  increase  of  loads  on  pipes  in  ditches. 

Table  3. — Approximate  Safe  Values  for  C  to  Use  in  Formula  L  =  CLi 

L  —  loads  per  unit  of  length,  on  pipes  in  ditches  directly  under  Li,  due  to  Li.  L\  =  short  superloads  on 
ditches,  per  unit  of  length,  of  length  A  along  ditch. 


Sand  and  damp 
top  soil 

Saturated  top  soil 

Damp  yellow  clay 

Saturated  yellow 
clay 

H 

Ka 

=  K 

Ka  = 

\Ka- 

=  K 

Ka  = 

=  K 

Ka  = 

Ka- 

=  K 

B 

A  = 

A 

A 

A 

A 

A 

A 

A 

B 

B 
10 

B 

B 
10 

B 

B 
10 

B 

B 
10 

B 

B 
10 

B 

B 
10 

B 

B 
10 

B 

B 
10 

0.0 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.00 

1.10 

0.5 

0.77 

0.32 

0.70 

0.12 

0.78 

0.33 

0.71 

0.13 

0.79 

0.34 

0.72 

0.13 

0.81 

0.34 

0.74 

0.13 

1.0 

0.59 

0.11 

0.49 

0.02 

0.61 

0.11 

0.51 

0.02 

0.63 

0.11 

0.52 

0.02 

0.66 

0.12 

0.55 

0.02 

1.5 

0.46 

0.03 

0.34 

0.48 

0.04 

0.36 

0.51 

0.04 

0.38 

0.54 

0.04 

0.40 

2.0 

0.35 

0.01 

0.24 

0.38 

0.01 

0.26 

0.40 

0.01 

0.27 

0.44 

0.01 

0.30 

2.5 

0.27 

0.  17 

0.29 

0.18 

0.32 

0.20 

0.35 

0.22 

3.0 

0.21 

0.  12 

0.23 

0.13 

0.25 

0.  14 

0.29 

0.16 

4.0 

0.12 

0.06 

0.14 

0.07 

0.16 

0.08 

0.19 

0.09 

5.0 

0.07 

0.03 

0.09 

0.03 

0. 10 

0.04 

0.13 

0.05 

6.0 

0.04 

0.01 

0.05 

0.02 

0.06 

0.02 

0.08 

0.03 

8.0 

0.02 

0.02 

0.03 

0.01 

0.04 

0.01 

10.0 

0,01 

0.01 

0.01 

0.02 

Sec.  17-316] 


HYDRAULIC  STRUCTURES 


781 


H  =  height  of  fill  in  ditch,  above  top  of  pipe. 

B  —  breadth  of  ditch,  a  little  below  top  of  pipe. 

K  =  ratio  of  lateral  pressure  to  vertical  in  the  ditch  filling. 

Ka  =  ratio  of  longitudinal  pressure  to  vertical  in  the  ditch  filling. 

Values  of  C  for  Ka  =  0  are  given  in  Table  2. 

The  formula  L  =  CLi  holds  true  only  directly  under  Li.  Beyond  Li  in  either  direction,  the  intensity  of  load 
on  the  pipe  diminishes  rapidly. 

Calculations  made  from  Table  3  are  not  very  reliable  since  we  are  usually  uncertain  as  to  the  proper  value  to 
take  for  Ka,  and  there  is  great  need  of  a  series  of  tests  of  the  actual  loads  on  pipes  caused  by  short  superloads,  but 
such  tests  would  be  very  difficult  to  make  and  test  results  are  not  available. 

In  the  meantime,  Table  3  will  be  of  some  value  to  engineers  of  good  judgment  in  assisting  them  to  make  rea- 
sonable safe  allowances  for  the  probable  effect  on  the  loads  on  pipes  in  ditches  from  heavy  concentrated  loads  on 
wagon  wheels,  traction  engines,  and  road  rollers. 

316.  Strength  of  Pipe. — The  theoretical  analysis  of  stresses  in  culvert  pipe  is 
that  of  thin  elastic  rings  and  is  similar  to  the  general  method  employed  for  arches.  The  dif- 
ference in  the  intensity  of  the  load  at  the  crown  and  at  the  extremities  of  the  horizontal  diameter, 
due  to  the  difference  in  the  depths  of  the  earth,  is  considered  negligible,  and  the  pressure  and  its 
distribution  on  the  lower  half  of  the  ring  is  assumed  to  be  the  same  as  that  on  the  upper  half. 

Theory  gives  the  following  values  of  the  bending  moment  at  the  top  and  bottom  sections  of 
a  pipe: 

I.  For  single  concentrated  load  (top  and  bottom),  M  =  0.159Pd. 

II.  For  total  uniformly  distributed  load  over  entire  horizontal  projection  (top  and  bottom), 
M  =  0m25Wd. 

III.  For  a  uniformly  distributed  load  over  the  top  fourth  of  the  circumference  and  with 
the  pipe  supported  on  its  bottom  quarter  circumference,  M  =  0.0845TFd.  Where 

d  =  diameter  of  pipe. 

P  =  concentrated  load  at  top. 

W  =  total  uniformly  distributed  load  above  horizontal  diameter. 

M  =  bending  moment  in  pipe  in  a  unit  length. 
The  bending  moments  at  the  ends  of  the  horizontal  diameters  under  the  above  conditions  of 
loading  are: 

I.  M  =  -OmiPd 
II.  M  =  -0m25Wd 
III.  M  =  -0.077Wd 

The  above  moments  will  be  reduced  for  any  lateral  restraint  or  lateral  pressure.  In  fact  for 
equal  uniform  horizontal  and  uniform  vertical  forces  (which  may  be  considered  equivalent  to  a 
uniform  radial  pressure)  the  moments  due  to  the  lateral  forces  have  equal  but  opposite  signs 
to  those  given  for  Case  II  above,  and  it  can  be  proved  that  the  total  moments  at  all  points  are 
zero.  It  is  not  good  practice,  however,  to  rely  on  any  lateral  restraint  or  pressure  in  the  analy- 
sis of  the  strength  of  pipes.  Mathematical  analysis  shows  that  the  weight  of  pipes  causes  only 
five-eighths  as  much  bending  moment  at  the  lowest  point  of  the  pipe  as  does  an  equal  weight 
of  earth. 

Since  the  exact  load  and  the  nature  of  its  distribution  over  pipe  surface  is  usually  uncertain, 
the  probable  range  of  bending  moments  under  actual  conditions  of  construction  is  all  that 
laboratory  tests  can  be  expected  to  furnish.  In  a  series  of  tests  at  the  University  of  Illinois,^ 
reinforced-concrete  rings  and  circular  pipe  (48-in.  internal  diameter  and  4  in.  thick)  were  tested 
for  concentrated  loads  at  the  top  and  bottom  of  the  vertical  diameter  (Case  I  above),  and  for 
uniformly  distributed  loads  above  and  below  the  entire  horizontal  diameter  (Case  II  above). 
This  latter  loading  was  obtained  by  placing  the  pipe  in  a  tight  box  so  as  to  be  entirely  encircled 
with  sand  and  then  applying  a  load  to  the  top  surface  of  the  sand.  The  reinforcement  for 
most  of  the  rings  tested  consisted  of  3^^-in.  corrugated  rods  placed  near  the  intrados  at  top  and 
bottom  and  near  the  extrados  at  the  sides.    The  rings  were  only  24  in.  long,  but  the  pipe 

1  See  Bulletin  22  of  the  Engineering  Experiment  Station  of  the  University  of  Illinois,  written  by  Prof.  A.  N 
Talbot. 


782 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-31C 


sections  were  from  102  to  104  in.  in  length  with  the  usual  bell  and  pigot  points.  To  allow  the 
circumferential  reinforcement  in  the  pipes  to  be  circular  in  shape,  the  pipe  cross-sections  (Fi-g.  69. 
were  made  with  the  vertical  diameter  4  in.  longer  than  the  horizontal  diameter,  thus  bringing 
the  reinforcement  at  the  points  of  tension  in  the  loaded  pipe.  Using  the  yield  point  of  the 
steel  in  the  common  formula  for  the  bending  resistance  of  a  reinforced  section,  there  was  found 


Fig.  71. — Standard  design  for  24-in.  circular  culvert,  Iowa  Highway  Commission. 


a  close  agreement  between  the  theoretical  and  experimental  values  for  the  strength  of  pipe 
under  these  two  methods  of  loading. 

Marston  and  Anderson,  in  the  investigation  referred  to  in  the  preceding  article,  came  to 
the  conclusion  that  "the  typical  field  bedding  and  loading  of  pipes  in  ditches  are  such  that  their 
effect  on  the  pipe  can  be  reproduced  with  practical  exactness  in  laboratory  tests  by  bedding 


the  pipes  in  sand  during  the  tests  for  90  deg.  of  the  circumference  at  the  bottom  and  also  for 
90  deg.  at  the  top."  This  method  of  loading  is  Case  III  above.  In  the  Iowa  investigation 
the  weight  of  the  pipe  as  well  as  that  of  the  backfilling  was  taken  into  consideration. 

31c.  Circular  Culverts  Cast  in  Place. — A  cast-in-place  culvert  with  circular 
opening  is  shown  in  Fig.  71.  Fig  72  shows  an  adjustable,  collapsible  wood  form  which  can 
be  very  economically  used  for  culverts  of  this  type. 


Sec.  17-32] 


HYDRAULIC  STRUCTURES 


783 


The  method  of  constructing  and  using  this  form  is  described  as  follows  in  a  booklet  entitled 
"Small  Concrete  Bridges  and  Culverts,"  published  by  the  Universal  Portland  Cement  Co.: 

This  form  is  constructed  of  two  by  four's  beveled  and  strung  on  wires,  as  shown  in  Fig.  72.  The  number  of 
staves  to  be  used,  varying  with  the  size  of  the  culvert,  are  placed  side  by  side  with  a  wire  drawn  through  each  end 
of  the  stave  as  shown.  The  form  is  then  rolled  around  a  circular  head  size  of  the  proposed  culvert  and  wire  bands  are 
tied  tightly  around  it  on  the  outside.  Wedges  are  then  driven  as  shown  in  Fig.  72  to  hold  the  staves  firmly  in  posi- 
tion.   After  the  culvert  has  been  built  the  wedges  are  removed  and  the  circular  heads  knocked  in;  the  staves  will 


then  collapse  and  are  easily  removed.  This  form  can  be  used  over  and  over  again  and  Mr.  Gearhart  states  that  its 
cost  should  not  exceed  $15  or  $20. 

32.  Box  Culverts. — The  box  type  of  culvert  is  especially  adapted  to  locations  where  the 
headroom  is  limited  and,  when  planned  for  such  locations,  has  a  great  advantage  over  the  arch. 
A  culvert  of  this  type,  for  example,  can  be  built  with  less  excavation  and  less  disturbance  to 
the  embankment  and  will  give  a  greater  distribution  of  load  upon  the  foundation  than  the 


^very  third  rod 


^Corr  Bars,  /p'c  toc.fop  and 
bo*tvm  slabs 


Longitudinal  Section 
Fig.  74. — Standard  culvert  of  6-ft.  span,  Hampden  R.  R. 


ordinary  form  of  arch  culvert.  Also,  the  formwork  for  this  type  is  much  simpler  and  the  cost 
of  construction  correspondingly  lower,  except  perhaps  in  some  cases  where  the  number  and 
size  of  culverts  to  be  constructed  warrants  the  use  of  commercial  arch  forms  of  collapsible 
steel.  Box  culverts  are  not  always  employed  only  under  shallow  fills,  as  is  evident  from  Fig. 
76. 


784 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-32 


Botrom  Level   

pi        \'''- 3'-o' or  more  depending 
^  — |j  ^   on  local  conditions 

I'-o"  Longitudinal  Section 


4  <.^.— ^>  <....  e'-o"—-  • 


K  -  14-10"  -->! 

,l>'Pods,l4'  (Z8'  cuts  t)  "V 


X     Cross  Section 

i Waterway  69^  sq.ft.)  ^   /^'- T"!' 

End  Elevation 

Fig.  75. — Double  6  X  6-ft.  box  culvert,  A.  T.  &  S.  Fe.  Ry.  system. 


Sec.  17-32a] 


HYDRAULIC  STRUCTURES 


785 


32a.  Forms  of  Box  Culverts. — There  are  two  distinct  forms  of  box  culverts 
which  may  be  distinguished  by  the  terms  open-box  and  closed-box.  In  the  open-box  (Fig.  73) 
the  side  walls  have  dependent  footings,  while  in  the  closed-box  (called  simply  box)  the  load 
is  supported  by  the  floor  (Fig.  74).  Double-box  culverts  (Fig.  75  )  are  generally  used  where  the 
span  is  equal  to,  or  greater  than,  twice  the  height,  as  the  use  of  a  single  box  beyond  these  pro- 
portions greatly  increases  the  cost. 

326.  Loading. — For  small  box  culverts  built  in  trenches  the  load  on  the  top 
slab  may  be  approximately  estimated  by  means  of  the  tables  in  Art.  31a.  For  large  box  cul- 
verts and  for  all  culverts  not  built  by  trench  construction,  no  allowance  should  be  made  for 
the  arching  action  of  the  material,  which  means  that  such  culverts  should  be  proportioned  to 
carry  the  entire  weight  of  the  fill  above  the  cover  slab.  The  lateral  pressure  of  the  earth 
(including  live-load  surcharge)  is  usually  assumed  as  that  due  to  a  fluid  weighing  about  30 
lb.  per  cu.  ft. — that  is,  a  weight  about  one-fourth  the  weight  of  earth.  It  is  obvious  that  the 
pressure  due  to  live  load  does  not  spread  out  through  the  filling  at  the  ordinary  angle  of  repose 
of  the  material,  but  has  a  side  slope,  or  line  of  zero  stress,  much  more  nearly  vertical.  It  is 
frequently  assumed  that  the  live  load  is  carried  down  at  a  slope  of  horizontal:!  vertical. 
In  railroad  embankments  this  slope  is  taken  from  the  ends  of  the  ties. 

An  allowance  is  usually  made  for  impact  of  the  live  load  in  the  design  of  railroad  culverts. 
Some  designers  allow  50%  for  impact  on  all  banks  up  to  40  ft.  high.  A  more  conservative 
plan  often  followed  is  to  allow  100%  for  fills  of  less  than  2  ft.,  75%  for  fills  between  2  ft.  and 
4  ft.,  and  50%  for  all  fills  over  4  ft. 

32c.  Design  of  Cross-section. — The  top  slab  of  a  box  culvert  is  partially  fixed, 
but  it  is  the  general  practice  to  design  this  slab  as  simply  supported  and  to  reinforce  at  the  cor- 
ners against  negative  bending.  Negative  reinforcement,  however,  is  not  always  provided  (see 
Fig.  75),  in  which  case  the  sides  and  top  act  as  simple  beams  and  more  or  less  cracking  occurs 
on  the  outside  near  the  corners.  The  walls  or  sides  of  a  box  culvert  are  usually  designed 
somewhat  empirically,  but  are  always  provided  with  sufficient  strength  to  support  the  lateral 
earth  pressure,  neglecting  any  outward  bending  due  to  the  bending  of  the  cover  slab.  In 
open-box  construction,  cross  struts  are  often  used  to  assist  in  holding  the  footings  against 
the  pressures  on  the  walls  and  also  to  provide  bearing  area  in  addition  to  that  furnished  by 
wall  footings  (Fig.  77).  The  struts  are  designed  as  beams  with  a  span  equal  to  the  width  of 
the  culvert,  and  the  struts  are  so  spaced  and  proportioned  as  to  obtain  a  uniform  soil  pressure 
throughout.  When  a  bottom  slab  is  employed  and  assumed  to  support  the  load,  its  thickness 
is  made  the  same  as  that  of  the  cover  slab  since  the  load  for  both  slabs  is  substantially  the 
same.  Longitudinal  reinforcement  should  be  provided  on  account  of  the  possibility  of  beam 
action  due  to  unequal  settlement.  The  amount  of  this  reinforcement  should  depend  upon  the 
character  of  the  foundation.  Where  the  foundations  are  very  bad,  it  is  the  practice  of  some 
engineers  to  figure  the  culvert  as  a  whole  to  act  as  a  beam,  considering  the  length  of  beam  as 
12  times  its  depth.  In  long  culverts  under  railroad  tracks  the  load  decreases  beyond  the  ends 
of  the  ties  and  the  cross-section  should  decrease  whenever  a  material  saving  is  found  to  result. 

In  Fig.  77,  which  illustrates  a  standard  box  culvert  adopted  by  the  Chicago,  Milwaukee  & 
St.  Paul  Railway,  the  cover  is  designed  as  a  simply  supported  slab  with  span  equal  to  clear 
span  when  fillets  are  used  and  to  clear  span  plus  one-half  the  maximum  cover  thickness  (but 
not  to  exceed  1  ft.)  when  no  fillets  are  provided.  Stirrups  and  bent  rods  are  employed  to  take 
care  of  two-thirds  of  the  shear  when  the  shear  exceeds  40  lb.,  bent  rods  being  also  used  to  care 
for  any  negative  moments  which  may  develop  due  to  connection  with  side  walls.  Longi- 
tudinal steel  is  employed  with  a  sectional  area  of  about  H  5  o  of  the  area  of  the  entire  concrete 
section.  The  side  walls,  cross  struts,  and  footings  are  proportioned  in  the  same  manner  as 
above  described.  Keyways  are  formed  in  top  of  footings  and  side  walls  so  as  to  offer  shearing 
resistance  to  movement  of  side  walls  due  to  lateral  earth  pressure.  For  fills  up  to  40  ft.,  the 
load  on  the  footings  is  assumed  to  include  the  live  load  and  dead  load  of  culvert,  and  the  fill 
directly  above  the  culvert  for  the  width  overall  including  footings.    For  fills  over  40  ft.  high, 

50 


786 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-32C 


the  total  weight  resting  on  the  footings  is  considered  as  623^  %  of  the  culvert  weight  plus  62^^  % 
of  the  fill  above  the  footings.  The  live  load  is  disregarded  and,  for  ease  in  computation,  the 
weight  of  culvert  is  taken  as  equal  to  the  fill  it  displaces.  Wing  walls  over  8  ft.  in  height  or 
making  an  angle  of  less  than  60  deg.  with  the  headwall  are  made  self-supporting  cantilevers 
with  a  joint  at  connection  with  the  barrel.  Wingwalls  for  all  other  conditions  are  made  con- 
tinuous with  the  main  part  of  the  culvert.  The  section  of  the  culvert  coming  under  the  track 
is  made  approximately  equal  in  length  to  the  theoretical  spread  of  the  live  load,  which  is  equal 
to  the  distance  out  to  out  of  ties  (8  ft.  for  single  track.  21  ft.  for  double  track)  plus  the  height 


^'^ Vert  Pods  7-6 '\ 
f Dowels.  2^- 


4 


-Base  of  hy/  ra/f 


V  V 


I  i  1 1 1 


10- 


-..J,L...'.>L...,._: 


iDowe/s 


■'-  -.-> 


s/:-8 


Sectional  Elevation  at  Center  Lin?  of  Culvert 


I  Break 


<s'-w-A  St/rrvpa. 


Plan 


i"Verf..7-e 


'Dowels.  3'  l;':^; 


■  ■  p4l.f-.  ^-jJ — :  ^md 


j-->ji./:^/'>ik-  y" 


Section  dt 
Center  Line  of  TracK, 

Fig.  77— Single  box  culvert,  C.  M.  &  St.  P.  Ry. 


of  culvert  plus  one-half  the  height  of  fill  above  the  cover  slab.  The  invert  is  paved  with  a 
concrete  slab  in  all  spaces  between  struts  so  as  to  form  a  continuous  concrete  invert. 

Accurate  analysis  may  be  made  of  the  moments  in  box  culverts  when  such  culverts  are 
reinforced  so  as  to  act  monolithically.  The  following  formulas  and  diagrams  are  given  so 
that  the  moments  from  such  analysis  may  be  readily  determined. 

The  open-box  culvert  may  well  be  divided  into  two  classes  for  analysis,  each  claas  de- 
pending on  the  material  upon  which  the  footings  rest.  If  the  structure  rests  upon  rock, 
cemented  gravel,  or  some  other  material  having  a  high  allowable  bearing  stress,  the  plane  of 
the  base  of  each  side  wall  will  be  held  at  a  practically  constant  slope;  that  is,  the  side  may  be 
considered  fixed  at  the  bottom.  On  the  other  hand,  if  the  allowable  bearing  pressure  of  the 
supporting  material  is  low,  the  plane  of  the  base  will  become  inclined  until  the  moment  at  the 


Sec.  17-32c] 


HYDRAULIC  STRUCTURES 


787 


footing  has  been  reduced  to  a  value  that  will  be  resisted  by  the  moment  of  the  upward  pressure 
on  the  base.    Since  in  such  a  case  the  resisting  moment  is  small,  an  altogether  different  dis- 
tribution of  moment  will  occur  throughout  the  structure.    It  will  be  slightly  on  the  safe  side 
to  regard  the  sides  as  hinged  at  their  base. 
The  following  nomenclature  will  be  used: 

h  =  span  of  frame  (c.  to  c.  of  side  walls). 

h  =  height  of  frame  (c.  to  c.  of  top  and  bottom  slabs). 

R  =     =  ratio  of  span  to  height. 

.  Ic  =  moment  of  inertia  of  cross-section  of  top  or  bottom  slab  (considered  alike)  for 
one  unit  of  length  of  the  barrel. 
Id  =  moment  of  inertia  of  cross-section  of  either  side  wall  (considered  alike)  for 
one  unit  of  length  of  the  barrel. 
Ic 

<S  =       =  ratio  of  the  moment  of  inertia  of  the  horizontal  slabs  to  that  of  the  sides. 

w  =  uniform  load  per  unit  area  on  top  or  bottom  slab. 
p  =  uniform  load  per  unit  area  on  side  walls. 
P  =  concentrated  load. 
He  =  thrust  at  the  center  of  the  top  slab. 

Vc  =  zero  for  symmetrical  loading,  as  is  the  case  in  the  analysis  of  culverts. 
Mc  =  moment  at  the  center  of  the  top  slab. 
Md  and 

Mb  =  moment  at  center  of  side  walls  and  center  of  bottom  slab,  respectively. 
Ma  and 

Mb  =  moment  at  the  upper  and  lower  corners,  respectively. 
Type  I.    The  Closed  Frame  J— 

1  Assume  the  rectangular  culvert  of  Fig.  78  to  be  rigidly  fixed  at  the  center  of  the  bottom  slab.  With  this  con- 
dition assumed,  a  unit  length  of  the  culvert  may  be  treated  in  the  same  manner  as  a  symmetrical  arch  with  fixed 
ends  (see  Art.  18,  Sect.  16)  and  the  following  expressions  result: 

C      ds  Cds       r     ds  r  ds 

Mil- (MY 


in  which 

TO  =  moment  at  any  point  on  either  half  of  culvert  of  all  external  loads  between  point  and  crown  section — 
all  values  of  m  to  be  substituted  in  equations  as  positive. 

^  =  integration  referred  to  one-half  of  culvert  only. 
X,  y  =  coordinates  of  any  point. 

From  these  equations  were  developed  the  formulas  for  Types  I  and  II  given  above. 
The  bending  moment  at  any  point  may  be  expressed  as  follows: 

Mc  =  Mc  +  Hey  —  m 
Mr  =  Mc  +  Hey  —  m 


788 


Case  1. 


Case  2. 


Case  3. 


CONCRETE  ENGINEERS'  HANDBOOK 

R^ 


[Sec.  17-32C 


hit 


B 


wb=P 


SA/tl 


,iiiiiini|M 


ttitmttlir 


wb 


A 

<  b- 

-> 

Jl 

r?/pe  //. — O-pen  Frame  ivith  Fixed  Walls. 
Case  1. — 


£ 


2  ^Ic 


8     3i2  +  *S 


Ma   =  Mc 


M, 


Ph 


Mc  +  Hch  -  —  =  Ma  +  i^c/i 


He  =  0 


Mc        MB  2i\R+S) 

Md  =  Ma  =M 


Mc 


He  =  ^ 


Md  =  Mc  +  ^ 
Mb  =  Mb  =  Mc 


He 

Mc 

Ma 
M, 


P/    3R^  \ 
8\S  +  2r) 
Pb/S  -\-  R\ 
4  \S  +  2r) 

Mc  j- 

4 

Ma  +  Hch 


Case  2.- 


wb 


UIIIIU 


-I. 


1  See  footnote  on  p.  789. 


b-T-H 


^wb(    R^  \ 
4  \2R  +  Sj 
ivb^  /2^-f3^\ 
24  \2R  +  S  ) 


Mc 


Ma  =  Mc  - 


Mb  =  Mc 


wb^ 


wb^ 


Hch  =  Ma  +  Hch. 


Sec.  17-32c] 


HYDRAULIC  STRUCTURES 


789 


Case  3 — 


«  b- 

.X 

Mc  = 

rr     ^Ph  (SR  + 


He 

In  sides  M(max)  occurs  at       from  top. 


M(max)  =  Mc  + 


T^T/pe  ///. — Open  Frame  Hinged  at  the  Base.  ^ 
Case  1. — 


He' 
2p 


8         +  3i?/ 


Mc=^  -  Hh 
4 


Case  2- 


I'c'  ; 
 b-  rH 


Ma 

H  = 

Mc  = 
Ma  = 


Hh 


\2S  +  3RJ 


wbl  R 

^  -  Hh 


-Hh 


Case  3. — 


Ph 


^^^^ 

-Id 


ph 


3pA  /  >S  +  2/e  \ 
4   \2*5  +  Sr) 

^  _  ph 

2 

M  (max)  for  the  sides  = 


H 

Mc  =  Ma 


Hh 


i/i  V  S  \ 
4  \2S  +  3i?/ 


2p 


^  at  max.  moment 


1  The  analysis  of  this  type  of  frame  follows  that  for  a  two-hinged  arch.  Let  M'  be  the  bending  moment,  at  any 
section,  of  the  vertical  forces  only,  as  for  a  simple  horizontal  beam.  Then  for  any  point  there  results  the  total  mo- 
ment M  =  M'  —  Hy  in  which  y  is  measured  from  the  horizontal  connecting  the  hinges,  and  H  is  the  thrust  acting 
along  this  line  and  upon  the  hinges.  From  "Curved  Beams"  (see  Art.  15,  Sect.  16)  the  increase  in  span  is,  with  E 
constant, 

ds 


4f 


'1 


The  span,  however,  is  not  permitted  to  increase,  due  to  the  resistance  offered  by  H. 
Substituting  for  M  its  value  given  above. 


JiM' 


from  which 


H  = 


-  Hy)y:-^^ 


Since  the  thrust  only  is  statically  indeterminate,  its  solution  for  any  case  permits  statical  solution  of  moment  by 
the  equation  for  M  given  above. 


Sec.  17-32c] 


HYDRAULIC  STRUCTURES 


793 


794 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  n-S2d 


Diagrams. — The  statically  indeterminate  functions  He  and  Mc  for  Types  I  and  II,  and 
H  for  Type  III  may  be  read  from  the  following  graphs.  The  use  of  the  diagrams  will  be  found 
to  aid  greatly  the  repetition  of  solutions  caused  by  having  to  assume  at  the  outset  some  values 
of  Ic  and  Id.    These  true  values  cannot  be  obtained  until  a  tentative  design  is  made,  based 

Ic 

upon  the  stresses  in  the  frame  having  an  adopted  stiffness  ratio  =  S.  In  usual  cases 
one  may  well  begin  the  design  by  assuming  S  =  4.    The  approximate  sections  required  in  sides, 


top  and  bottom  may  be  obtained  from  the  moments  under  this  assumption.  The  values  Ic 
and  Id  may  then  be  calculated  from  these  approximate  sections,  thus  determining  a  new  and 
much  closer  value  of  S.  The  whole  solution  is  then  repeated  until  the  required  sections  check 
the  assumed  value  of  S. 

32d.  Construction. — The  inside  forms  for  small  box  culverts  are  usually  arranged 
to  be  collapsible  or  at  least  so  that  the  frames  against  which  the  lagging  is  placed  may  be  easily 


Fig.  79. — Forms  for  2-ft.  box  culvert. 


knocked  out  after  the  concrete  has  properly  set.  In  Fig.  79  the  inner  forms  consist  of  boards 
placed  against  frames  made  of  three  pieces  of  2  by  4-in.  and  one  piece  of  2  by  6-in.  joists,  notched 
as  shown.  The  2  by  6-in.  piece  at  the  top  is  not  nailed  in  order  that  it  may  be  readily  knocked 
out  after  the  concrete  has  hardened.    The  removal  of  this  piece  allows  the  2  by  4-in.  joists  to 


Sec.  n-^2d] 


HYDRAULIC  STRUCTURES 


795 


be  withdrawn,  thus  releasing  the  boards.  Where  the  soil  is  hard  and  compact,  the  outer  forms 
may  be  omitted  and  the  concrete  deposited  directly  in  the  trench  made  to  exact  size  of  culvert 
cross-section.    Another  type  of  small  box  culvert  form  is  shown  in  Fig.  80. 


Fig.  80. — Forms  for  small  box  culverts,  Iowa  Highway  Commission. 


Fig.  81.— Box-culvert  forms,  C.  M.  &  St.  P.  Ry. 


/^Bars,^'^c.  foe. ,  t'Sars.  3^c. ioC. 


Fig.  82.— Box-culvert  forms,  C.  B.  &  Q.  R.  R. 

The  forms  for  large  box  culverts  need  no  special  consideration  as  they  are  similar  to  the 
forms  for  walls  and  floor  slabs  in  ordinary  construction.  Standard  form  details  adopted  by 
two  prominent  railroads  are  shown  in  Figs.  81  and  82. 


796 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-33 


Collap,sible  steel  forms  are  now  being  used  to  a  considerable  extent  in  culvert  construction, 
and  in  most  cases  with  success.  The  Whalen  steel  form  is  show^n  in  Fig.  83.  It  is  built  in 
but  one  size,  yet  by  its  unit  method  of  construction,  it  readily  lends  itself  to  the  building  of 
various-sized  culverts.  Although  built  in  arched  top  sections,  a  proper  assemblage  of  these 
sections  makes  it  possible  to  build  most  any  size  of  flat  top  culvert. 

If  running  water  is  encountered  which  cannot  be  temporarily  diverted  or  dammed,  the  water 
in  the  case  of  small  culverts  should  be  carried  in  a  new  trench  around  one  side  of  the  back 
forms.  In  the  case  of  the  larger  structures  the  trench  excavated  for  the  culvert  should  be  ar- 
ranged to  flume  the  stream  through  between  the  abutments. 


Fig.  83. — Whalen  steel  form. 


33.  Arch  Culverts. — The  arch  type  of  culvert  should  be  employed  where  an  artistic  design 
is  especially  desirable,  and  should  also  be  used  in  all  cases  where  the  fill  to  be  supported  is  ex- 
cessively high  and  the  foundations  suitable.  High  fills  over  box  culverts  necessitate  a  slab 
of  considerable  thickness  and  the  arch  becomes  the  more  economical  under  such  conditions 
because  of  the  fact  that  an  increase  in  fill  does  not  produce  a  correponding  increase  in  ring 
stress.  Arch  culverts  of  reinforced  concrete  are  not  usually  designed  for  spans  less  than  about 
8  ft.,  as  plain  concrete  seems  to  answer  the  purpose  for  such  small  structures. 

33a.  Design  of  Cross-section. — In  the  ordinary  type  of  arch  culvert  represented 
in  Fig.  84,  the  arch  ring  may  be  analyzed  in  the  same  manner  as  described  for  arch  bridges  in 
Art.  16,  Sect.  16.  A  uniform  live  load  only  is  considered  and  this  is  placed  over  the  whole 
span.  Although  steel  is  used,  the  line  of  pressure  is  usually  kept  everywhere  within  the  middle 
third.  In  determining  the  dead  load  on  the  arch  no  allowance  is  made  for  the  arch  action  of 
the  fill,  but  the  horizontal  components  of  the  earth  pressure  are  taken  into  account.  Longitu- 
dinal reinforcement  is  needed  to  prevent  objectionable  cracks  caused  by  the  shrinkage  of  concrete 


Sec.  17-33M 


HYDRAULIC  STRUCTURES 


797 


in  hardening  and  the  contraction  due  to  a  lowering  of  the  temperature,  and  also  to  distribute 
the  load. 

Inverts  are  employed  in  the  designs  shown  in  Figs.  85  and  86  in  order  to  provide  additional 
bearing  area  and  thus  reduce  the  large  abutments  which  would  otherwise  be  needed  in  order 
to  bring  the  pressure  on  the  soil  to  a  safe  value.  An  invert  also  tends  to  prevent  any  possibility 
of  water  undermining  the  structure  and  the  foundation  need  not  always  be  carried  to  the  same 
depth  as  when  the  abutments  aie  independent  of  each  other. 


Fig.  84. — Standard  design  for  10-ft.  arch  culvert,  State  of  Missouri  Highway  Department.     (Actual  dimensions 
and  shape  of  foundations  governed  by  conditions  of  soil  at  location  of  site.) 


Section  A-A     Section  B-B  ^\"--^" 


^  p" 

\"  - 

1   ^.-^ 

\</o  Spaces  @  18"-  ->| 

,-Z-/"Bars 

M 

|m  If 

 i 

3'-3'- 

<-'•-->[ '']<--  e-e"^'-  !<-'-'•> 
<-  /e'-o--  > 

<-            l6'-0'-  ► 

/- 

Sectional  Elevation  ^ 
Fig.  85. — Standard  arch  culvert  for  fills  up  to  40  ft.  high,  C.  M.  &  St.  P.  Ry. 

When  the  arch  ring  and  invert  are  thoroughly  tied  together  so  as  to  act  as  a  monolith  (a 
rare  case  except  in  masonry  sewer  design),  the  entire  culvert  may  be  analyzed  after  the  manner 
of  the  arch.    For  the  analysis  of  this  form  of  arch  see  Art.  33  on  the  design  of  conduits. 

335.  Forms. — The  centers  and  forms  for  the  arch  culvert  are  similar  to  those 
required  for  the  arch  bridge  of  small  span.    Where  inverts  are  employed,  the  concrete  for  the 


798 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-33& 


End  Section  End  Elevation 


Maxiwum  Fill  over  Croivr?  ■  90^f.~ 


Section  of  Barrel 
Fig.  86. — Double-barrel  culvert,  D.  L.  «&;  W.  R.  R 


^^4"x  6f4'-0"c.-foc.  to 
Fig.  87. — Centering  for  arch  culvert,  C.  M.  &  St.  P.  Ry. 


Bo+tom  View  of  Cen-tiering 


Fig.  88. — Centering  for  arch  culverts. 


Sec.  17-34] 


HYDRAULIC  STRUCTURES 


799 


footings  and  floor  in  the  stream  bed  should  be  deposited  first  and  then  the  centers  for  the  arch 
erected  on  this  concrete.  Fig.  87  shows  the  type  of  arch  culvert  centers  and  forms  used  by  the 
Chicago,  Milwaukee  &  St.  Paul  Railway.    Other  types  of  centers  are  shown  in  Figs.  88  and  89. 


Two  fhicJrnesses  of  3' planir 
tv  form  ring 


.^Driff  Bo/ts 


Fig.  89. — Details  of  centering,  Canoe  Creek  culvert,  near  Cloe,  Pa.,  B.  R.  &  P.  Ry. 


CONDUITS  AND  SEWERS 

Sewers  and  pipe  lines  fall  into  two  groups,  since  the  former  is  acted  upon  by  external  pres- 
sures only,  and  the  latter  primarily  withstands  internal  pressure  with  the  possible  addition  of 
external  pressures  due  to  intermittent  support,  or  to  burying. 

34.  Stresses  Due  to  Internal  Pressure. — Let  the  internal  pressure  on  a  pipe  be  P  lb.  per 
sq.  in.  Then  the  total  tension  at  any  longitudinal  section  through  one  side  of  the  pipe,  for 
1  in.  of  length,  is  FR  (see  Fig.  90).    This  is  resisted  by  A/s  =  p^/'s-    From  this 

PR 

Values  of  fs  have  ranged  from  8000  to  16,000  lb.  per  sq.  in.  with  good  results  in  all  cases. 
Pressures  up  to  100  lb.  per  sq.  in.  do  not  seem  to  force  seepage  through  the  minute  cracks.  It 
is  important  that  the  steel  used  be  of  high  bonding  capacity  to  distribute 
the  cracks,  hence  fabric,  or  for  larger  pipes,  deformed  bars  with  thorough 
splicing  should  be  used. 

35.  External  Earth  Pressure  on  Circular  Pipe. — For  earth  pressure  on 
pipe  in  ditches,  see  Art.  31a. 

36.  Large  Conduits  and  Sewers  not  Circular. — Definite  conditions  of  flow 
have  for  hydraulic  reasons  developed  various  types  of  conduit  and  sewer  sec- 
tions. Such  sections  consist  of  two  parts:  (1)  the  invert,  or  floor  of  the  conduit;  and  (2)  the 
arch,  or  walls  and  roof  of  the  structure.  The  invert  may  be  parabolic,  elliptical,  semicircular 
or  a  catenary,  while  the  arch  may  be  semicircular,  parabolic,  elliptical  or  segmental.  A  dis- 
cussion of  the  hydraulic  advantages  of  various  sections  will  be  found  in  Metcalf  and  Eddy's 

American  Sewerage  Practice,"  Vol.  I,  Chap.  XL 

When  the  sewer  or  conduit  rests  directly  upon  rock,  the  invert  is  merely  a  pavement  and 
may  be  made  relatively  thin.  The  arch  may  then  be  analyzed  by  the  methods  given  for  the 
elastic  arch,  considering  it  to  have  fixed  ends  (Case  I,  Fig.  91). 

The  pressures  acting  upon  the  arch  may  be  found  as  follows.  The  rib  is  divided  into  con- 
venient subdivisions,  as  described  in  the  analysis  of  the  elastic  arch.  The  intensity  of  vertical 
pressure,  say  for  division  3,  Fig.  91,  is  computed  as  described  in  Art.  31a  and  multiplied  by  the 
horizontal  projection  of  division  13,  to  obtain  Viz.  The  intensity  of  horizontal  pressure  is 
Ce  times  the  intensity  of  vertical  pressure  (see  Diagram  1,  "Retaining  Walls,"  page  577), 
and  this  is  multiplied  by  the  vertical  projection  of  division  13  to  obtain  Hn.  Applying  His 
and  Vis  at  the  centroid  of  division  13  and  completing  the  parallelogram,  P13  may  be  found. 
The  other  loads  are  then  found  in  a  similar  manner. 

When  the  structure  rests  on  yielding  material  (Case  II,  Fig.  91),  the  section  may  be  con- 
sidered fixed  at  BB  and  cut  at  the  crown  as  for  the  usual  arch  analysis.    The  rib  is  subdivided 


800 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-3(3 


from  the  crown  around  to  BB,  and  treated  precisely  as  an  arch.  It  is  assumed  that  there  are 
vertical  forces  acting  upward  on  the  invert  equal  in  amount  to  the  total  downward  vertical 
forces,  and  uniformly  distributed  over  the  invert.    The  oblique  resultant  force  on  block  16  is 


Fig.  91. 


due  to  the  combining  of  the  upward  vertical  force  with  the  earth  pressure  acting  on  the  left 
side  of  the  block.  After  having  computed  He,  by  the  usual  arch  analysis,  the  force  polygon 
may  be  drawn,  and  the  closing  line  will  be  Hb-    Rays  may  then  be  drawn,  since  the  pole  0 


1 


is  now  located  and  the  pressure  line  drawn  on  the  conduit  section.  The  shears  and  moments 
may  be  computed  as  for  arch  analysis.  Shear  will  usually  be  large  near  the  outer  ends  of  the 
invert,  as  is  shown  in  Fig.  91.  A  typical  method  of  placing  reinforcement  in  horseshoe  sec- 
tions is  shown  in  Fig.  92. 


Sec.  17-36] 


HYDRAULIC  STRUCTURES 


801 


Note  - On  hard  bofhm  no  reinfbrcemenf  required 
Fig.  94. 


51 


802 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  17-37 


37.  Construction. — Some  large  sewer  sections  are  shown  in  Figs.  93  and  94,  Fig.  93 
shows  a  typical  section  of  the  Monroe  St.  sewer  in  Chicago.  Fig.  94  shows  a  horseshoe  section 
in  Evanston,  111.  A  1  :  13-^  :  4^^  mix  was  used  in  the  latter  case.  A  large  number  of  typical 
sections  are  to  be  found  in  Metcalf  and  Eddy's  ''American  Sewerage  Practice,"  Vol.  1,  Chap.  XII, 
together  with  descriptions  of  each. 

38.  Longitudinal  Reinforcement. — Temperature  and  shrinkage  stresses  require  about  0.4  % 
of  longitudinal  reinforcement  in  pipes  and  conduits. 

Pipes  resting  at  intervals  on  saddles  are  required  to  carry  their  own  weight  and  should  be 
reinforced  longitudinally  to  resist  the  flexure  set  up.    The  bending  moment  may  be  assumed 

at  support  and  center  of  span  to  be       where  I  is  the  span  in  feet,  and  w  is  the  load  per  foot 


„3'      Bl  ■i'LcmiM/ncr/ Aars) A 


Section  D-D    Section  "C-C" 
CHICAGO,  BURUNGTON,  &  QUINCY  R.R    MICHIGAN  CENTRAL  R.  R. 

Fig.  95. — Three  designs  of  reinforced-concrete  pipe  for  railway  culverts. 


which  the  pipe  is  obliged  to  carry.  Knowing  the  bending  moment,  and  the  dimensions  of  the 
pipe,  the  steel  requirements  and  unit  stresses  in  concrete  and  steel  maybe  taken  from  Diagram  2, 
Sect.  18,  page  816. 

Illustrative  Problem. — Inside  diameter  of  pipe  8  ft.,  thickness  of  shell  4  in.    Find  spacing  of  saddles  for 
longitudinal  shearing  stress  of  35  lb.  per  sq.  ir.,  and  provide  proper  flexural  reinforcement. 
Weight  of  pipe  =  8.3  X  ir  X  H  X  150  =     650  lb.  per  ft. 
Weight  of  water  =  16  X  ir  X  62.5  3140  lb.  per  ft. 

Total,    3790  lb.  per  ft. 

V 

From  Art.  15,  Sect.  18,  page  818,^=  3.15t'. 

22,050 

Allowable  F  =  50  X  4  X  3.15  X  35  =  22,050  lb.  Clear  spacing  of  saddles  =  g^^^  =  5.82  ft.,  say  6.8  ft.  on 
centers. 

M  175,350 

Bending  moment  =  M2 (3790)  (6.8)2(12)  =  175,300 in.-lb.  =  (2500)  (4)  ^  ^^^^'■""g      Diagram  2, 

page  816,  it  is  seen  that  at  this  extremely  low  value,  the  steel  and  concrete  unit  stresses  are  very  low  if  a  small  amount 
of  longitudinal  steel  is  in  place.    Use  0.4  %  for  temperature  and  flexure. 


Sec.  17-39] 


HYDRAULIC  STRUCTURES 


803 


39.  Examples  of  Reinforced-concrete  Pipe. — Figs.  95  and  96  show  several  types  of  rein- 
forced pre-cast  pipes.  Most  of  the  pipe  lines  laid  are  of  pre-cast  units.  For  culverts  and  sewers 
the  pipe  may  be  oval  or  circular.  For  water  under  pressure  the  pipe  should  be  circular,  and 
the  joints  carefully  made.  Two  types  of  joints  are  common,  bell  and  spigot,  and  sleeve  joints, 
both  of  which  are  shown  in  the  figure. 


■d'-s'- 

6-0'  ■ 


f.  'k      o'.''!"  6:'«  i; 


i<-  --32,  f'^Rods,  4"c.foc.  >l 

Longitudinal  section  Won  vertical  axis 


Longitudinal  section "C"  on  ^  point's  A 
Fig.  96. — Reinforced-concrete  culvert  pipe,  Chicago  &  Northwestern  Ry. 

40.  Forms  for  Sewers. — Because  of  desirability  to  repeat  the  use  of  form  material,  an 
arrangement  of  collapsible  form  units  is  best.  Steel  forms  are  advantageous  for  this  reason, 
especially  for  heavy  work. 

Usually  the  sewer  or  conduit  is  cast  in  stages,  the  invert  being  poured  first,  and  if  bricked, 
the  pavement  next  laid.  The  arch  centering  and  the  steel  for  the  arch  are  then  placed.  The 
wall  sections  are  next  set  and  the  arch  poured  and  finished.  The  joint  with  the  floor  should 
be  well  tied  with  dowel  rods.    The  centering  should  be  arranged  so  that  it  may  be  easily 


"struck,"  or  loosened  for  removal.  Fig.  97  shows  a  simple  arrangement  for  circular  sections. 
The  same  general  principle  is  also  used  for  arch  forms  both  in  wood  and  steel. 

The  backfill  should  cover  the  sewer  before  the  centering,  or  core,  is  struck.  General 
practice  {Eng.  Rec,  vol.  58,  p.  664)  indicates  that  under  favorable  circumstances  forms  may  be 
struck  in  36  to  48  hr.  for  sewers  smaller  than  10  ft.,  and  72  hr.  for  larger  sewers.  Temperature 
and  humidity  will  greatly  affect  the  setting  of  concrete,  and  should  be  considered  as  modifying 
the  above  rule. 


I 


SECTION  18 


MISCELLANEOUS  STRUCTURES 

DEEP  GRAIN  BINS  OR  SILOS 

Deep  bins  will  be  considered  of  such  proportions  that  the  plane  of  rupture  drawn  from  the 
bottom  of  one  side  will  not  pass  out  at  the  free  surface  of  the  material  retained.  Analysis, 
therefore,  cannot  be  made  according  to  the  theories  of  retaining  walls. 

1.  Action  of  Grain  in  Deep  Bins. — A  study  of  the  action  of  grain  in  a  deep  bin  shows  that 
the  grain  forms  a  dome  from  one  side  to  the  other,  which  is  supported  at  its  perimeter  by  the 
friction  between  the  grain  and  the  side  of  the  bin.  This  dome  supports  a  portion  of  the  grain 
above  it,  the  remainder  being  carried  by  further  dome  action  to  the  sides.  Compression  thus 
exists  upon  the  horizontal  sections  of  the  wall,  which  varies  in  some  ndanner  with  the  grain 
and  the  depth.  The  lateral  radial  pressure  of  the  grain  likewise  varies  in  some  manner  with 
the  depth  and  the  grain. 

2.  Janssen's  Formulas  for  Pressure  in  Deep  Bins.^ — 

<t>  =  angle  of  repose  of  the  filling. 
(j>'  =  angle  of  friction  of  the  filling  on  the  bin  walls. 
u  =  tan  (f)  =  coefficient  of  friction  of  filling  on  filling. 
u'  =  tan  0'  =  coefficient  of  friction  of  filling  on  the  bin  walls. 
w  =  weight  of  filling  in  pounds  per  cubic  foot. 
V  =  vertical  pressure  of  the  filling  in  pounds  per  square  foot. 
L  =  lateral  pressure  of  the  filling  in  pounds  per  square  foot. 
L  =  kV  OT 

K    -  y 

A  =  area  of  bin  in  square  feet, 
U  =  circumference  of  bin  in  feet. 

R  =  Yj  =  hydraulic  radius  of  bin. 

h  =  depth  of  granular  material  at  any  point. 
Then 

V  =  ^^j^l  ~      ^  number  whose  common  log  is  ^  gQ^^g^  J 
L  =  kV 

Values  of  u'  and  k  for  different  grains  and  bin  materials  are  given  in  Tables  1  and  2. 

Illustrative  Problem. — Given  wheat  weighing  50  lb.  per  cu.  ft.;  u'  =  0.444;  k  =  0.5;  depth  of  material 
50  ft.;  diameter  of  bin  12  ft.    Required  vertical  and  horizontal  pressures  at  base. 

^       A  36 

^  =  c7  =  r2  =  3 

ku'h    _  (0.5)  (0.444)  (50)  ^ 
2.303ie  (2.303)  (3) 

The  number  whose  common  logarithm  is  1.605  is  40.3  and  1      40.3  =  0.025 

L  =  kV  =  (0.5) (660)  =  330  lb.  per  sq.  ft. 
1  For  derivation  of  formulas  see  Ketchum's  "Structural  Engineers'  Handbook,"  1st  Ed.,  p.  319. 

805 


806 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  18-2 


Table   1.^ — Weights  and    Coefficients    of  Friction  of  Various  Kinds  of  Grains 

ON  Bin  Walls  (Airy) 


Weight  of 

a  cubic 
foot  loosely 
filled  into 
measure 
(pounds) 

Coefl&cients  of  friction 

Grain  on 
grain  u 
(tan  <p) 

Grain  on 

rough 
board  u' 
(tan  <f>') 

Grain  on 
smooth 
board  u' 
(tan  <(>') 

Grain  on 
iron  u' 
(tan  4>') 

Grain  on 
cement  u' 
(tan  <l>') 

Wheat .  .  . 

49 

0.466 

0.412 

0.361 

0.414 

0.444 

Barley .  .  . 

39 

0.507 

0.424 

0.325 

0.376 

0.452 

Oats  

28 

0.532 

0.450 

0.369 

0.412 

0.466 

Corn  

44 

0.521 

0.344 

0.308 

0.374 

0.423 

Beans. .  .  . 

46 

0.616 

0.435 

0.322 

0.366 

0.442 

Peas  

50 

0.472 

0.287 

0.268 

0.263 

0.296 

Tares.  .  .  . 

49 

0.554 

0.424 

0.359 

0.364 

0.394 

Flaxseed. 

41 

0.456 

0.407 

0.308 

0.339 

0.414 

Table  2.^ — Values  of     =  ^  for  Wheat  and  Other  Grains  in  Different  Bins  (Pleisner) 


Bins 

k  =  L/V 

Wheat 

Rye 

Rape 

Flax-seed 

Cribbed  bin  

Ringed  cribbed  bin  

Small  plank  bin  

Large  plank  bin  

Reinforced-concrete  bin.  

0 . 4  to  0 . 5 
0.4to0.5 
0 . 34  to  0 . 46 
0.3 
0.3  to  0.35 

0.23  to  0.32 
0  .3  to  0  .34 
0.3  to  0 . 45 
0.23  to  0.28 
0.3 

0  . 5  to  0  .  6 

0 . 5  to  0 . 6 

The  formula  for  L  has  been  used  in  plotting  Diagram  1,  for  wheat  retained  in  a  reinforced- 
concrete  bin.    The  above  problem  could  have  been  solved  directly  from  this  diagram. 

3.  Conclusions  from  Tests. — Prof.  Ketchum  has  drawn  the  following  valuable  conclu- 
sions ^  from  tests*  made  by  him  and  other  experimenters  upon  model  and  full-sized  grain 
bins: 

1.  The  pressure  of  grain  on  bin  walls  and  bottoms  follows  a  law  (which  for  convenience 
will  be  called  the  law  of  ''semi-fluids"),  which  is  entirely  different  from  the  law  of  the  pressure 
of  fluids. 

2.  The  lateral  pressure  of  grain  on  bin  walls  is  less  than  the  vertical  pressure  (0.3  to  0.6 
of  the  vertical  pressure,  depending  on  the  grain,  etc.),  and  increases  very  little  after  a  depth 
of  2}'i  to  3  times  the  width  or  diameter  of  the  bin  is  reached. 


1  From  Ketchum's  "Walls,  Bins  and  Grain  Elevators,"  p.  327. 

2  From  Ketchum's  "Structural  Engineers'  Handbook,"  p.  321. 

3  Ketchum's  "Structural  Engineers'  Handbook,"  p.  325. 

*  Ketchum's  "Walls,  Bins  and  Grain  Elevators,"  Chap.  XVII. 


Sec.  18-3] 


MISCELLANEOUS  STRUCTURES 


807 


3.  The  ratio  of  lateral  to  vertical  pressures  k  is  not  a  constant,  but  varies  with  different 
grains  and  bins.    The  value  of  k  can  only  be  determined  by  experiment. 

4.  The  pressure  of  moving  grain  is  verj^  slightly  greater  than  the  pressure  of  grain  at  rest 
(maximum  variation  for  ordinary  conditions  is,  probably,  10%). 

5.  Discharge  gates  in  bins  should  be  located  at  or  near  the  center  of  the  bin. 

6.  If  the  discharge  gates  are  located  in  the  sides  of  the  bins,  the  lateral  pressure  due 
to  moving  grain  is  decreased  near  the  discharge  gate  and  is  materially  increased  on  the  side  op- 
posite the  gate  (for  common  conditions  this  increased  pressure  may  be  2  to  4  times  the 
lateral  pressure  of  grain  at  rest). 

7.  Tie  rods  decrease  the  flow  but  do  not  materially  affect  the  pressure. 

Diagram  1 


Lat-eral  pressure  In  lb.  per  f t. 

8.  The  maximum  lateral  pressures  occur  immediately  after  filling,  and  are  slightly  greater 
in  a  bin  filled  rapidly  than  in  a  bin  filled  slowly.  Maximum  lateral  pressures  occur  in  deep  bins 
during  filling. 

9.  The  calculated  pressures  by  either  Janssen's  or  Airy's  formulas  agree  very  closely  with 
actual  pressures. 

10.  The  unit  pressures  determined  on  small  surfaces  agree  very  closely  with  unit  pressures 
on  large  surfaces. 

11.  Grain  bins  designed  by  the  fluid  theory  are  in  many  cases  unsafe  as  no  provision  is 
made  for  the  side  walls  to  carry  the  weight  of  the  grain,  and  the  walls  are  crippled. 

12.  Calculation  of  the  strength  of  wooden  bins  that  have  been  in  successful  operation  shows 
that  the  fluid  theory  is  untenable,  while  steel  bins  designed  according  to  the  fluid  theory  have 
failed  by  crippling  the  side  plates. 


808 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  18-4 


Experiments  by  Willis  Whitedi  and  by  Prof.  Ketchum  with  wheat  "have  shown  that  the 
flow  from  an  orifice  is  independei  t  of  the  head  and  varies  as  the  cube  of  the  diameter  of  the 
orifice." 

4.  Design  of  Walls. 

4a.  Vertical  Load  Carried  by  Walls. — Prof.  Ketchum^  has  shown  that  the 
vertical  load  of  grain  carried  by  1  ft.  of  circumference  of  the  wall  at  a  depth  y  will  be  very 
approximately 

Pu'  =  wR  (approx.) 

where  P  is  the  total  side  pressure  on  a  vertical  strip  y  high  and  1  ft.  wide.  The  unit  stress 
thus  obtained  must  be  added  to  that  caused  by  the  dead  load  of  the  structure. 

46.  Wind  Stresses  on  a  Horizontal  Section. — The  wind  stresses  in  a  deep  bin  are 
very  small  as  a  rule,  and  it  is  common  practice  to  permit  the  concrete  to  take  tension  on  the 
windward  side  up  to  about  200  lb.  per  sq.  in.,  assuming  the  tensile  stress  to  be  low,  the  unit 
stress  in  the  concrete  in  tension  and  compression  will  be 

21 

Assuming  a  wind  pressure  of  30  lb.  per  sq.  ft.  of  vertical  projected  area  on  a  height  of  h  ft.  of 
the  bin, 

h  +  nh 

in  which  D  =  outside  diameter  or  greatest  dimension  in  feet,  and  Ic  and  7s  the  moments  of 
inertia  of  the  concrete  and  steel  sections,  respectively,  about  a  diameter,  expressed  in  inches*. 
The  steel  unit  stress  is  nfc  approximately.  For  a  round  bin  of  one  cell,  isolated,  use  two-thirds 
of  the  stress  thus  obtained. 

If  the  tensile  unit  stress  in  the  concrete  exceeds  200  lb.  per  sq.  in.,  the  section  should  be 
analyzed  as  for  a  chimney  of  similar  dimensions. 

4c.  Thickness  of  Walls. — The  stresses  obtained  from  vertical  and  wind  loads 
are  combined  to  obtain  the  maximum  unit  stress  in  the  concrete.  Common  practice  uses  the 
same  working  stresses  in  this  structure  as  in  buildings.  The  thickness  of  wall  is  then  pro- 
portioned to  provide  for  these  unit  stresses.  The  same  thickness  of  wall  is  usually  maintained 
for  the  full  height  to  permit  the  use  of  moving  forms. 

4(i.  Horizontal  Reinforcement. — Circular  Sections. — The  lateral  pressure  tends 
to  burst  the  circular  bin  along  some  vertical  plane.  Reinforcement  against  this  is  provided  in 
the  same  manner  as  that  for  circular  tanks.  The  area  of  steel  As  per  foot  of  height,  due  to  the 
lateral  pressure  of  P  lb.  per  sq.  ft.,  is 

Prs 


 ^ 

^--^g  Mr 


f. 

where  rs  is  the  radius  in  feet  of  the  steel  hooping.  The  amount  of 
steel  would  be  proportional  to  the  abscissas  to  the  pressure  curve 
(see  Diagram  1,  page  807). 

4e.  Rectangular  Sections. — There  is  a  tendency  for 
^       p  ^  fl^^  sides  of  the  polygonal  bin  to  bulge,  and  the  angle  made  by 

two  adjacent  forces  to  open  out  (see  Fig.  1).  The  moments, 
determined  by  the  method  of  slope  deflections  (see  Sect.  10)  may  be  written  readily  in  the 
following  forms: 

Moment  at  any  corner  =  Ma  =  —  — (TX-W^) — " 

1  Proc.  Eng.  Soc.  of  West.  Penn.,  April,  1901. 

2  Structural  Engineers'  Handbook,"  p.  324, 


Sec.  18-4/] 


MISCELLANEOUS  STRUCTURES 


809 


V2[     l+b  J 

Ma  =         -bi  +  n 

Ma  j2 

M.  =^  -  Ma 

Md    =  ^  Ma 

in  which  Ma  is  chosen  from  the  proper  case  above.    For  square  cells, 

The  moments  given  above  must  be  provided  for  by  horizontal  bars  running  across  the 
inside  of  the  corner  and  crossing  to  the  outer  face  at  the  point  of  inflection.  When  the  bins 
are  grouped,  the  moments  may  be  caused  from  pressure  on  either  side  of  an  intermediate  wall. 

Sufficient  reinforcement  should  be  provided  in  the  walls  ac  and  bd  to  take  the  pull  of  the 
wall  ab  or  cd  caused  by  the  pressure  p2.    The  tension  in  ac  or  bd  is  '^V'^h  and  in  ab  or  cd  is 

The  pressure  pi  and  p2  may  be  found  from  the  foregoing  formulas  and  Diagram  1,  page  807, 
since  the  pressure  on  the  side  of  a  rectangular  bin  may  be  computed  by  computing  the  pressure 

for  a  circular  or  square  bin  having  the  same  hydraulic  radius,  R  =  jj- 

4/.  Hexagonal  Bins. — In  groups  of  circular  bins  the  interspaces  are  irregular 
in  shape  and  do  not  hold  as  much  as  do  the  main  cells.  The  hexagonal  bin  removes  this 
difficulty.    Moments  at  corners  and  sides : 

M corner    =    "  K2?>&^ 
Mside       =  y24.Vb^ 

in  which  b  is  the  length  of  any  side. 

5.  Construction. — The  foundation  for  a  group  of  deep  bins  is  usually  a  mat,  unless  the 
foundation  is  unyielding.  Pressures  on  the  soil  should  be  examined  when  half  of  the  group  is 
loaded,  and  wind  is  acting. 

Round  cells  are  commonly  placed  in  such  a  manner  that  at  the  points  of  tangency  the  wall 
is  of  one  thickness,  so  that  the  ring  reinforcement  from  one  cell  laps  over  that  of  the  adjacent 
one.  This,  with  the  vertical  steel  passing  through  the  link  thus  made,  provides  bonding  between 
cells. 

Polygonal  bins  are  arranged  with  walls  in  common,  reinforced  to  take  the  pressure  from 
either  side.  The  steel  may  well  be  arranged  as  for  a  continuous  slab,  the  two  systems  crossing 
each  other  at  right  angles  at  the  corners. 

Construction  is  usually  continuous,  the  forms  being  jacked  up  on  the  vertical  reinforce- 
ment, or  on  vertical  rods  for  the  purpose,  imbedded  in  the  walls.  Metal  forms  are  commonly 
used,  since  a  smooth  surface  may  be  obtained.  It  is  customary,  when  using  moving  forms,  to 
make  the  walls  the  same  thickness  from  top  to  bottom. 

The  concrete  bins  of  the  Great  Northern  Ry.'s  grain  elevator  at  West  Superior,  Wis.,^ 

1  Eng.  News,  Aug.  4,  1910. 


When  Ii  =  h 
When  pi  =  p2 

For  square  cells,  b  =  I  and  pi  = 
At  the  center  of  the  sides. 


810 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  18-5 


is  shown  in  Fig.  2.  The  walls  are  of  1  :  2  :  4  concrete.  The  stresses  used  in  the  design  were: 
steel  in  tension,  16,000;  concrete  in  compression,  600;  bond,  100  lb.  persq.  in.;7i  =  12.  The 
bins  are  110  ft.  high.    The  capacity  of  the  72  cells  with  interspaces  is  about  2,400,000  bu. 

Fig.  3  is  a  typical  section  of  rectangular  bins  in  the  elevator  of  the  F.  C.  Ayres  Mercantile 
Co.,  Denver,  Colo.  A  detailed  description  will  be  found  in  Ketchum's  "Walls,  Bins  and  Grain 
Elevators,"  2d  Ed.,  page  454. 


[<—  to'-a'-  ■>{<■-   ^o'-3'■  - — >{<•  -  ^(^'-3'-  

Fia.  2. — Concrete  bins  of  Great  Northern  Ry's  grain  elevator,  West  Superior,  Wis. 


Fig.  3. — Rectangular  bins  in  elevator  of  F.  C.  Ayres  Mercantile  Co.,  Denver,  Colo. 


SHALLOW  BINS 

If  the  plane  of  rupture,  commencing  from  the  bottom  of  one  side  of  a  bin,  strikes  the  free 
surface  of  the  retained  material,  the  bin  is  said  to  be  shallow.  Such  bins  are  commonly  used  for 
the  storage  of  coal,  coke,  sand,  ashes,  etc.  Pressures  against  the  various  sides  are  determined 
by  the  methods  commonly  employed  to  determine  earth  pressures  against  walls.  Two  condi- 
tions of  loading  will  be  given  here :  (1)  level-full  and  (2)  heaped  bins.  Bins  with  full  sloped  sides 
and  with  partially  vertical  sides  will  be  analyzed. 


Sec.  18-6] 


MISCELLANEOUS  STRUCTURES 


811 


6.  Sloped  Sides— Level  Full  (Case  I). — Let  ABC,  Fig.  4,  represent  a  bin  with  sloped  sides. 
On  a  vertical  plane  through  B  the  pressure  may  at  once  be  determined  as  for  a  vertical  retaining 
wall  holding  the  prism  BDC  (see  Rebhann's  construction,  Art.  16,  Sect.  13).  The  triangle  of 
pressure  aBD  indicates  the  total  pressure  acting  on  the  plane  BD,  the  resultant  being  Pi, 
acting  liBD  above  B.  Let  Pi  be  produced  to  meet  the  weight 
W  of  the  prism  ABD  applied  at  the  center  of  gravity  O  of  the 
triangle  ABD.  The  resultant  thus  obtained  is  P2.  This  may 
be  resolved  into  the  forces  P3  and  P4.  P3  is  then  the  resultant 
normal  pressure  acting  on  AB.  If  the  plane  AB  were  smooth, 
P4  would  represent  a  component  acting  against  DB;  but  since 
the  plane  AB  is  rough,  P4  becomes  a  thrust  down  the  plane 
against  B,  if  the  angle  between  the  forces  P3  and  P4  is  equal 
to,  or  less  than,  the  angle  of  friction  between  the  plane  and 
the  material. 

Since  P3  is  the  resultant  pressure  on  AB,  it  passes  through  the  centroid  of  the  pressure  tri- 
angle AbB,  and  its  magnitude  is  equal  to  the  area  AbB.  The  unit  pressure  bB  may  thus  readily 
be  determined. 

7.  Partly  Vertical  Sides — Level  Full  (Case  II). — So  far  as  concerns  the  pressure  on  the  side 

AB  (Fig.  5),  it  will  be  seen  to  carry  the  same  load  as  a 
similar  portion  of  the  sloping  side  AB,  Fig.  4. 

Locate  the  point  A'.    As  before,  determine  Pi  and  W 
(the  latter  applied  at  0,  the  center  of  gravity  of  A'BD), 
and  find  their  resultant  P2.    P3  is  the  component  of  P2 
normal  to  A'B,   and  represents  the  resultant  of  normal 
pressure  for  the  plane  A'B.    Its  magnitude  is  equal  to  the 
area  of  BA'b.    The  unit  pressures  Bb  and  Ac  may  thus  be 
found,  defining  the  trapezoid  AcbB,  which  represents  the 
total  pressure  acting  on,  and  normal  to,  AB. 
The  pressure  on  the  vertical  side  HA  is  represented  by  the  pressure  triangle  HAd,  which  is 
equal  to  the  corresponding  portion  of  the  triangle  BDa,  and  is  therefore  the  pressure  against  a 
vertical  retaining  wall  of  the  height  HA,  and  supporting  the  same  material. 

8.  Sloped  Sides — Fill  Heaped  to  Angle  of  Repose  (Case  III). — No  method  has  been  given  in 
the  discussion  of  retaining  walls  for 
finding  the  thrust  with  a  negative 
surcharge.     The  following  is  an 
application  of  Rebhann's  method. 

The  pressures  on  a  vertical 
plane  through  B,  as  BD  (Fig.  6a), 
should  balance  either  side.  As- 
sume that  the  thrust  on  BD  acts 
horizontally.  Lay  off  BC  making 
the  angle  <f>  (angle  of  internal 
friction)  with  the  horizontal  BT, 
and  extending  to  DCC.  Draw 
DD'  making  the  angle  </>  with  BD 

(hence  normal  to  BC).  With  D'C  as  the  diameter  draw  arc  D'MC,  and  to  it  draw  the 
tangent  BM  from  B.  Make  BN  =  BM,  and  draw  NQ  parallel  to  DD'.  Make  RN  =  QN. 
The  area  of  the  triangle  RQN  times  the  weight  per  cubic  foot  of  the  material  in  the  fill  equals 
the  thrust  Pi  (Fig.  66)  against  BD. 

Let  Pi  be  extended  to  meet  W\  the  weight  of  the  prism  ABD.  Their  resultant  is  P2,  whose 
component  normal  to  AB  is  P3.  The  true  position  of  P3  should  be  }iAB  from  B.  Its  magni- 
tude equals  the  area  of  the  triangle  ABa]  and  knowing  the  length  AB,  the  unit  pressure  Ba 
may  be  found. 


812 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  18-9 


9.  Partly  Vertical  Sides — Fill  Heaped  (Case  IV) . — As  in  Case  III,  the  pressure  Pi  against 
BD  is  found,  as  in  Fig.  6a.  Pi  is  then  combined  with  W,  the  weight  of  a  prism  A'DB,  to  form 
P2  (Fig.  7).  The  component  normal  to  A'B  is  P3,  and  represents  the  area  of  the  pressure 
triangle  A'Ba.  Knowing  this  area,  and  the  length  A'B,  the  unit  pressures  Ba  and  Ac  may  be 
determined.    The  total  pressure  on  -45  is  given  by  the  trapezoid  AcBa. 


Fig.  7.  Fig.  8. 


In  some  bins  a  flat  portion  is  put  into  the  bottom  as  in  Fig.  8.  In  this  case  the  vertical 
plane  may  be  extended  to  meet  the  extended  plane  A' ABB'  at  B'.  The  pressure  Pi  on  DB' 
is  then  found  as  in  Case  III,  and  combined  with  W,  whence  the  normal  pressure  P3  is  found. 
This  is  the  total  normal  pressure  that  would  act  on  the  plane  A'B',  and  hence  represents  in 
magnitude  the  area  A'B'b'.  The  unit  pressure  B'b'  could  be  found,  and  likewise  Ac  and  Ba. 
The  actual  normal  pressure  on  A 5  is  shown  by  the  trapezoid  AcBa. 

10.  Thrust  due  to  P4. — The  thrust  P4  or  the  portion  of  P4  actually  acting  on  plane  AB, 
should  be  provided  for  in  the  design  of  the  slab  AB  and  the  supports  at  A  and  B.  In  Figs.  4 
and  66  the  thrust  acting  at  B  is  equal  to  P4.  In  Fig.  7  the  thrust  at  B  is  equal  to  P4  times  the 
ratio  oi  AB  to  A'B;  and  similarly  in  Fig.  8  the  thrust  at  B  is  equal  to  P4  times  the  ratio  oi  AB 
to  A'B'. 

If  the  span  of  the  slab  AB  is  in  the  direction  AB,  the  stresses  in  it  should  be  determined  by 
methods  of  combined  flexure  and  direct  stress.  If  the  span  is  normal  to  the  drawing,  however, 
simple  bending  takes  place. 

11.  Data  for  Bin  Design. — Table  1  gives  the  weights  and  angle  of  repose  of  several  materials 
commonly  stored  in  shallow  bins.    For  data  on  sand,  earth,  rock,  etc.,  see  table  on  page  575. 


Table  1.^ — Weight  and  Angle  of  Repose  of  Coal,  Coke,  Ashes  and  Ore 


Material 

Weight  (lb. 
per  cu.  ft.) 

Angle  of  re- 
pose <i>  (degree) 

Authority 

50 

35 

Link  Belt  Machinery  Co. 

Bituminous  coal  

47 

35 

Link  Belt  Engineering  Co. 

Bituminous  coal  

47  to  56 

Cambria  Steel 

52 

27 

Link  Belt  Machinery  Co. 

52.1 

27 

Link  Belt  Engineering  Co. 

Anthracite  coal  fine  

27 

K.  A.  Muellenhoff 

52  to  56 

Cambria  Steel 

45 

Wellman-Seaver-Morgan  Co. 

Slaked  coal  

53 

37>^ 

Gilbert  and  Barth 

Coke  

23  to  32 

Cambria  Steel 

Ashes  

40 

40 

Link  Belt  Machinery  Co. 

Ashes,  soft  coal  

40  to  45 

Cambria  Steel 

Ore,  soft  iron  

35 

Wellman-Seaver-Morgan  Co. 

1  From  Ketchum's  "Structural  Engineers'  Handbook,"  p.  311. 


Sec.  18-12]  MISCELLANEOUS  STRUCTURES  813 

Table  2  gives  some  approximate  friction  angles  for  various  materials  against  different 
bin  linings. 

Table  2.^ — Angles  of  Friction  of  Different  Materials  on  Bin  Walls 


Steel  plate  </>' 

Wood  cribbed 

Concrete  0' 

Material 

in  degrees 

<j>'  in  degrees 

in  degrees 

Bituminous  coal 

18 

35 

35 

Anthracite  coal 

16 

25 

27 

31 

40 

40 

Coke  

25 

40 

40 

Sand  

18 

30 

30 

Fig.  9. — Plan  and  section  of  Duquesne  Light  Co.'s  coal-storage  pit  at  Pittsburgh, 


12.  Submerged  Storage  for  Coal. — Coal  stored  in  large  quantities  is  commonly  stored  in 
water,  to  prevent  combustion.  Bins  or  pits  filled  with  water  and  coal  should  be  designed  to 
resist  the  water  pressure,  as  though  full  of  water.  Pits  are  then  designed  like  open  reservoirs, 
except  that  the  pavement  for  the  pit  must  be  heavier  than  that  for  the  reservoir,  to  withstand 
the  dumping  of  the  coal  from  the  trestle  overhead  (see  Fig.  9). 

Ashes  are  frequently  stored  in  pits  of  this  nature,  and  very  often  water  is  run  in  (see  Fig. 

10). 

When  clam-shells  or  other  forms  of  grab  bucket  are  used  to  handle  the  material  in  the  pits, 
rails  are  commonly  embedded  in  the  pavement  about  3  ft.  apart,  with  the  heads  protruding 
about  }^  in.  above  the  concrete,  to  protect  it  from  the  jaws  of  the  bucket.  This  detail  may  be 
noted  in  Fig.  10. 

1  From  Kbtchum's  "Structural  Engineers'  Handbook,"  p.  312. 


814 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  18-12 


i  of  track  ,  (~>  -Valve  box 


 tofpt 


-Cross 
gi'-der 


t  of  track 


 --H 

Cross  section  of  pit 


Section  thru  end  wall 


Fig.  10. 


Fig, 


Sec.  18-13] 


MISCELLANEOUS  STRUCTURES 


815 


13.  Dock  Pockets. — Storage  pockets  in  docks  for  ore,  and  coal,  etc.,  are  usually  unsymniet- 
rical.  The  commonest  form  is  that  in  Fig.  11.  The  pressure  upon  the  face  AB  may  be  found 
as  for  the  vertical  plane  DB,  Fig.  5.  Thus  P  is  the  resultant  of  the  pressures  on  AB,  represented 
by  triangle  ABb,  and  equals  the  area  of  triangle  QNR  times  the  weight  per  cubic  foot  of  the 
material  retained. 


Fig.  12. — Details  of  superstructure  of  Minneapolis,  St.  Paul  &  Sault  Ste.  Marie  R.  R.  dock, 


The  ore  dock  of  the  Minneapolis,  St.  Paul  &  Sault  Ste.  Marie  R.  R.  at  Ashland,  Wis.,i  is 
shown  in  Fig.  12.  The  front  of  the  pockets  are  circular  in  plan,  causing  the  wall  stresses  due  to 
the  thrust  of  the  ore  to  be  tensile.  This  feature  is  patented  by  Max  Toltz,  who  was  the  designer 
of  the  dock.  The  concrete  in  the  substructure  was  1:3:5  while  that  in  the  superstructure  was 
1:2:4  mix.    The  horizontal  thrust  on  the  bin  walls  at  a  depth  h  was  computed  from  p  =  30/i, 

»  Eng.  News,  vol.  76,  Aug.  10,  1916,  p.  243. 


816 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  18-14 


CHIMNEYS 

The  analysis  of  stresses  in  reinforced-concrete  chimneys  involves  stresses  due  to  (1)  dead 
load,  (2)  wind,  and  (3)  temperature. 

14.  Dead-load  Stresses. — The  dead-load  stress  in  the  concrete  may  be  written 


Up 


and 

in  which  h  is  the  height  of  chimney  in  feet  above  the  section,  and  //  is  the  steel  unit  stress  in 
compression.    For  prehminary  estimate /c  =  1.04/i  (approx.). 


0.5 


Diagram  2 

Percentage  of  longitudinal  steel 
1.0         1.5  20         25         3.0         35  4.0 


05 


1.0         1.5         ZO         2.5         3.0         3.5  4.0 
Percentage  of  longitudinal  steel 


16.  Stresses  on  Annular  Sections  in  Flexure. — The  following  notation  will  be  used  (see 
sketch,  Diagram  2): 

R  =  radius  of  center  of  chimney  wall  (inches)  =  also  radius  of  reinforcing  steel  (inches). 
t  =  thickness  of  wall  (inches). 

p  =  %  of  longitudinal  reinforcement,  based  on  cross-sectional  area  (  =  A,  Ac). 
kR  =  perpendicular  distance  from  center  of  chimney  to  neutral  axis  (inches). 


Sec.  18-15]  MISCELLANEOUS  STRUCTURES  817 

The  moment  of  the  tension  area  of  steel  (arc  NT  A)  about  the  neutral  axis  is 

Sir  r-  h  ~\ 

2nptR''-  r  '2  (sin  d  -  k)d9  =  2nptRA  (1  -  /c^)^^  +  k  sin'^k  +^\  (1) 

Jtt  -  sin-•^•  L  ^  J 

The  moment  of  the  compression  area,  whose  transformed  stress  width  may  be  expressed  by 
[  1  +  (n  —  l)p]t,  about  the  neutral  axis  is  similarly 

TT  —  sin~'A; 

2RH[l  +  (n  -  l)p]J  z  (sin  d  -  k)dd  =  2Rh[1  +  {n  -  l)p]  \  {I  -  k^Y'^  + 

2  L 

A;sin-'A;-^J  (2) 

Since  these  two  moments  balance  about  the  neutral  axis,  they  may  be  equated,  from  whence 
is  derived  the  expression 

[(1  _  k2y,i  +  /csin-i/c  -  ^1 

P  =  p-  ^-  T  .  (3) 

(1  -  /c2)H  +  k  s'm-'k  -  ^  -  kirn] 

Equation  (3)  has  been  plotted  at  the  top  of  Diagram  2,  assuming  n  =  15. 
The  moment  of  inertia  of  the  transformed  section  may  be  written 

/TT  -  sin-'A:  Stt 
^  (sin  d  -  2A;sin0  +  k'')d6  +  2R^pnt  C  2  (sin^-d  -  2k 

2  J  IT  —  sin"'A; 

sin  d  +  k^)dd  =  RH  |  (1  -  p)  [^(1  +  2A;2)      -  sin-^A;)  -  3fc(l  -  k^Y^'A^  +  irpn{\  +  2k'')  |  (4) 

Let  Cs  =  distance  (inches)  from  the  neutral  axis  to  the  extreme  fiber  of  steel  in  tension 
(on  the  transformed  section). 
Cs'  =  distance  (inches)  from  the  neutral  axis  to  the  extreme  fiber  of  steel  in  compression 
(on  the  transformed  section), 
and        Ce  =  distance  (inches)  from  the  neutral  axis  to  the  extreme  fiber  of  concrete  in  com- 
pression. 

Then      Cs  =  Rn(l  +  k);       c/  =  Rn(l  -  /c);       Cc  =  R{1  -  k)  (5) 

If  M  is  the  bending  moment  in  inch-pounds  on  any  given  cross-section  due  to  external  loads,  then 
from  mechanics, 

f,=Ml'  f-^Mf  =  (6) 

in  which  /«'  =  fiber  stress  of  steel  in  compression,  and  fs  and  fc  the  same  as  in  beam  analysis. 
By  substituting  equations  (4)  and  (5)  into  equation  (6)  the  curves  of  Diagram  1  were  plotted, 
assuming  n  =  15.  This  diagram  does  not  include  the  stresses  due  to  dead  load,  but  gives  only 
those  stresses  due  to  bending. 

It  may  be  noted  that  jc  relates  to  the  compression  in  the  concrete  at  the  center  of  the  chim- 
ney wall,  and  not  at  the  outer  face  (see  sketch.  Diagram  2).  The  maximum  compression  in 
the  concrete  may  be  given  by 


/c(max) 


The  fractional  term  in  the  brackets  is  the  increase  over/c  to  obtain /c  (max).    The  %  increase 
in  concrete  compression  stress  over/c  to  obtain /c  (max)  is  plotted  on  Diagram  2(a)  for  various 
values  of  t/R.    The  application  of  these  curves  relates  to  the  stress  due  to  flexure  only. 
52 


818  CONCRETE  ENGINEERS'  HANDBOOK  [Sec.  18-16 

Longitudinal  Shear  at  Neutral  Axis. — The  intensity  of  longitudinal  shearing  stress  at  the 
neutral  axis  may  be  given  by 

^  =  ^  (8) 

for  an  annular  section,  in  which  V  is  the  total  transverse  shear  on  the  section  and  Mr  equals 
the  sum  of  the  moments  of  the  tension  and  compression  areas  as  given  in  equations  (1)  and  (2). 
Substituting  into  equation  (8)  there  results 


Rt 


2  I  (1  -  p)[^(l  +  2fc2)      -  -  Ska  -  k^y^j  +7rpn(l  +2/c2) 

(1  -  -  k^y^  +  k  sm-%  -         +  '^Ma  -  k^y^  +  k  sin'^  k] 


When  n  =  15  the  term  in  the  brackets  becomes  3.15  for  the  usual  ranges  of  k,  whence 

^  =  3.15Z;  (9) 

From  this  equation  the  longitudinal  shearing  stress  v  may  be  computed. 

16.  Wind  Stresses  in  Chimneys  of  Reinforced  Concrete. — The  action  of  wind  pressure 
alone  upon  a  chimney  is  similar  to  the  action  of  a  distributed  load  on  a  cantilever  beam  of 
annular  section.  The  force  of  the  wind  is  usually  assumed,  for  a  cylindrical  surface,  to  be 
two-thirds  that  on  a  plane  surface.  Thus,  at  30  lb.  per  sq.  ft.,  the  pressure  per  foot  of  height  of 
chimney  would  be  20D,  or  40JS. 

The  stresses  caused  by  the  wind  may  be  determined  by  referring  to  Art.  15.  A  problem 
will  best  illustrate  the  procedure. 

Illustrative  Problem. — Required  %  of  vertical  steel,  and  thickness  of  shell  at  the  base  of  a  chimney  200  ft. 
high  and  8  ft.  mean  diameter,  such  that  the  steel  stress  for  wind  shall  not  exceed  12,000  lb.  per  sq.  in.,  and  the  con- 
crete stress  for  wind  shall  not  exceed  400  lb.  per  sq.  in. 

Moment  on  section  =  ilf  =  20  X  8  X  200  X  12  X  100  =  38,400,000  in.-lb. 
M 

=  1575  for  fs  =  12,000  and  fc  =  400  (from  Diagram  2) 

_  38.400,000 
*  ~  (4  X  12)2  X  1575  "  ^^-^ 

The  vertical  steel  required  is  3.65%.  Should  a  smaller  percentage  be  desirable,  the  steel  stress  would  govern. 
Thus  with  3%  vertical  steel,  M/R^t  =  1320  for  fs  =  12,000.  Then 

38,400,000 
^  =  (48)2  X  1320 

This  serves  to  illustrate  the  efifect  of  a  governing  stress  when  balanced  stresses  are  not  used.  In  the  last  instance 
fc  =  370  lb.  per  sq.  in. 

17.  Chimney  with  No  Vertical  Reinforcement. — Short  stacks,  and  the  upper  part  of  tall 
stacks,  may  not  have  sufficient  moment  due  to  wind  to  cause  tension  on  the  windward  side. 
Assuming  a  wind  pressure  of  20  lb.  per  sq.  ft.  on  a  vertical  projection,  and  noting  that  the 
boundary  of  the  kern  of  a  thin  hollow  circular  section  is  R/2  from  the  center, 

y  =  23.6  Rt  (ft.) 

in  which  y  is  the  height  of  chimney  in  feet,  above  the  section  on  which  the  resultant  cuts  the 
kernal  boundary,  and  R  and  t  are  the  mean  radius  and  thickness  of  shell,  respectively,  also  in 
feet.    The  compressive  unit  stress  in  the  concrete,  with  no  steel,  is 

W 

fc  =  2.08  ^ 


where  W  is  the  weight  above  the  section,  and  A  is  the  sectional  area  in  square  inches. 

The  presence  of  vertical  steel  will  affect  the  stresses,  hence  the  formulas  of  Art.  15  will 
be  found  useful  for  determining  the  flexural  stresses. 


Sec.  18-18] 


MISCELLANEOUS  STRUCTURES 


819 


It  should  be  noted  that  chimneys  without  vertical  steel  are  subject  to  severe  temperature 
stresses  if  used  under  conditions  where  inside  temperatures  are  those  of  flue  gases,  or  under 
conditions  which  give  a  temperature  drop  of  100°F.  or  more  through  the  shell. 

18.  Longitudinal  Shear  in  Chimneys. — Because  the  shell  of  concrete  chimneys  is  relatively 
thin,  the  unit  shear  on  a  longitudinal  section  requires  consideration.  Equation  (9),  Art.  15, 
gives  a  means  of  solution  of  the  longitudinal  shearing  stresses.  The  transverse  shear 
V  =  2yR  X  20  =  4:0yR,  in  which  y  is  the  height  of  chimney  above  the  section  considered 
and  R  is  in  feet.    From  equation  (9), 

y  =  0.079vt  X  12  =  O.MSvt. 
When  V  =  40,  the  following  table  will  give  the  relation  of  t  to  h: 


t 

4 

5 

6 

7 

8 

9 

10 

11 

12 

h 

151.2 

189.0 

226.8 

264.6 

302.4 

340.2 

378.0 

415.8 

453.6 

When  V  =  SO: 

t 

4 

5 

6 

7 

8 

9 

10 

11 

12 

h 

113.4 

141.8 

170.1 

198.5 

226.8 

255.2 

283.5 

311.9 

340.2 

The  above  heights  will  give  the  limits  for  the  given  shearing  unit  stresses  and  thicknesses,  on 
the  basis  of  a  wind  pressure  of  ^^(30)  lb.  per  sq.  ft.  of  projected  area. 

19.  Temperature  Stresses  in  Chimneys. — Flue  gases  have  a  temperature  sufficient  to 
commonly  give  the  chimney  shell  a  temperature  of  400°  to  500°F.  at  the  inner  face  near  the 
flue,  and  seldom  exceed  700°F.i  At  a  point  three-quarters  of  the  height  above  the  base  it  is 
found  that  the  temperatures  have  not  decreased  more  than  10  to  20%  of  the  flue-level  tem- 
peratures. 

The  fact  that  the  inner  face  of  the  shell  tends  to  expand  laterally  and  vertically  causes 
compression  in  the  concrete  and  tension  in  the  steel,  in  both  directions.  Assuming  a  constant 
modulus  of  elasticity  for  concrete  in  compression  for  the  above  temperature  range,  and  assuming 
also  a  straight-line  temperature  gradient  through  the  shell,  Turneaure  and  Maurer  have  built 
up  a  theory  for  the  estimation  of  these  temperature  stresses.  Applications  of  this  analysis 
yield  a  very  high  value  of  compression  in  the  concrete  vertically,  and  a  moderate  value  (average 
about  400  to  500  lb.  per  sq.  in.)  in  a  lateral  direction.  Appearance  of  large  cracks  in  a  lateral, 
as  well  as  vertical,  direction,  particularly  near  the  top  of  the  inner  lining  if  one  is  present,  bears 
out  the  fact  that  large  stresses  do  exist. 

Prevention  of  temperature  cracks  cannot  alone  be  made  by  heavier  reinforcement.  The 
custom  has  been  to  extend  a  clay  lining  (in  some  instances  though  perhaps  not  in  all  cases  war- 
ranted, a  fire-clay  lining)  from  the  flue-line  to  one-third  the  chimney  height,  having  an  air 
space  between  the  lining  and  the  outer  shell  of  2  to  6  in.  It  is  becoming  evident,  in  the  light 
of  past  experience,  that  the  lining  should  extend  at  least  two-thirds  the  height  of  the  chimney. 
It  is  essential,  also,  that  the  air  space  between  the  lining  and  shell  be  provided  with  vents  so 
that  a  good  circulation  may  be  obtained.    This  is  as  important  as  any  other  feature  of  design. 

Because  of  the  meagre  information  concerning  the  properties  of  concrete  under  high  tem- 
peratures, it  is  not  possible  to  build  up  a  close  theory  of  the  stresses  due  to  temperature.  The 

'  Report  on  reinforced-concrete  chimneys  to  Assoc.  Am.  Port.  Cem.  Mfrs.  by  Sanford  E.  Thompson  (1910). 


820 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  18-20 


discussion  of  Turneaure  and  Maurer^  will  offer  a  valuable  guide  to  the  estimation  of  the  impor- 
tance of  these  stresses,  in  the  light  of  temperature  data  at  present  available. 

20.  Chimney  Construction. — The  shell  is  usually  made  with  a  smooth  exterior  in  recently 
constructed  chimneys,  and  changes  in  thickness  to  obtain  lighter  sections  at  the  top  are  made 
by  stepping  the  inner  face.  The  forms  used  are  usually  steel  either  cylindrical  or  tapering, 
and  are  jacked  up  on  the  vertical  reinforcement  (see  construction  of  deep  grain  bins  or  silos, 
Art.  5.),  so  that  pouring  is  nearly  continuous.  Moderately  dry  1  :  3  concrete  is  generally  used, 
and  is  well  tamped.  The  mix  should  not  be  so  dry  that  upon  tamping,  moisture  is  not  brought 
to  the  surface  readily.  Care  should  be  taken  to  have  a  maximum  silica  (sand)  surface  on  the 
inside.    The  steel  used  may  well  be  deformed,  to  distribute  the  temperature  cracks. 


21.  Bases  for  Chimneys. — Chimneys  are  often  placed  on  yielding  soil,  using  a  large  base 
slab.  The  common  forms  of  bases  are  squares,  circles,  and  octagons.  Conditions  of  pressure 
under  these  slabs  maybe  grouped  in  two  cases:  (1)  resultant  within  the  kern,  (2)  resultant  out- 
side the  kern. 

Kern  sections  for  the  forms  of  bases  named  are  shown  hatched  in  Fig.  13. 
The  section  moduli,  S,  for  these  figures  are  given  below: 


Figure 

Square 

Circle 

Octagon 

S  about 
axis  X-X 

63  (about  X'-X' 
6~  0.11863) 

(approx.) 

0.6906/2^ 

When  the  resultant  pressure  lies  within  the  kern  of  the  base  figure,  the  soil  pressure  at 
the  edge  may  be  found  by 

W 


Fig.  14. 


Fig.  15. 


A  table  of  allowable  soil  pressures  is  given  in  Art.  1,  Sect.  12. 

The  design  of  the  base  slab  for  moment  and  shear  may  be  found  in  the  design  of  footings, 
Art.  7,  Sect.  12. 

1  "Principles  of  Reinforced  Concrete  Construction,"  2d  Ed.,  p.  413. 


Sec.  18-21] 


MISCELLANEOUS  STRUCTURES 


821 


Square  Bases. — When  tension  exists  between  the  foundation  and  the  windward  toe,  there 
is  what  might  be  considered  a  neutral  axis  and  only  part  of  the  foundation  is  under  pressure 
(see  Figs.  14  and  15).    The  following  formulas  result: 

For  direction  of  wind  parallel  to  a  side  of  the  square  (Fig.  14) 

X  =  Sxq  —  ~ 


pi 


0-4") 


w 

62 


Diagram  3 


0     J     2    .3     .4    .5    .6     ,7    .8    .9  1.0 
Values  cff  1< 


For  direction  of  wind  parallel  to  a  long  diameter  of  the  square  (Fig.  15) 

1 


Xo 

r 

Pi 


7  3  _L 


6  -  6A;  +  /c3 
2-  k  W 


2  —  k  W 
If  the  quantity  be  denoted  by  L,  then  pi  =  L -r-' 


Diagram  3  gives  values  of  k  and  L  for  various  values  of  — •    Dotted  lines  with  arrows  indicate 

r 


how  to  obtain  the  values  of  k  and  L  for  a  given  value  of 


Xo 


SECTION  19 


ESTIMATING 

By  Leslie  H.  Allen^ 
ESTIMATING  UNIT  COSTS 

1.  Division  of  the  Work. — Reinforced-concrete  work  may  be  considered  under  the  follow- 
ing four  main  divisions: 

1.  The  concrete  itself. 

2.  The  forms  or  falsework. 

3.  The  steel  reinforcement. 

4.  The  finish  of  the  exposed  surfaces. 

Each  of  these  divisions  should  be  considered  separately  when  making  an  estimate. 

In  the  prices  mentioned  in  this  chapter,  the  cost  of  labor  is  based  upon  the  rates  paid  in 
the  large  cities  at  the  present  time  (namely:  carpenters  65  cts.  per  hr.,  laborers  35  cts.  per  hr., 
carpenter  foremen  $7  per  day)  and  include  the  overhead  expense  of  superintendent  and  time- 
keepers in  charge  of  the  work. 

2.  Estimating  Unit  Cost  of  Concrete. — With  regard  to  the  concrete  itself,  we  shall  take 
into  account:  (a)  the  cement,  sand,  stone,  and  water;  (b)  the  labor  of  unloading,  mixing,  and 
placing  of  these  materials;  and  (c)  the  plant  necessary  to  accomplish  this  end. 

2a.  Materials. — The  cost  of  cement  in  carload  lots  is,  as  a  rule,  about  $1.50 
per  bbl.  at  the  cement  mill.  If  the  cement  is  delivered  in  paper  bags,  there  is  an  extra  charge 
of  10  cts.  per  bbl.  for  bags.  If  delivered  in  cloth,  the  extra  charge  is  40  cts.,  but  this  40  cts.  is 
refunded  by  the  mills  if  the  cloth  bags  are  returned  in  good  condition.  If  furnished  in  wooden 
barrels,  there  is  a  charge  of  40  cts.,  and  the  barrel  is  not  returnable.  It  is  usually  considered 
the  most  economical  to  buy  cement  in  cloth  bags  and  return  the  bags  when  empty.  The 
freight  on  a  barrel  of  cement  on  a  haul  of  say  500  miles  would  be  about  40  cts.,  so  that  the  total 
cost  of  a  barrel  of  cement  in  cloth  bags  after  returning  and  crediting  the  bags  would  be  $1.90 
per  bbl.  The  cost  of  testing  cement  is  from  3  to  5  cts.  per  bbl.  It  is  customary  among  con- 
tractors and  engineers  to  have  the  whole  shipment  of  cement  tested  at  a  testing  laboratory, 
and  from  $5  to  $6  per  carload  is  about  the  usual  charge.  The  cost  of  unloading  cement  and 
placing  it  in  a  storehouse  close  to  the  track  is  about  5  cts.  per  bbl.  If  the  railroad  tra  cks 
do  not  run  to  the  site  of  the  construction  work,  there  must  also  be  added  the  cost  of  teaming, 
which  would  amount  on  a  distance  of  1  mile  to  about  5  cts.  per  bbl.  In  addition  to  this  must 
be  figured  the  cost  of  handling  and  returning  empty  sacks,  the  freight  on  same,  and  the  loss 
of  a  few  damaged  or  torn  bags.  This  is  usually  estimated  at  about  3  cts.  per  bbl.  Tabulating 
the  above,  the  cost  of  cement  per  bbl.  ready  for  use  would  appear  as  follows: 


Cement  ,   $1.50 

Freight   0.40 

Cloth  sacks   0.40 

Total  cost  of  cement  f  .o.b.  cars  at  job   $2 . 30  per  bbl. 

Deduct  credit  for  empty  sacks   0 . 40 

$1.90 

Add  cost  of  testing   0.03 

Add  cost  of  unloading   0.05 

Add  cost  of  teaming,  if  any   0.05 

Add  cost  of  bundling  and  returning  empty  bags,  and  loss  on  same   0.03 

Net  price  of  cement  ready  for  use  in  concrete   $2 . 06  per  bbl. 

'  With  Aberthaw  Construction  Co.,  Boston,  Mass. 

823 


824 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  19-2& 


It  is  usual  to  obtain  quotations  from  the  cement  companies  for  cement  for  jobs  on  which 
estimates  are  being  made.  These  quotations  always  include  the  freight  and  the  bags,  and  to 
arrive  at  the  net  cost  it  is  necessary  to  deduct  for  the  bags  and  add  for  the  supplementary  items, 
according  to  the  above  list. 

Sand  usually  costs  about  50  cts.  per  cu.  yd.  to  dig  and  load  on  teams  or  cars.  If  it  has  to 
be  screened  or  washed,  it  will  cost  from  60  to  70  cts.  per  cu.  yd.  Teaming  or  freight  will  vary 
according  to  the  length  of  haul,  but  will  usually  bring  the  cost  of  sand,  ready  for  use,  up  to 
$1.30  per  cu.  yd.,  f.o.b.  the  job.  If  it  comes  by  rail,  there  should  be  added  to  this  15  cts.  per 
cu.  yd.  for  unloading  from  cars. 

Crushed  stone  can  be  bought  at  from  $1.00  to  $1.25  per  ton  at  the  crusher,  to  which  must  be 
added  the  cost  of  teaming  or  freight,  which  will  vary  according  to  the  length  of  haul.  On  a 
haul  of  moderate  length  it  is  usual  to  pay  from  30  to  50  cts.  per  ton,  so  that  the  cost  of  crushed 
stone  (f.o.b.  the  job  ready  for  use)  generally  varies  between  $1.30  and  $1.75  per  ton.  To  this 
should  be  added  about  25  cts.  per  ton  if  it  has  to  be  unloaded  from  railroad  cars.  If  gravel  of 
suitable  size  and  quality  is  available  for  use,  it  can  generally  be  obtained  for  $1.50  per  cu.  yd., 
a  considerable  saving  on  the  price  of  crushed  stone.  In  comparing  the  price  of  gravel  and 
crushed  stone,  1  cu.  ft.  of  crushed  trap  rock  or  granite  may  be  considered  as  weighing  100  lb. 

Large  bridges  and  other  structures  are  sometimes  built  in  places  that  are  very  difficult  of 
access  and  in  consequence  the  cost  of  teaming  materials  may  be  much  greater  than  above 
mentioned.  In  some  cases  it  may  be  found  necessary  to  set  up  a  crushing  plant  for  the  supply 
of  stone.  The  contractor,  however,  always  avoids  this,  if  possible,  as  the  cost  of  operating  a 
small  temporary  plant  is  always  greater  than  that  of  running  a  large  permanent  plant,  and  it 
pays  to  buy  crushed  stone  from  such  a  plant,  even  if  rock  from  the  excavations  is  available. 

26.  Labor. — The  labor  of  mixing  and  placing  concrete  varies  considerably, 
according  to  the  conditions  of  the  job  and  the  nature  of  the  work.  It  is  obvious  that  to  mix 
and  place  concrete  in  heavy  bridge  abutments  and  concrete  dams  would  cost  a  great  deal  less 
than  to  place  concrete  in  floor  slabs  3  or  4  in.  thick,  in  arch  ribs,  or  in  beam  and  column  forms, 
as  the  former  would  not  require  so  much  spading  and  spreading. 

Assuming  a  well  laid-out  job  and  a  machine  mixer  taking  4  bags  to  the  batch,  the  cost  of 
mixing  concrete  should  be  from  70  to  80  cts.  per  cu.  yd.  The  operations  will  consist  of  loading 
wheelbarrows  with  sand  and  stone  and  wheeling  them  up  to  the  mixer  and  charging  same,  bring- 
ing cement  from  the  cement  shed  and  putting  it  into  the  mixer,  and  the  work  of  an  engineer 
in  running  the  mixer  and  discharging  the  concrete  into  wheelbarrows. 

The  cost  of  placing  concrete  will  include  the  wheeling  and  dumping  of  the  concrete  in  place, 
and  the  spreading  and  spading  of  the  concrete  in  the  forms.  This  should  cost  about  90  cts. 
per  cu.  yd.  in  average  work.  In  columns  and  thin  walls,  where  there  is  a  lot  of  spading  and  where 
care  has  to  be  used  to  get  a  good  surface  on  the  concrete,  this  cost  would  be  about  doubled. 
On  heavy  masses  of  concrete,  such  as  dams  and  thick  retaining  walls,  these  prices  can  be  con- 
siderably reduced,  especially  if  the  plant  is  well  laid  out  and  the  equipment  is  good.  Concrete 
has  been  mixed  and  placed  by  mixer  and  derrick,  or  tracks  and  cars,  for  as  low  as  50  cts.  per 
cu.  yd. 

The  following  is  an  approximate  schedule  of  labor  prices  for  mixing  and  placing  concrete: 


Mixing  and  placing  in  footings   $1 .75  per  cu.  yd. 

Mixing  and  placing  in  floor  slabs  not  exceeding  4^  in.  thick.  ...    2.00  per  cu.  yd. 

Mixing  and  placing  in  floor  slabs  exceeding  5  in.  thick   1.25  per  cu.  yd. 

Mixing  and  placing  in  columns  and  thin  walls   2 . 00  per  cu.  yd. 

Mixing  and  placing  in  walls  exceeding  18  in.  in  thickness   1.25  per  cu.  yd. 

Mixing  and  placing  in  dams  and  thick  retaining  walls   1.00  per  cu.  yd. 


On  some  jobs  it  is  possible  to  unload  sand  and  gravel  direct  from  railroad  cars  to  the  wheel- 
barrows which  charge  the  mixer.  In  such  cases  the  materials  would  be  handled  once  instead 
of  twice  before  going  into  the  mixer,  and  a  saving  of  about  25  cts.  per  cu.  yd.  would  result. 


Sec.  19-2c] 


ESTIMATING 


825 


It  is  usual  to  specify  that  large  stones  may  be  embedded  Jn  massive  concrete  work  to  reduce 
the  cost  of  same.  These  stones  are  generally  placed  not  less  than  6  in.  apart  and  are  kept  at 
least  12  in.  away  from  the  face  of  the  work.  Some  specifications  will  allow  stones  that  one  man 
can  handle;  others  will  allow  any  stone  that  the  derricks  can  lift.  It  will  be  found  that  from  20 
to  50%  of  the  volume  of  a  massive  pier  can  be  composed  of  large  stone  in  this  way.  The  cost 
of  placing  these  stones,  or  "plums"  as  they  are  commonly  called,  should  not  exceed  $1.25  per 
cu.  yd.  If  the  rock  has  first  to  be  excavated  for  the  purpose,  the  cost  of  the  rock  excavation  must 
be  added. 

2c.  Plant. — The  cost  of  tools  and  plant  and  supplies  on  a  job  varies  a  good  deal 
according  to  the  nature  and  size  of  the  work.  But,  assuming  a  building  job  containing  5000 
cu.  yd.  of  concrete  work  carried  out  by  a  contractor  of  ability,  it  will  usually  be  found  that  the 
cost  of  plant,  tools,  and  supplies,  temporary  buildings,  office,  cement  shed,  etc.,  will  amount  to 
about  $6000.  Of  this  amount,  about  $1000  would  be  spent  on  labor  in  setting  up  the  plant  and 
dismantling  it;  $300  for  freight;  $2000  for  small  tools  and  depreciation  of  mixer,  hoisting 
engines  and  large  tools;  and  $2700  for  coal  or  power,  small  tools,  supplies  and  sundries.  The 
writer's  practice  is  to  estimate  $1.25  for  every  yard  of  concrete  on  building  jobs  containing 
between  4000  and  10,000  yd.  of  concrete.  On  larger  jobs  than  this,  the  proportion  would  be 
smaller,  probably  about  0.85  to  $1.00  and,  on  smaller  jobs  than  those  containing  3000  yd.,  the 
proportion  would  be  higher — from  $1.40  to  $2.00  per  cu.  yd.  On  jobs  containing  less  than  600 
cu.  yd.  of  concrete,  machine  mixing  is  not  usually  economical,  and  in  that  case  it  will  be 
necessary  to  estimate  for  mixing  by  hand,  which  will  cost  about  $2  per  cu.  yd.  more  than  the 
prices  given  above  for  labor  instead  of  including  a  charge  for  plant. 

As  a  general  rule,  the  plant  required  in  bridge  construction  is  more  costly  than  that  for 
building  construction.  This  is  particularly  the  case  where  cableways  are  used.  It  is  best  to 
calculate  separately  the  cost  of  labor  and  depreciation  on  each  item  of  plant  in  each  case  and  add 
the  cost  for  supplies,  fuel,  and  small  tools.  In  general,  however,  it-  will  be  found  that  the  total 
cost  of  plant  for  bridges,  as  in  buildings,  will  vary  pretty  closely  with  the  yardage  of  concrete. 
In  the  writer's  practice  he  has  found  that  figures  of  $7000  for  plant  on  a  5000-yd.  job,  $8000  on  a 
6000-yd.  job,  $6000  on  a  4000-yd.  job,  and  so  on,  check  up  quite  closely  with  actual  costs. 
These  figures,  of  course,  do  not  include  plant  for  excavating,  drilling,  etc. 

2d.  Summary. — The  conditions  on  construction  work  do  not  approach  those 
of  laboratory  work,  and  there  is  always  a  considerable  waste  of  cement,  sand,  and  stone.  It 
has  been  found  in  practice,  that,  when  estimating,  it  is  not  safe  to  allow  less  than  the  following 
amounts  of  cement  for  different  proportions  of  mix: 

1:1^:3  mix   2 . 00  bbl.  per  cu.  yd. 

1:2:4  mix   1 . 66  bbl.  per  cu.  yd. 

1  : 23^  :  5  mix   1 . 40  bbl.  per  cu.  yd. 

1  :  3  : 6  mix   1 .20  bbl.  per  cu.  yd. 

The  amount  of  sand  and  stone  required  varies  considerably  according  to  the  percentage  of 
voids.  This  variation  cannot  be  taken  into  account  in  the  usual  methods  of  estimating — as  it 
can  only  be  ascertained  by  careful  tests  and  varies  from  time  to  time,  even  when  the  source  of 
supply  is  the  same — and  therefore  it  is  usual  to  allow  3-^  cu.  yd.  of  sand  per  cu.  yd.  of 
concrete,  and  1  cu.  yd.  of  crushed  stone — ^figuring  crushed  stone  to  weigh  100  lb.  per  cu.  ft. 

The  cost  of  1  cu.  yd.  of  concrete  on  a  job  containing  5000  cu.  yd.  of  reinforced-concrete 
work  in  floors  and  columns,  etc.,  may  be  estimated  as  follows: 

Cement  1.66  bbl.  at  $2.06   $3.42 

Sand  0.5  yd.  at  $1.30   0.65 

Stone  1.35  tons  at  $1.60   2.16 

Labor   1.65 

Plant   1.25 

Total   $9.13  per  cu.  yd. 


826 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  19-3a 


The  following  illustrates  the  method  of  estimating  the  cost  of  concrete  on  a  large  typical 
bridge  job: 

Abutments  and  piers — 1  :  2}4  -  5  mix: 

Cement  1 . 4  bbl.,    @  $2 . 10  net   $2 . 94 

Sand  0.5  cu.  yd.,@  1.30   0.65 

Crushed  stone  1 . 35  tons,    @1.60   2.16 

Labor,  mixing  and  placing   1 .00 

Plant   1.30 


Total   $8.05  per  cu.  yd. 

Abutments  and  piers — 1  : 2)4  '  5  mix — with  30%  of  large  stones: 

7  cu.  yd.  concrete  as  above,    @  $8 . 05   $56 . 35 

3  cu.  yd.  placing  large  stones,  @  1 . 50   4 . 50 


Arch  ribs  and  deck  slabs — 1  : 2  :  4  mix : 

Cement  1 . 66  bbl.,  @  $2 . 10 

Sand  0.5  cu.  yd.,  @  1.30 

Crushed  stone  1.35  tons,   @  1 . 60 . 


$60 

.85 

6 

.08 

$3 

.49 

0 

,65 

2. 

16 

1 

.30 

1 

30 

Total   $8 . 90  per  cu.  yd. 

The  above  costs  do  not  include  forms,  steel,  or  finishing  of  surfaces. 
3.  Estimating  Unit  Cost  of  Forms. 

3a.  Considerations  Involved. — Forms  for  building  work  should  be  measured  by 
the  square  foot  of  surface  (measuring  all  sides  that  touch  the  concrete)  and  priced  according 
to  the  labor  involved  in  erecting,  studding,  bracing  and  stripping.  Strictly  speaking,  formwork 
is  the  labor  of  supporting  wet  concrete,  and  the  material — that  is,  the  lumber  used — is  only 
incidental  to  this  labor;  therefore  it  is  not  correct  to  take  off  the  amount  of  lumber  used  and 
price  it  according  to  the  number  of  board  feet  thus  estimated.  It  is  the  practice  of  some  firms 
to  estimate  forms  by  the  latter  method  but  such  a  practice  is  misleading,  not  only  on  the  theo- 
retical ground  taken  above,  but  on  the  practical  ground  that  no  two  contractors  would  use  the 
same  amount  of  lumber  in  erecting  a  given  piece  of  formwork.  Besides,  it  is  not  possible  to 
determine  beforehand  just  how  much  lumber  will  be  used  for  the  same,  since  careful  drawings 
of  the  forms  are  not  usually  available.  In  the  writer's  practice,  he  has  always  found  that  even 
though  enough  lumber  to  complete  the  work  is  ordered  when  a  job  is  started  it  is  always  neces- 
sary, on  account  of  loss  and  waste  of  lumber,  to  order  a  great  deal  more  before  the  job  is  finished. 
The  forms  for  a  building  consist  principally  of: 

Forms  to  floors.  Forms  to  walls. 

Forms  to  beams  and  girders.  Forms  to  footings. 

Forms  to  columns. 

Each  of  these  should  be  measured  separately  and  priced  at  separate  and  different  rates. 

The  most  uncertain  and  difficult  item  to  estimate  in  bridge  and  similar  construction  is  the 
formwork.  It  is  best  to  estimate  by  the  square  foot  of  surface  contact,  as  in  building  work, 
and  to  this  add  for  the  staging  required  for  long  arch  spans. 


Sec.  ld-36] 


ESTIMATING 


827 


36.  Materials. — The  writer's  experience,  based  on  the  cost  accounts  of  many 
reinforced-concrete  buildings,  large  and  small,  shows  that  a  good  rule  for  estimating  the  cost 
of  lumber,  nails,  oil,  and  wire  used  in  the  construction  of  forms  to  a  factory  building,  is  to 
reckon  from  $3.50  to  $5.50  per  100  sq.  ft.  for  these  items,  a  good  average  being  $4.00  per  100 
sq.  ft.  This  figure  is  higher  than  that  used  by  a  good  many  estimators  at  the  present  day, 
but  is  based  on  actual  experience  of  costs  kept  on  a  large  number  of  jobs,  and  the  writer  is 
constantly  proving  that  this  figure  is  correct. 

In  estimating  bridge  form  work  (the  lumber,  nails,  oil,  etc.)  $5  per  100  sq.  ft.  should  be 
a  sufficient  allowance. 

3c.  Labor. — The  cost  of  forms  to  floor  slabs  in  buildings  will  take  into  account: 

1.  Making  up  panels. 

2.  Setting  up  posts  and  bracing  same. 

3.  Putting  girts  and  ledgers  on  tops  of  the  posts. 

4.  Laying  the  panels  on  the  same. 

5.  Stripping  the  centering  after  the  concrete  has  set. 

The  labor  of  making  up  form  panels  will  average  about  43^  cts.  per  sq.  ft.,  and  as  these  are  gener- 
ally used  3  or  4  times,  l}^  ct.  per  sq.  ft.  on  the  whole  area  is  a  good  figure  to  use  in  esti- 
mating. The  labor  of  erecting  studs  and  bracing  will  average  about  3  cts.  per  sq.  ft.,  and  the 
cost  of  putting  on  joists  and  girts  and  laying  down  panels  will  also  cost  about  3  cts.  per  sq.  ft., 
giving  a  total  labor  cost  of  erecting  forms  of  7)4  cts.  per  sq.  ft.  Add  to  this  1}4  ct.  per  sq.  ft.  for 
stripping,  and  we  get  a  labor  cost  of  8^  cts.  per  sq.  ft.  as  a  total.  On  a  small  and  irregular  build- 
ing, of  course  this  cost  will  be  much  higher,  but  for  a  plain,  large  factory  a  low  cost  such  as  this 
can  often  be  reached.  If  the  height  from  floor  to  ceiling  is  over  16  ft.,  this  price  should  be 
increased,  as  the  studs  will  have  to  be  spliced  and  extra  bracing  will  have  to  be  put  in.  Two 
or  three  cents  a  square  foot  should  therefore  be  added  in  such  a  case. 

The  cost  of  beam  and  girder  forms  includes  the  cost  of  the  following  operations: 

1.  Making  beam  bottoms  and  beam  sides. 

2.  Erecting  same  on  the  posts  and  joists  which  support  the  floor  slab. 

3.  Stripping. 

The  cost  of  making  up  will  be  about  6  cts.  per  sq.  ft.,  and  as  beam  bottoms  are  left  in  longer 
than  the  slab  forms,  it  is  not  safe  to  figure  on  using  these  more  than  twice,  giving  an  average 
cost  of  3  cts.  per  sq.  ft.  for  making  beam  forms.  Erecting  the  same  will  cost  about  6  cts.  per 
sq.  ft.,  and  stripping  13^  ct.  per  sq.  ft.,  giving  a  total  cost  of  10)^  cts.  per  sq.  ft.  for  beam  and 
girder  forms.  If  beams  and  girders  are  haunched  at  the  ends,  50  cts.  more  should  be  allowed 
each  time  for  the  haunching. 

The  labor  of  forming  columns  may  be  subdivided  into: 

1.  Making  up  panels.  4.  Bolting. 

2.  Erecting  panels  and  placing  yokes.  5.  Stripping. 

3.  Plumbing. 

The  cost  of  making  up  panels,  which  are  usually  of  13^-in.  stock,  will  be  found  to  average 
between  5  and  6  cts.  per  sq.  ft.  Allowing  that  these  will  be  used  3  times,  the  cost  per 
square  foot  of  formwork  would  be  about  2  cts.  The  erecting,  plumbing,  and  bolting  will  be 
about  9  cts.  per  sq.  ft.,  and  the  cost  of  stripping  about  13^  cts.  per  sq.  ft.,  giving  a  total  labor 
cost  of  12)4  cts.  per  sq.  ft.  for  labor  on  column  forms. 

Columns  less  than  8  ft.  high  cost  a  good  deal  more  per  square  foot  than  higher  columns, 
owing  to  the  fact  that  there  is  just  as  much  time  and  labor  spent  in  plumbing,  erecting,  and 
bolting  up  as  if  the  columns  were  twice  as  high  with  twice  the  amount  of  surface  area. 

In  a  similar  way,  the  cost  of  erecting  wall  forms  and  footing  forms  nay  be  found. 

No  general  rules  or  instructions  can  be  given  for  estimating  bridge  and  other  formwork, 
except  to  say  that  the  labor  should  be  estimated  at  not  less  than  13  cts.  per  sq.  ft. 


828  CONCRETE  ENGINEERS'  HANDBOOK  [Sec. 

Zd.  Summary. — The  costs  of  forms  per  square  foot  to  a  reinforced-concrete 
building  may  be  tabulated  as  follows: 

Forms  to  floor  slabs: 

Lumber,  nails,  oil,  etc   SO. 04 

Labor  making  panels   0.015 

Labor  erecting  studs  and  bracing   0 . 03 

Labor  laying  panels   0 . 03 

Labor  stripping   0 . 0125 

Total   $0.1275 

Forms  to  beams  and  girders: 

Lumber,  nails  and  oil   $0.04 

Labor  making   0 . 03 

Labor  erecting   0 . 06 

Labor  stripping   0 . 015 

Total  „   $0,145 

Forms  to  columns: 

Lumber,  nails,  oil,  etc   $0.04 

Labor  making  panels    0  . 02 

Labor  erecting,  plumbing,  and  bolting   0.09 

Labor  stripping   0.015 

Total   $0,165 

Forms  to  footings: 

Lumber,  nails,  and  oil   $0 . 04 

Labor  making  and  erecting   0 . 08 

Labor  stripping   0.015 

Total....   $0,135 

Forms  to  walls: 

Lumber,  nails,  oil,  etc   $0.04 

Labor  making   0 . 03 

Labor  erecting  and  plumbing   0 . 08 

Labor  stripping   0.015 

Total   $0,165 


4.  Estimating  Unit  Cost  of  Steel  Reinforcement. — The  cost  of  steel  reinforcement,  if 
ordered  in  time  to  wait  for  delivery  direct  from  the  mill,  will  average  about  $3.00  per  100  lb. 
The  freight  rate  on  a  haul  of  about  500  miles  will  be  about  18  cts.,  giving  a  total  of  $3.18  per 
100  lb.  for  steel  bars,  f.o.b.  cars  at  the  job.  At  the  time  of  publication  of  this  book  (Feb. 
1918),  deliveries  are  so  very  slow  that  the  universal  practice  is  to  buy  steel  only  from  stock  at  a 
delivered  price  of  about  $4.00  per  100  lb.  The  cost  of  steel  bars  varies  according  to  the  size 
of  the  bar.  Bars  of  from  1}4  to  H  in.  diameter  are  taken  at  the  lowest  rate,  which  is  called 
the  base  price.    Small  bars  take  a  higher  rate  as  follows: 


Sec.  19-5] 


ESTIMATING 


829 


From  mill 


From  local 


warehouse 


%  in.  and  i^'le  in. 
}i  in.  and  %q  in.. 


base  plus  5  cts. 
base  plus  10  cts. 
base  plus  20  cts. 
base  plus  25  cts. 
.base  plus  35  cts. 
base  plus  50  cts. 


base  plus  10  cts. 
base  plus  15  cts. 
base  plus  30  cts. 
base  plus  40  cts. 
base  plus  55  cts. 
base  plus  75  cts. 


This  differential  is  an  important  factor  in  design  as  well  as  in  estimating.  For  example,  assume 
a  floor  200  by  100  ft.  having  a  slab  6  in.  thick  and  an  area  of  steel  per  square  foot  of  0.462  sq. 
in.    The  total  weight  of  steel  required  (allowing  for  laps)  would  be  33,301  lb. 

Cost  of  H-in.  square  bars  6)^  in.  on  centers,  33,301  lb.  @  $4.15  per  1001b.  =  $1381.95. 

Cost  of  ^-in.  round  bars  3  in.  on  centers,  33,301  lb.  '@  $4.40  per  100  lb.       =  $1465.20. 

Thus  there  is  a  difference  of  $83.25  in  favor  of  J^-in.  bars  if  taken  from  stock  deliveries. 
It  is  usual  in  estimating  on  a  building  in  normal  times  to  figure  on  taking  the  steel  for  the  foot- 
ings and  the  lower  part  of  the  building,  enough  for  the  first  5  or  6  weeks  work,  out  of  local 
warehouse  stock  and  buy  the  rest  direct  from  the  mill. 

The  cost  of  unloading  steel  and  piling  it  on  the  job  is  about  50  cts.  per  ton,  and,  if  it  has 
to  be  teamed  from  the  freight  yards  to  the  site  of  the  work,  this  will  cost  60  cts.  per  ton  and 
upward. 

The  cost  of  bending  and  placing  steel  in  a  building  will  vary  according  to  the  amount  of 
work  that  is  done.  Thus,  placing  steel  bars  ^^-in.  diameter  in  a  floor  slab  will  cost  about  $6 
per  ton.  If  the  bars  have  to  be  bent  up  at  the  end,  $3  per  ton  should  be  added.  Bending  and 
placing  steel  bars  and  stirrups  in  beams  will  cost  from  $8  to  $10  per  ton.  Wiring  up  and  placing 
steel  bars  in  columns  and  placing  hoops  around  them  will  cost  from  $10  to  $12  per  ton.  Placing 
steel  of  ^-in.  and  %-in.  diameter  in  walls  will  cost  from  $15  to  $20  per  ton. 

These  prices  are  sufficient  to  include  the  cost  of  wire,  tools  for  bending,  etc.;  $12  per  ton 
is  a  good  average  price  for  labor  on  steel  reinforcement  all  through  the  job. 

The  cost  of  steel  reinforcement  in  a  reinforced-concrete  building  may  be  estimated  as 
follows: 

Steel  from  warehouse  stock  @$4.00  per  100  lb   $80.00  per  ton 

Unloading,  teaming,  and  piling   1.10  per  ton 

Labor,  bending  and  placing   12.00  per  ton 

Tools,  wire,  and  sundries   0 . 75  per  ton 


5.  Estimating  Unit  Cost  of  Surface  Finish. — One  hundred  square  feet  of  granolithic  finish 
laid  1  in.  thick  in  the  proportion  of  1  of  cement,  1  of  sand,  and  1  of  fine  crushed  stone,  will  require 
1  bbl.  of  cement,  4  cu.  ft.  of  sand,  and  4  cu.  ft.  of  crushed  stone.  This  may  therefore  be  esti- 
mated as  follows: 


Total 


$94 . 10  per  ton 


1  bbl.  cement  @$2 .06  per  bbl. . . . 

4  cu.  ft.  sand  @$1 .35  per  cu.  yd, 

400  lb.  fine  crushed  stone. . .  .  @$2 .25  per  ton. . . 


$2.06 
0.20 
0.45 


Labor  mixing  and  placing  

Finishers'  time  trowelling  surface 


$2.71 
1.00 
1.40 


Total  cost  per  100  sq.  ft. 


$5.11 


830 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  19-6 


If  the  surface  of  the  concrete  has  to  be  cleaned  off  with  acid  or  sand  blasting,  this  will  cost  from 
2  to  3  cts.  per  sq.  ft.  additional. 

The  exterior  surfaces  of  concrete  columns  and  beams  are  frequently  rubbed  smooth  with 
carborundum  stone,  using  a  little  water  and  cement.  ^  The  cost  of  this  work,  including  hanging 
swing  stages  for  the  finishers,  will  be  from  4  to  6  cts.  per  sq.  ft. 

For  ornamental  effect,  external  surfaces  are  sometimes  picked  with  a  pointed  tool  or 
crandall  hammer.    The  cost  of  this  runs  between  6  and  10  cts.  per  sq.  ft. 

ESTIMATING  QUANTITIES 

6.  Systematic  Procedure  Advisable. — The  operation  of  estimating  quantities  is  that  of 
calculating  (from  plans  supplied)  quantities  of  labor  and  material  which  go  to  make  up  the 
completed  building.  This  is  usually  called  taking  off  or  scaling.  This  should  be  done  quite 
independently  of  the  pricing  or  the  arithmetical  work  of  extending  the  quantities  to  obtain  the 
totals  of  the  quantities  of  work.  The  secret  of  accurate,  speedy  taking  off  is  to  be  found  in  a 
systematic  way  of  going  about  the  work.  No  printed  forms,  tables,  or  special  rules  for  taking 
off  will  insure  against  error,  but  the  surest  way  of  making  an  accurate  estimate  is  to  have  a  good 
system  to  work  on  and  a  clear  and  easily  followed  way  of  setting  down  the  items.  A  good 
method  is  to  use  plain  squared  paper  8  by  10}^  in.,  ruled  in  nine  columns.  In  the  first 
column  is  placed  a  description  of  the  items  measured;  the  next  four  columns  are  for  the 
number,  length,  width,  and  height  of  the  members  of  the  building;  the  next  two  are  for 
arithmetical  calculations  and  totals;  and  the  last  two  for  unit  and  total  price.  It  is  very  im- 
portant to  keep  length,  breadth,  and  height  in  the  same  order  in  every  item.  Each  can  then 
be  readily  identified.  In  taking  off  a  reinforced-concrete  building,  start  with  the  structural 
members  in  the  order  in  which  they  are  built;  that  is,  first  take  concrete  footings,  then  columns, 
then  floor  slabs,  then  beams  and  girders,  then  curtain  walls  and  partitions,  then  cornice,  and 
then  stairs  and  landings.  Take  all  the  concrete  first,  one  item  at  a  time  and  complete  it.  When 
all  the  concrete  is  taken  off,  proceed  to  take  off  the  forms,  and  after  that  take  off  the  reinforce- 
ment, and  then  the  finish  to  the  surfaces.  After  that  take  off  excavation,  windows  and  doors, 
roofing  and  other  incidental  items  necessary  to  complete  the  cost  of  the  building. 

In  putting  down  the  dimensions,  it  is  well  to  put  a  note  identifying  each  item,  thus: 
Concrete  columns: 

Basement,    (mark  A)  5  X  1>^  X  13^  X  10 

(mark  B)  4  X  1>^  X  1^^  X  10 

(mark  C)  7  X  IH  X  IH  X  10 

First  floor,  (mark  A)  5X13^X13^X10 

(mark  B)  4  X  13^  X  1^  X  10 

(mark  C)  7  X  13^  X  13^  X  10 

It  takes  a  little  more  time  to  do  this,  but  it  is  well  worth  the  labor,  and  any  item  can  be  readily 
identified  afterward.  Also  if  an  item  is  left  out  in  error,  it  can  be  more  easily  detected.  It 
is  good  practice  to  put  all  dimensions  in  feet  and  fractions.  Some  estimators  work  in  feet  and 
inches  and  some  in  feet  and  decimals.  There  seems  to  be  the  least  chance  for  error  in  using 
fractions,  but  this  is  a  matter  of  individual  judgment. 

7.  Riiles  for  Measurement  of  Concrete  Work. — The  following  rules  should  govern  the 
measurement  of  concrete  work: 

All  concrete  should  be  measured  by  the  cubic  foot  or  cubic  yard,  and  in  all  cases  forms 
should  be  measured  separately.  All  concrete  should  be  measured  net  as  placed  or  poured  in 
the  structure  or  building,  and  an  excess  measurement  of  concrete  should  never  be  taken  to 
pay  for  the  cost  of  forms  or  extra  labor  in  placing.  All  openings  and  voids  in  concrete  should 
be  deducted,  but  no  deduction  should  be  made  for  steel  reinforcement,  I-beams,  bolts,  etc., 

1  See  Art.  526,  Sect.  2. 


Sec.  19-8] 


ESTIMATING 


831 


embedded  in  the  concrete,  except  where  such  have  a  sectional  area  of  more  than  1  sq.  ft.  No 
deduction  should  be  made  for  chamfered,  beveled,  or  splayed  angles  to  columns,  beams,  and 
other  work. 

For  beams  and  girders  it  is  usual  to  show  on  the  plan  the  depth  of  concrete  from  the  top 
of  the  slab.  Thus,  if  the  quantity  of  concrete  for  the  slab  has  been  taken  right  through,  it 
will  be  necessary  to  consider  only  the  extra  concrete  below  the  slab  in  taking  off  beam  and 
girder  quantities.  For  example,  in  a  floor  6  in.  thick  having  12  by  30-in.  girders,  the  concrete 
to  take  off  for  the  girders  should  be  considered  as  1  ft.  wide  by  2  ft.  deep,  since  the  other  6  in. 
is  included  in  the  slab. 

Each  class  of  concrete  having  a  different  proportion  of  cement,  sand,  or  aggregate  should 
be  measured  and  described  separately.  Concrete  in  the  different  members  of  a  building  or 
structure  should  be  measured  and  described  separately  according  to  the  accessibility,  location, 
or  purpose  of  the  work;  concrete  in  floor  slabs  should  be  measured  and  priced  separately  from 
columns  or  walls,  and  so  on.  Concrete  with  large  stones  and  rocks  embedded  in  same  (cyclo- 
pean  masonry)  should  be  measured  as  one  item  and  described  according  to  the  richness  of  the 
mix  and  the  percentage  of  rock  in  same.  Concrete  in  stairs  should  be  measured  by  the  cubic 
foot,  and  it  is  usual  to  include  surface  finish  with  same  in  this  case,  as  it  forms  such  a  small 
item  in  the  cost. 

8.  Estimating  Amount  of  Formwork. — Forms  should  be  measured  in  square  feet,  taking 
the  area  of  the  surface  of  the  concrete  which  is  actually  touched  by  the  forms  or  falsework. 
Forms  should  in  all  cases  be  measured  and  described  as  a  separate  item  and  never  included 
with  the  concrete.  No  deduction  should  be  made  in  measurement  of  surface  of  concrete  sup- 
ported by  forms  because  of  forms  being  taken  down  and  re-used  2  or  3  times  in  the  course  of 
construction. 

It  is  not  necessary  to  consider  struts,  posts,  bracing,  bolts,  wire  ties,  oiling,  cleaning,  and 
repairing  forms,  as  these  should  be  covered  by  the  price  put  on  the  square  foot  measurements. 

Forms  to  the  different  parts  of  a  building  should  be  measured  and  described  separately 
according  to  their  nature;  that  is,  forms  to  floor  slabs,  walls,  columns,  footings,  etc.,  should  be 
separated  from  each  other.  No  allowance  need  be  made  for  angle  fillets  or  bevels  to  beams 
and  columns,  etc.,  but  curved  moldings  should  be  measured  and  described  separately. 

No  deduction  in  measurement  of  forms  should  be  made  for  openings  having  an  area  of  less 
than  25  sq.  ft.  as  the  labor  in  forming  same  is  often  greater  than  the  cost  of  the  omitted  area. 
No  deduction  should  be  made  in  floor  forms  for  heads  of  columns,  or  in  column  and  girder  forms 
for  ends  of  girders,  cross  beams,  etc.  No  allowance  should  be  made  for  pockets  in  column 
forms  for  clearing  out  rubbish. 


Fig.  1. 


The  correct  measurement  of  column  forms  is  the  girth  of  the  four  sides,  or  circumference, 
multiplied  by  the  height  from  the  floor  surface  to  the  under  side  of  floor  slab  above.  Forms 
to  octagonal,  hexagonal,  and  circular  cojumns  should  be  measured  and  priced  separately  from 
forms  to  square  columns.  Caps  and  bases  to  columns  and  other  ornamental  work  should  be 
enumerated  and  fully  described  by  sketches  in  the  estimate  with  overall  dimensions. 

The  correct  measurement  of  beam  forms  is  the  net  length  between  columns  multiplied  by 
the  sum  of  the  breadth  (5)  and  twice  the  depth  below  the  slab  {d),  except  for  beams  at  edge  of 
floor  or  around  openings,  which  shall  have  the  thickness  of  the  floor  (0  added  to  the  sum  of  the 
breadth  and  twice  the  depth  (see  Fig.  1). 


832 


CONCRETE  ENGINEERS'  HANDBOOK 


[Sec.  19-9 


Wall  forms  should  be  measured  for  both  sides  of  concrete  walls. 

Forms  to  the  upper  side  of  sloping  slabs  such  as  saw-tooth  roofs  should  be  measured  when- 
ever the  slope  of  such  slab  with  the  horizontal  exceeds  an  angle  of  25  deg. 

Moldings  in  formwork  should  be  measured  by  the  linear  foot.  Forms  to  circular  work 
should  always  be  measured  separately  from  forms  to  straight  work. 

No  measurement  or  allowance  should  be  made  for  construction  joints  in  slabs,  beams,  etc., 
to  stop  the  day's  concreting,  but  construction  joints  or  expansion  joints  in  dams  and  other 
large  masses  of  concrete  should  be  measured  by  the  square  foot  as  they  occur. 

Forms  to  cornices  should  be  measured  by  the  linear  foot  and  the  girth  stated.  Plain 
forms  to  back  of  cornice  should  be  measured  separately.  Forms  to  window  sills,  copings,  and 
similar  work  should  be  measured  by  the  linear  foot.  Forms  to  the  underside  of  stairs  should 
be  measured  by  the  superficial  foot,  and  forms  to  the  front  edge  by  the  linear  foot.  Forms  to 
the  ends  of  steps  should  be  measured  by  number. 

9.  Estimating  Amount  of  Steel. — Reinforcing  bars  should  be  measured  by  the  linear  foot 
and  reduced  to  weight  in  pounds  for  pricing.  The  net  weight  placed  in  the  building  should  be 
taken  and  no  allowance  made  for  waste  and  cutting,  or  wire  ties  and  spacers,  etc.,  but  laps  should 
be  allowed  for  as  called  for  by  the  plans  or  by  the  necessities  of  the  design.  Deformed  bars 
should  be  measured  separately  from  plain. 

The  cost  of  bending  and  placing  in  columns  and  beams  is  greater  than  in  slabs,  but  as  the 
difference  is  not  great  it  is  not  usual  to  make  any  distinctions  but  to  take  olf  the  whole  of  the 
steel  together,  except  in  special  cases. 

Pipe  sleeves,  turnbuckles,  clamps,  threaded  ends,  nuts,  forgings,  and  other  special  items 
should  be  measured  separately  by  number  and  size,  and  allowed  for  in  addition  to  the  weight. 
Wire  cloth,  expanded  metal,  and  other  steel  fabrics  sold  in  sheets  are  measured  and  described 
by  the  square  foot.  The  size  of  mesh  and  weight  per  square  foot  of  steel  will  govern  the  price, 
and  should  be  stated.    All  laps  should  be  measured  and  allowed  for. 

10.  Estimating  Amount  of  Surface  Finish. — Finish  of  concrete  surfaces  should  be  measured 
by  the  square  foot.  Finish  should  always  be  measured  and  described  separately.  No  measure- 
ment or  allowance  should  be  made  for  going  over  concrete  work  after  removal  of  forms,  and 
patching  up  voids  and  stone  pockets,  removing  fins,  etc.,  as  this  is  part  of  the  labor  incidental 
to  placing  the  concrete  and  the  cost  will  depend  upon  the  care  used  in  spading  the  concrete 
into  the  forms. 

Granolithic  finish  should  be  measured  by  the  square  foot  and  should  include  all  labor  and 
materials  for  the  thickness  specified.  Finish  laid  integral  with  the  slab  should  be  measured 
separately  from  finish  laid  after  the  slab  has  set.  No  allowance  should  be  made  for  protection 
of  finish  with  sawdust,  sand,  or  covering  in  to  protect  from  weather.  Grooved  surfaces,  gutters, 
curbing,  etc.,  should  be  measured  separately  from  plain  granolithic  and  should  be  measured 
by  the  square  foot  or  linear  foot,  as  the  case  may  require. 

Putting  on  cement  wash,  rubbing  with  carborundum,  scrubbing  with  wire  brushes,  tooling, 
and  picking,  are  other  surface  labors  that  should  each  be  separately  measured  and  priced. 
The  price  should  include  the  use  of  swing  stages,  tools,  and  materials  required. 


APPENDIX  A 


STANDARD  SPECIFICATIONS  AND  TESTS  FOR  PORTLAND  CEMENT^ 

These  specifications  are  the  result  of  several  years'  work  of  a  special  committee  representing  a  United  States 
Government  Departmental  Committee,  the  Board  of  Direction  of  the  American  Society  of  Civil  Engineers,  and 
Committee  C-1  on  Cement  of  the  American  Society  for  Testing  Materials  in  cooperation  with  Committee  C-1. 

Specifications 

1.  Definition. — Portland  cement  is  the  product  obtained  by  finely  pulverizing  clinker  produced  by  calcining 
to  incipient  fusion,  an  intimate  and  properly  proportioned  mixture  of  argillaceous  and  calcareous  materials,  with  no 
additions  subsequent  to  calcination  excepting  water  and  calcined  or  uncalcined  gypsum. 

I.  Chemical  Properties 

2.  Chemical  Limits. — The  following  limits  shall  not  be  exceeded 

Loss  on  ignition,  %  

Insoluble  residue,  %  

Sulphuric  anhydride  (S03),%  

Magnesia  (MgO),  %  

II.  Physical  Properties 

3.  Specific  Gravity. — The  specific  gravity  of  cement  shall  be  not  less  than  3.10  (3.07  for  white  Portland 
cement).  Should  the  test  of  cement  as  received  fall  below  this  requirement  a  second  test  may  be  made  upon  an 
ignited  sample.    The  specific  gravity  test  will  not  be  made  unless  specifically  ordered. 

4.  Fineness. — The  residue  on  a  standard  No.  200  sieve  shall  not  exceed  22  %  by  weight. 

5.  Soundness. — A  pat  of  neat  cement  shall  remain  firm  and  hard,  and  show  no  signs  of  distortion,  cracking, 
checking,  or  disintegration  in  the  steam  test  for  soundness. 

6.  Time  of  Setting. — The  cement  shall  not  develop  initial  set  in  less  than  45  min.  when  the  Vicat  needle  is  used 
or  60  min.  when  the  Gillmore  needle  is  used.    Final  set  shall  be  attained  within  10  hr. 

7.  Tensile  Strength. — The  average  tensile  strength  in  pounds  per  square  inch  of  not  less  than  three  standard 
mortar  briquettes  (see  Sec.  51)  composed  of  1  part  cement  and  3  parts  standard  sand,  by  weight,  shall  be  equal  to  or 
higher  than  the  following: 


Age  at  test, 
days 

Storage  of  briquettes 

Tensile  strength, 
lb.  per  sq.  in. 

7 

28 

1  day  in  moist  air,  6  days  in  water 
1  day  in  moist  air,  27  days  in  water 

200 
300 

8.  The  average  tensile  strength  of  standard  mortar  at  28  days  shall  be  higher  than  the  strength  at  7  days. 

III.  Packages,  Marking  and  Storage 

9.  Packages  and  Marking. — The  cement  shall  be  delivered  in  suitable  bags  or  barrels  with  the  brand  and 
name  of  the  manufacturer  plainly  marked  thereon,  unless  shipped  in  bulk.  A  bag  shall  contain  94  lb.  net.  A  barrel 
shall  contain  376  lb.  net. 


4.00 
0.85 
2.00 
5.00 


1  These  specifications  and  tests  were  adopted  by  letter  ballot  of  the  American  Society  for  Testing  Materials 
on  Sept.  1,  1916,  and  became  effective  Jan.  1,  1917. 

53  8  33 


834 


CONCRETE  ENGINEERS'  HANDBOOK 


10.  Sto/age. — The  cement  shall  be  stored  in  such  a  manner  as  to  permit  easy  access  for  proper  inspection  and 
identification  of  each  shipment,  and  in  a  suitable  weather-tight  building  which  will  protect  the  cement  from 
dampness. 

IV.  Inspection 

11.  Inspection. — Every  facility  shall  be  provided  the  purchaser  foi;  careful  sampling  and  inspection  at  either 
the  mill  or  at  the  site  of  the  work,  as  may  be  specified  by  the  purchaser.  At  least  10  days  from  the  time  of  sampling 
shall  be  allowed  for  the  completion  of  the  7-day  test,  and  at  least  31  days  shall  be  allowed  for  the  completion  of  the 
28-day  test.  The  cement  shall  be  tested  in  accordance  with  the  methods  hereinafter  prescribed.  The  28-day  test 
shall  be  waived  only  when  specifically  so  ordered. 

V.  Rejection 

12.  Rejection. — The  cement  may  be  rejected  if  it  fails  to  meet  any  of  the  requirements  of  these  specifications. 

13.  Cement  shall  not  be  rejected  on  account  of  failure  to  meet  the  fineness  requirement  if  upon  retest  after 
drying  at  100°C.  for  1  hr.  it  meets  this  requirement. 

14.  Cement  failing  to  meet  the  test  for  soundness  in  steam  may  be  accepted  if  it  passes  a  retest  using  a  new 
sample  at  any  time  within  28  days  thereafter. 

15.  Packages  varying  more  than  5%  from  the  specified  weight  may  be  rejected:  and  if  the  average  weight  of 
packages  in  any  shipment,  as  shown  by  weighing  50  packages  taken  at  random,  is  less  than  that  specified,  the  entire 
shipment  may  be  rejected. 

Tests 

VI.  Sampling 

16.  Number  of  Samples. — Tests  may  be  made  on  individual  or  composite  samples  as  may  be  ordered.  Each 
test  sample  should  weigh  at  least  8  lb. 

17.  (a)  Individual  Sample. — If  sampled  in  cars  one  test  sample  shall  be  taken  from  each  50  bbl.  or  fraction 
thereof.    If  sampled  in  bins  one  sample  shall  be  taken  from  each  100  bbl. 

(6)  Composite  Sample. — If  sampled  in  cars  one  sample  shall  be  taken  from  one  sack  in  each  40  sacks  (or  1  bbl. 
in  each  10  bbl.)  and  combined  to  form  one  test  sample.  If  sampled  in  bins  or  warehouses  one  test  sample  shall  repre- 
sent not  more  than  200  bbl. 

18.  Method  of  Sampling. — Cement  may  be  sampled  at  the  mill  by  any  of  the  following  methods  that  may  be 
practicable,  as  ordered: 

(o)  From  the  Conveyor  Delivering  to  the  Bin. — At  least  8  lb.  of  cement  shall  be  taken  from  approximately  each 
100  bbl.  passing  over  the  conveyor. 

(b)  From  Filled  Bins  by  Means  of  Proper  Sampling  Tubes. — Tubes  inserted  vertically  may  be  used  for  sampling 
cement  to  a  maximum  depth  of  10  ft.  Tubes  inserted  horizontally  may  be  used  where  the  construction  of  the  bin 
permits.    Samples  shall  be  taken  from  points  well  distributed  over  the  face  of  the  bin. 

(c)  From  Filled  Bins  at  Points  of  Discharge. — Sufficient  cement  shall  be  drawn  from  the  discharge  openings  to 
obtain  samples  representative  of  the  cement  contained  in  the  bin,  as  determined  by  the  appearance  at  the  discharge 
openings  of  indicators  placed  on  the  surface  of  the  cement  directly  above  these  openings  before  drawing  of  the 
cement  is  started. 

19.  Treatment  of  Sample. — Samples  preferably  shall  be  shipped  and  stored  in  air-tight  containers.  Samples 
shall  be  passed  through  a  sieve  having  20  meshes  per  linear  inch  in  order  to  thoroughly  mix  the  sample,  break 
up  lumps  and  remove  foreign  materials. 

VII.  Chemical  Analysis 
Loss  on  Ignition 

20.  Method. — One  gram  of  cement  shall  be  heated  in  a  weighed  covered  platinum  crucible,  of  20  to  25-c.c. 
capacity,  as  follows,  using  either  method  (a)  or  (6)  as  ordered: 

(a)  The  crucible  shall  be  placed  in  a  hole  in  an  asbestos  board,  clamped  horizontally  so  that  about  three-fifths 
of  the  crucible  projects  below,  and  blasted  at  a  full  red  heat  for  15  min.  with  an  inclined  flame;  the  loss  in  weight 
shall  be  checked  by  a  second  blasting  for  5  min.  Care  shall  be  taken  to  wipe  off  particles  of  asbestos  that  may  ad- 
here to  the  crucible  when  withdrawn  from  the  hole  in  the  board.  Greater  neatness  and  shortening  of  the  time  of 
heating  are  secured  by  making  a  hole  to  fit  the  crucible  in  a  circular  disc  of  sheet  platinum  and  placing  this  disc  over 
a  somewhat  larger  hole  in  an  asbestos  board. 

(6)  The  crucible  shall  be  placed  in  a  muffle  at  any  temperature  between  900  and  1000°C.  for  15  min.  and  the 
loss  in  weight  shall  be  checked  by  a  second  heating  for  5  min. 

21.  Permissible  Variation. — A  permissible  variation  of  0.25  will  be  allowed,  and  all  results  in  excess  of  the  speci- 
fied limit  but  within  this  permissible  variation  shall  be  reported  as  4  %.  - 

Insoluble  Residue 

22.  Method. — To  a  1-gram  sample  of  cement  shall  be  added  10  c.c.  of  water  and  5  c.c.  of  concentrated  hydro- 
chloric acid ;  the  liquid  shall  be  warmed  until  effervescence  ceases.    The  solution  shall  be  diluted  to  50  c.c.  and  di- 


APPENDIX  A 


835 


gested,  on  a  steam  bath  or  hot  plate  until  it  is  evident  that  decomposition  of  the  cement  is  complete.  The  residue 
shall  be  filtered,  washed  with  cold  water,  and  the  filter  paper  and  contents  digested  in  about  30  c.o.  of  a  5  %  solu- 
tion of  sodium  carbonate,  the  liquid  being  held  at  a  temperature  just  short  of  boiling  for  15  min.  The  remaining 
residue  shall  be  filtered,  washed  with  cold  water,  then  with  a  few  drops  of  hot  hydrochloric  acid,  1  : 9,  and  finally 
with  hot  water,  and  then  ignited  at  a  red  heat  and  weighed  as  the  insoluble  residue. 

23.  Permissible  Variation. — A  permissible  variation  of  0.15  will  be  allowed,  and  all  results  in  excess  of  the 
specified  limit  but  within  this  permissible  variation  shall  be  reported  as  0.85%. 

Sulphuric  Anhydride 

24.  Method. — One  gram  of  the  cement  shall  be  dissolved  in  5  c.c.  of  concentrated  hydrochloric  acid  diluted 
with  5  c.c.  of  water,  with  gentle  warming;  when  solution  is  complete  40  c.c.  of  water  shall  be  added,  the  solution  fil- 
tered, and  the  residue  washed  thoroughly  with  water.  The  solution  shall  be  diluted  to  250  c.c,  heated  to  boiling 
and  10  c.c.  of  a  hot  10%  solution  of  barium  chloride  shall  be  added  slowly,  drop  by  drop,  from  a  pipette  and  the 
boiling  continued  until  the  precipitate  is  well  formed.  The  solution  shall  be  digested  on  the  steam  bath  until  the 
precipitate  has  settled.  The  precipitate  shall  be  filtered,  washed,  and  the  paper  and  contents  placed  in  a  weighed 
platinum  crucible  and  the  paper  slowly  charred  and  consumed  without  flaming.  The  barium  sulphate  shall  then 
be  ignited  and  weighed.  The  weight  obtained  multiplied  by  34.3  gives  the  percentage  of  sulphuric  anhydride.  The 
acid  filtrate  obtained  in  the  determination  of  the  insoluble  residue  may  be  used  for  the  estimation  of  sulphuric  anhy- 
dride instead  of  using  a  separate  sample. 

25.  Permissible  Variation. — A  permissible  variation  of  0.10  will  be  allowed,  and  all  results  in  excess  of  the 
specified  limit  but  within  this  permissible  variation  shall  be  reported  as  2.00%. 

Magnesia 

26.  Method. — To  0.5  gram  of  the  cement  in  an  evaporating  dish  shall  be  added  10  c.c.  of  water  to  prevent 
lumping  and  then  10  c.c.  of  concentrated  hydrochloric  acid.  The  liquid  shall  be  gently  heated  and  agitated  until 
attack  is  complete.  The  solution  shall  then  be  evaporated  to  complete  dryness  on  a  steam  or  water  bath.  To 
hasten  dehydration  the  residue  may  be  heated  to  150  or  even  200°C.  for  to  1  hr.  The  residue  shall  be  treated 
with  10  c.c.  of  concentrated  hydrochloric  acid  diluted  with  an  equal  amount  of  water.  The  dish  shall  be  covered 
and  the  solution  digested  for  10  min.  on  a  steam  bath  or  water  bath.  The  diluted  solution  shall  be  filtered  and  the 
separated  silica  washed  thoroughly  with  water. i  Five  cubic  centimeters  of  concentrated  hydrochloric  acid  and  suf- 
ficient bromine  water  to  precipitate  any  manganese  which  may  be  present,  shall  be  added  to  the  filtrate  (about  250 
c.c).  This  shall  be  made  alkaline  with  ammonium  hydroxide,  boiled  until  there  is  but  a  faint  odor  of  ammonia,  and 
the  precipitated  iron  and  aluminum  hydroxides,  after  settling,  shall  be  washed  with  hot  water,  once  by  decantation 
and  slightly  on  the  filter.  Setting  aside  the  filtrate,  the  precipitate  shall  be  transferred  by  a  jet  of  hot  water  to  the 
precipitating  vessel  and  dissolved  in  10  c.c  of  hot  hydrochloric  acid.  The  paper  shall  be  extracted  with  acid,  the 
solution  and  washings  being  added  to  the  main  solution.  The  aluminum  and  iron  shall  then  be  reprecipitated  at 
boiling  heat  by  ammonium  hydroxide  and  bromine  water  in  a  volume  of  about  100  c.c,  and  the  second  precipitate 
shall  be  collected  and  washed  on  the  filter  used  in  the  first  instance  if  this  is  still  intact.  To  the  combined  filtrates 
from  the  hydroxides  of  iron  and  aluminum,  reduced  in  volume  if  need  be,  1  c.c.  of  ammonium  hydroxide  shall  be 
added,  the  solution  brought  to  boiling,  25  c.c.  of  a  saturated  solution  of  boiling  ammonium  oxalate  added,  and  the 
boiling  continued  until  the  precipitated  calcium  oxalate  has  assumed  a  well-defined  granular  form.  The  precipi- 
tate after  1  hr.  shall  be  filtered  and  washed,  then  with  the  filter  shall  be  placed  wet  in  a  platinum  crucible,  and  the 
paper  burned  off  over  a  small  flame  of  a  Bunsen  burner;  after  ignition  it  shall  be  redissolved  in  hydrochloric  acid  and 
the  solution  diluted  to  100  c.c.  Ammonia  shall  be  added  in  slight  excess,  and  the  liquid  boiled.  The  lime  shall  then 
be  reprecipitated  by  ammonium  oxalate,  allowed  to  stand  until  settled,  filtered  and  washed.  The  combined  fil- 
trates from  the  calcium  precipitates  shall  be  acidified  with  hydrochloric  acid,  concentrated  on  the  steam  bath  to 
about  150  c.c,  and  made  slightly  alkaline  with  ammonium  hydroxide,  boiled  and  filtered  (to  remove  a  little  alumi- 
num and  iron  and  perhaps  calcium).  When  cool,  10  c.c.  of  saturated  solution  of  sodium-ammonium-hydrogen 
phosphate  shall  be  added  with  constant  stirring.  When  the  crystallin  ammonium-magnesium  orthophosphate  has 
formed,  ammonia  shall  be  added  in  moderate  excess.  The  solution  shall  be  set  aside  for  several  hours  in  a  cool  place, 
filtered  and  washed  with  water  containing  2.5%  of  NH3.  The  precipitate  shall  be  dissolved  in  a  small  quantity  of 
hot  hydrochloric  acid,  the  solution  diluted  to  about  100  c.c,  1  c.c.  of  a  saturated  solution  of  sodium-ammonium- 
hydrogen  phosphate  added,  and  ammonia  drop  by  drop,  with  constan  stirring,  until  the  precipitate  is  again 
formed  as  described  and  the  ammonia  is  in  moderate  excess.  The  precipitate  shall  then  be  allowed  to  stand  about 
2  hr., filtered  and  washed  as  before.  The  paper  and  contents  shall  be  placed  in  a  weighed  platinum  crucible,  the 
paper  slowly  charred,  and  the  resulting  carbon  carefully  burned  off.  The  precipitate  shall  then  be  ignited  to  con- 
stant weight  over  a  Meker  burner,  or  a  blast  not  strong  enough  to  soften  or  melt  the  pyrophosphate.  The  weight  of 
magnesium  pyrophosphate  obtained  multiplied  by  72.5  gives  the  percentage  of  magnesia.  The  precipitate  so 
obtained  always  contains  some  calcium  and  usually  small  quantities  of  iron,  aluminum,  and  manganese  as 
phosphates. 

27.  Permissible  Variation. — A  permissible  variation  of  0.4  will  be  allowed,  and  all  results  in  excess  of  the 
specified  limit  but  within  this  permissible  variation  shall  be  reported  as  5.00  % . 

1  Since  this  procedure  does  not  involve  the  determination  of  silica,  a  second  evaporation  is  unnecessary. 


836 


CONCRETE  ENGINEERS'  HANDBOOK 


VIII.  Determination  of  Specific  Gravity 


28.  Apparatus. — The  determination  of  specific  gravity  shall  be  made  with  a  standardized  Le  Chatelier  appa- 
ratus which  conforms  to  the  requirements  illustrated  in  Fig.  1.    This  apparatus  is  standardized  by  the  United  States 

Bureau  of  Standards.   Kerosene  free  from  water,  or 

k-  --  Scm  ^ 

|/./5c/77-;--^ 


Capacity 
of  Bulk 
approx. 
ZSOcc ... 


shall  be  used  in 


benzine  not   lighter  than  62°B6. 
making  this  determination. 

29.  Method.— The  flask  shall  be  filled  with 
either  of  these  liquids  to  a  point  on  the  stem  between 
zero  and  1  c.c.  and  64  grams  of  cement,  of  the  same 
temperature  as  the  liquid,  shall  be  slowly  introduced, 
taking  care  that  the  cement  does  not  adhere  to  the 
inside  of  the  flask  above  the  liquid  and  to  free  the 
cement  from  air  by  rolling  the  flask  in  an  inclined 
position.  After  all  the  cement  is  introduced,  the 
level  of  the  liquid  will  rise  to  some  division  of  the 
graduated  neck;  the  difference  between  readings  is  the 
volume  displaced  by  64  grams  of  the  cement. 

The  specific  gravity  shall  then  be  obtained 
from  the  formula 


Specific  gravity 


Weight  of  cement  (grams) 


Displaced  volume  (c.c.) 

30.  The  flask,  during  the  operation,  shall  be 
kept  immersed  in  water,  in  order  to  avoid  variations 
in  the  temperature  of  the  liquid  in  the  flask,  which 
shall  not  exceed  0.5°C.  The  results  of  repeated  tests 
should  agree  within  0.01. 

31.  The  determination  of  specific  gravity  shall 
be  made  on  the  cement  as  received;  if  it  falls  below 
3.10,  a  second  determination  shall  be  made  after 
igniting  the  sample  as  described  in  Sect.  20. 

IX.  Determination  of  Fineness 


Have  two  9.1  cc 
Graduations  extend 
above  I  and 

below  0 Mark- 


32.  Apparatus. — Wire  cloth  for  standard  sieves 

for  cement  shall  be  woven  (not  twilled)  from  brass, 
bronze,  or  other  suitable  wire,  and  mounted  without 
distortion  on  frames  not  less  than  in.  below  the  top 
of  the  frame.  The  sieve  frames  shall  be  circular,  ap- 
proximately 8  in.  in  diameter,  and  may  be  provided 
with  a  pan  and  cover. 

33.  A  standard  No.  200  sieve  is  one  having 
nominally  an  0.0029-in.  opening  and  200  wires  per 
inch  standardized  by  the  U.  S.  Bureau  of  Standards, 
and  conforming  to  the  following  requirements: 

The  No.  200  sieve  should  have  200  wires  per 
inch,  and  the  number  of  wires  in  any  whole  inch  shall 
not  be  outside  the  limits  of  192  to  208.  No  opening 
between  adjacent  parallel  wires  shall  be  more  than 
0.0050  in.  in  width.  The  diameter  of  the  wire  should 
be  0.0021  in.  and  the  average  diameter  shall  not  be 
outsiae  the  limits  0.0010  to  0.0023  in.  The  value  of 
the  sieve  as  determined  by  sieving  tests  made  in  con- 
formity with  the  standard  specification  for  these 
tests  on  a  standardized  cement  which  gives  a  residue 
of  25  to  20  %  .  on  the  No.  200  sieve,  or  on  other 
similarly  graded  material,  shall  not  show  a  variation  of  more  than  1.5%  above  or  below  the  standards  maintained 
at  the  Bureau  of  Standards. 

34.  Method. — The  test  shall  be  made  with  50  grams  of  cement.  The  sieve  shall  be  thoroughly  clean  and  dry. 
The  cement  shall  be  placed  on  the  No.  200  sieve,  with  pan  and  cover  attached,  if  desired,  and  shall  be  held  in  one 
hand  in  a  slightly  inclined  position  so  that  the  sample  will  be  well  distributed  over  the  sieve,  at  the  same  time  gently 
striking  the  side  about  150  times  per  minute  against  the  palm  of  the  other  hand  on  the  up  stroke.  The  sieve  shall 
be  turned  every  25  strokes  about  one-sixth  of  a  revolution  in  the  same  direction.  The  operation  shall  continue 
until  not  more  than  0.05  gram  passes  through  in  1  min.  of  continuous  sieving.  The  fineness  shall  be  determined 
from  the  weight  of  the  residue  on  the  sieve  expressed  as  a  percentage  of  the  weight  of  the  original  sample. 


j«-    9  cm 

Fig.  1. — LeChatelier  apparatus. 


APPENDIX  A 


837 


35.  Mechanical  sieving  devices  may  be  used,  but  the  cement  shall  not  be  rejected  if  it  meets  the  fineness 
requirement  when  tested  by  the  hand  method  described  in  Sect.  34. 

36.  Permissible  Variation. — A  permissible  variation  of  1  will  be  allowed,  and  all  results  in  excess  of  the  speci- 
fied limit  but  within  this  permissible  variation  shall  be  reported  as  22  %. 

X.  Mixing  Cement  Pastes  and  Mortars 

37.  Method. — The  quantity  of  dry  material  to  be  mixed  at  one  time  shall  not  exceed  1000  grams  nor  be  less 
than  500  grams.  The  proportions  of  cement  or  cement  and  sand  shall  be  stated  by  weight  in  grams  of  the  dry  ma- 
terials; the  quantity  of  water  shall  be  expressed  in  cubic  centimeters  (I  c.c.  of  water  =  1  gram).  The  dry  materials 
shall  be  weighed,  placed  upon  a  non-absorbent  surface,  thoroughly  mixed  dry  if  sand  is  used,  and  a  crater  formed  in 
the  center,  into  which  the  proper  percentage  of  clean  water  shall  be  poured;  the  material  on  the  outer  edge  shall  be 
turned  into  the  crater  by  the  aid  of  a  trowel.  After  an  interval  of  H  min.  for  the  absorption  of  the  water  the  opera- 
tion shall  be  completed  by  continuous,  vigorous  mixing,  squeezing  and  kneading  with  the  hands  for  at  least  1  min.i 

38.  The  temperature  of  the  room  and  the  mixing  water  shall  be  maintained  as  nearly  as  practicable  at  21°C. 
(70°F.). 


Fig.  2. — Vicat  apparatus. 

XI.  Normal  Consistency 


39.  Apparatus. — The  Vicat  apparatus  consists  of  a  frame  A  (Fig.  2)  bearing  a  movable  rod  B,  weighing  300 
grams,  one  end  C  being  1  cm.  in  diameter  for  a  distance  of  6  cm.,  the  other  having  a  removable  needle  D,  1  mm.  in 
diameter,  6  cm.  long.  The  rod  is  reversible,  and  can  be  held  in  any  desired  position  by  a  screw  E,  and  has  midway 
between  the  ends  a  mark  F  which  moves  under  a  scale  (graduated  to  millimeters)  attached  to  the  frame  A.  The 
paste  is  held  in  a  conical,  hard-rubber  ring  G,  7  cm.  in  diameter  at  the  base,  4  cm.  high,  resting  on  a  glass  plate  H 
about  10  cm.  square. 

1  In  order  to  secure  uniformity  in  the  results  of  tests  for  the  time  of  setting  and  tensile  strength  the  manner  of 
mixing  above  described  should  be  carefully  followed.  At  least  one  minute  is  necessary  to  obtain  the  desired  plastic- 
ity which  is  not  appreciably  affected  by  continuing  the  mixing  for  several  minutes.  The  exact  time  necessary  is 
dependent  upon  the  personal  equation  of  the  operator.  The  error  in  mixing  should  be  on  the  side  of  over  mixing. 
During  the  operation  of  mixing,  the  hands  should  be  protected  by  rubber  gloves. 


838 


CONCRETE  ENGINEERS'  HANDBOOK 


40.  Method. — In  making  the  determination,  500  grams  of  cement,  with  a  measured  quantity  of  water,  shall  be 
kneaded  into  a  paste,  as  described  in  Sect.  37,  and  quickly  formed  into  a  ball  with  the  hands,  completing  the  opera- 
tion by  tossing  it  six  times  from  one  hand  to  the  other,  maintained  about  6  in.  apart;  the  ball  resting  in  the  palm  of 
one  hand  shall  be  pressed  into  the  larger  end  of  the  rubber  ring  held  in  the  other  hand,  completely  filling  the  ring 
with  paste;  the  excess  at  the  larger  end  shall  then  be  removed  by  a  single  movement  of  the  palm  of  the  hand;  the 
ring  shall  then  be  placed  on  its  larger  end  on  a  glass  plate  and  the  excess  paste  at  the  smaller  end  sliced  off  at  the  top 
of  the  ring  by  a  single  oblique  stroke  of  a  trowel  held  at  a  slight  angle  with  the  top  of  the  ring.  During  these  opera- 
tions care  shall  be  taken  not  to  compress  the  paste.  The  paste  confined  in  the  ring,  resting  on  the  plate,  shall  be 
placed  under  the  rod,  the  larger  end  of  which  shall  be  brought  in  contact  with  the  surface  of  the  paste;  the  scale  shall 
be  then  read,  and  the  rod  quickly  released.  The  paste  shall  be  of  normal  consistency  when  the  rod  settles  to  a  point 
10  mm.  below  the  original  surface  in  \2  min.  after  being  released.  The  apparatus  shall  be  free  from  all  vibrations 
during  the  test.  Trial  pastes  shall  be  made  with  varying  percentages  of  water  until  the  normal  consistency  is 
obtained.    The  amount  of  water  required  shall  be  expressed  in  percentage  by  weight  of  the  dry  cement. 

41.  The  consistency  of  standard  mortar  shall  depend  on  the  amount  of  water  required  to  produce  a  paste  of 
normal  consistency  from  the  same  sample  of  cement.  Having  determined  the  normal  consistency  of  the  sample,  the 
consistency  of  standard  mortar  made  from  the  same  sample  shall  be  as  indicated  in  Table  I,  the  values  being  in  per- 
centage of  the  combined  dry  weights  of  the  cement  and  standard  sand. 


Table  I. — Percentage  of  Water  for  Standard  Mortars 


Percentage  of  water 
for   neat  cement 
paste  of  normal 
consistency 

Percentage  of  water 
for  one  cement,  three 
standard  Ottawa 
sand 

Percentage  of  water 
for  neat  cement 
paste  of  normal 
consistency 

Percentage  of  water 
for  one  cement, 
three  standard  Ottawa 
sand 

15 

9.0 

23 

10.3 

16 

9.2 

24 

10.5 

17 

9.3 

25 

10.7 

18 

9.5 

26 

10.8 

19 

9.7 

27 

11.0 

20 

9.8 

28 

11.2 

21 

10.0 

29 

11.3 

22 

10.2 

30 

11.5 

XII.  Determination  of  Soundness^ 

42.  Apparatus. — A  steam  apparatus,  which  can  be  maintained  at  a  temperature  between  98  arid  100°C.,  or 
one  similar  to  that  shown  in  Fig.  3,  is  recommended.  The  capacity  of  this  apparatus  may  be  increased  by  using 
a  rack  for  holding  the  pats  in  a  vertical  or  inclined  position. 

43.  Method. — A  pat  from  cement  paste  of  normal  consistency  about  3  in.  in  diameter,  in.  thick  at  the  cen- 
ter, and  tapering  to  a  thin  edge,  shall  be  made  on  clean  glass  plates  about  4  in.  square,  and  stored  in  moist  air  for  24 
hr.  In  molding  the  pat,  the  cement  paste  shall  first  be  flattened  on  the  glass  and  the  pat  then  formed  by  drawing 
the  trowel  from  the  outer  edge  toward  the  center. 

44.  The  pat  shall  then  be  placed  in  an  atmosphere  of  steam  at  a  temperature  between  98  and  100°C.  upon  a 
suitable  support  1  in.  above  boiling  water  for  5  hr. 

45.  Should  the  pat  leave  the  plate,  distortion  may  be  detected  best  with  a  straight-edge  applied  to  the  surface 
which  was  in  contact  with  the  plate. 

XIII.  Determination  of  Time  of  Setting 

46.  The  following  are  alternate  methods,  either  of  which  may  be  used  as  ordered: 

47.  Vicat  Apparatus. — The  time  of  setting  shall  be  determined  with  the  Vicat  apparatus  described  in  Sect. 
39  (see  Fig.  2). 

48.  Vicat  Method. — A  paste  of  normal  consistency  shall  be  molded  in  the  hard-rubber  ring  G  as  described  in 
Sect.  40,  and  placed  under  the  rod  B,  the  smaller  end  of  which  shall  then  be  carefully  brought  into  contact  with  the 
surface  of  the  paste,  and  the  rod  quickly  released.    The  initial  set  shall  be  said  to  have  occurred  when  the  needle 

1  Unsoundness  is  usually  manifested  by  change  in  volume  which  causes  distortion,  cracking,  checking  or 
disintegration. 

Pats  improperly  made  or  exposed  to  drying  may  develop  what  are  known  as  shrinkage  cracks  within  the 
first  24  hours  and  are  not  an  indication  of  unsoundness.    These  conditions  are  illustrated  in  Fig.  4. 

The  failure  of  the  pats  to  remain  on  the  glass  or  the  cracking  of  the  glass  to  which  the  pats  are  attached 
does  not  necessarily  indicate  unsoundness. 


APPENDIX  A 


839 


=1 

-1- 

C 


840 


CONCRETE  ENGINEERS'  HANDBOOK 


APPENDIX  A 


841 


ceases  to  pass  a  point  5  mm.  above  the  glass  plate  in  \i  min.  after  being  released;  and  the  final  set,  when  the  needle 
does  not  sink  visibly  into  the  paste.  The  test  pieces  shall  be  kept  in  moist  air  during  the  test.  This  may  be  accom- 
plished by  placing  them  on  a  rack  over  water  contained  in  a  pan  and  covered  by  a  damp  cloth,  kept  from  contact 
with  them  by  means  of  a  wire  screen;  or  they  may  be  stored  in  a  moist  closet.  Care  shall  be  taken  to  keep  the 
needle  clean,  as  the  collection  of  cement  on  the  sides  of  the  needle  retards  the  penetration,  while  cement  on  the  point 
may  increase  the  penetration.  The  time  of  setting  is  affected  not  only  by  the  percentage  and  temperature  of  the 
water  used  and  the  amount  of  kneading  the  paste  receives,  but  by  the  temperature  and  humidity  of  the  air,  and  its 
determination  is  therefore  only  approximate. 

49.  Gillmore  Needles. — The  time  of  setting  shall  be  determined  by  the  Gillmore  needles.  The  Gillmore 
needles  should  preferably  be  mounted  as  shown  in  Fig.  56. 


(a)  Pat  with  top  surface  flattened  for  determining  time  of  setting  by  Gilmore  method. 


'^/////////yy/y//////////////////////////////////^^^ 

(b)  Gillmore  Needles. 
Fig.  5. 


60.  Gillmore  Method. — The  time  of  setting  shall  be  determined  as  follows:  A  pat  of  neat  cement  paste  about 
3  in.  in  diameter  and  l-i  in.  in  thickness  with  a  flat  top  Fig.  5a,  mixed  to  a  normal  consistency,  shall  be  kept  in 
moist  air  at  a  temperature  maintained  as  nearly  as  practicable. at  21°C.  (70°F.).  The  cement  shall  be  considered  to 
have  acquired  its  initial  set  when  the  pat  will  bear,  without  appreciable  indentation,  the  Gillmore  needle  H2  in.  in 
diameter,  loaded  to  weigh  H  lb.  The  final  set  has  been  acquired  when  the  pat  will  bear  without  appreciable  inden- 
tation, the  Gillmore  needle  l^i  in.  in  diameter,  loaded  to  weigh  1  lb.  In  making  the  test,  the  needles  shall  be  held 
in  a  vertical  position,  and  applied  lightly  to  the  surface  of  the  pat. 


XIV.  Tension  Tests 

61.  Form  of  Test  Piece. — The  form  of  test  piece  shown  in  Fig.  6  shall  be  used.  The  molds  shall  be  made  of 
non-corroding  metal  and  have  sufficient  material  in  the  sides  to  prevent  spreading  during  molding.  Gang  molds 
when  used  shall  be  of  the  type  shown  in  Fig.  7.    Molds  shall  be  wiped  with  an  oily  cloth  before  using. 

62.  Standard  Sand. — The  sand  to  be  used  shall  be  natural  sand  from  Ottawa,  111.,  screened  to  pass  a  No.  20 
sieve  and  retained  on  a  No.  30  sieve.  This  sand  may  be  obtained  from  the  Ottawa  Silica  Co.,  at  a  cost  of  2  cts.  per 
lb.,  f.o.b.  cars,  Ottawa,  111. 


842 


CONCRETE  ENGINEERS'  HANDBOOK 


63.  This  sand,  having  passed  the  No.  20  sieve,  shall  be  considered  standard  when  not  more  than  5  grains  pass 
the  No.  30  sieve  after  1  min.  continuous  sieving  of  a  .500-grain  sample. 

64.  The  sieves  shall  conform  to  the  following  specifications: 

The  No.  20  sieve  shall  have  between  19.5  and  20.5  wires  per  whole  inch  of  the  warp  wires  and  between  19  and 
21  wires  per  whole  inch  of  the  shoot  wires.  The  diameter  of  the  wire  should  be  0.0165  in.  and  the  average  diameter 
shall  not  be  outside  the  limits  of  0.0160  and  0.0170  in. 


Fig.  6. — Details  for  briquette. 


Fig.  7. — Gang  mold. 


The  No.  30  sieve  shall  have  bteween  29.5  and  30.5  wires  per  whole  inch  of  the  warp  wires  and  between  28.5 
and  31.5  wires  per  whole  inch  of  the  shoot  wires.  The  diameter  of  the  wire  should  be  0.0110  in.  and  the  average 
diameter  shall  not  be  outside  the  limits  0.0105  to  0.0115  in. 

65.  Molding. — Immediately  after  mixing,  the  standard  mortar  shall  be  placed  in  the  molds,  pressed  in  firmly 
with  the  thumbs  and  smoothed  off  with  a  trowel  without  ramming.  Additional  mortar  shall  be  heaped  above  the 
mold  and  smoothed  off  with  a  trowel ;  the  trowel  shall  be  drawn  over  the  mold  in  such  a  manner  as  to  exert  a  moder- 
ate pressure  on  the  material.  The  mold  shall  then  be  turned  over  and  the  operation  of  heaping,  thumbing  and 
smoothing  off  repeated. 


APPENDIX  A 


843 


66.  Testing. — Tests  shall  be  made  with  any  standard  machine.  The  briquettes  shall  be  tested  as  soon  as  they 
are  removed  from  the  water.  The  bearing  surfaces  of  the  clips  and  briquettes  shall  be  free  from  grains  of  sand  or 
dirt.    The  briquettes  shall  be  carefully  centered  and  the  load  applied  continuously  at  the  rate  of  600  lb.  per  min. 

67.  Testing  machines  should  be  frequently  calibrated  in  order  to  determine  their  accuracy. 

58.  Faulty  Briquettes. — Briquettes  that  are  manifestly  faulty,  or  which  give  strengths  differing  more  than 
15%  from  the  average  value  of  all  test  pieces  made  from  the  same  sample  and  broken  at  the  same  period,  shall  not 
be  considered  in  determining  the  tensile  strength. 

XV.  Storage  of  Test  Pieces 

69.  Apparatus. — The  moist  closet  may  consist  of  a  soapstone,  slate  or  concrete  box,  or  a  wooden  box  lined  with 
metal.  If  a  wooden  box  is  used,  the  interior  should  be  covered  with  felt  or  broad  wicking  kept  wet.  The  bottom  of 
the  moist  closet  should  be  covered  with  water.  The  interior  of  the  closet  should  be  provided  with  non-absorbent 
shelves  on  which  to  place  the  test  pieces,  the  shelves  being  so  arranged  that  they  may  be  withdrawn  readily. 

60.  Methods. — Unless  otherwise  specified,  all  test  pieces,  immediately  after  molding,  shall  be  placed  in  the 
moist  closet  for  from  20  to  24  hr. 

61.  The  briquettes  shall  be  kept  in  molds  on  glass  plates  in  the  moist  closet  for  at  least  20  hr.  After  24  hr.  in 
moist  air  the  briquettes  shall  be  immersed  in  clean  water  in  storage  tanks  of  non-corroding  material. 

62.  The  air  and  water  shall  be  maintained  as  nearly  as  practicable  at  a  temperature  of  21*^0.  (70**F.). 


APPENDIX  B 


WORKING  STRESSES  1 

1.  General  Assumptions. — The  following  working  stresses  are  recommended  for  static  loads.  Proper  allow- 
ances for  vibration  and  impact  are  to  be  added  to  live  loads  where  necessary  to  produce  an  equivalent  static  load 
before  applying  the  unit  stresses  in  proportioning  parts. 

In  selecting  the  permissible  working  stress  on  concrete,  the  designer  should  be  guided  by  the  working  stresses 
usually  allowed  for  other  materials  of  construction,  so  that  all  structures  of  the  same  class  composed  of  different 
materials  may  have  approximately  the  same  degree  of  safety. 

The  following  recommendations  as  to  allowable  stresses  are  given  in  the  form  of  percentages  of  the  ultimate 
strength  of  the  particular  concrete  which  is  to  be  used;  this  ultimate  strength  is  that  developed  at  an  age  of  28 
days,  in  cylinders  8  in.  in  diameter  and  16  in.  long,  of  the  consistency  described, 2  made  and  stored  under  laboratory 
conditions.  In  the  absence  of  definite  knowledge  in  advance  of  construction  as  to  just  what  strength  may  be 
expected,  the  Committee  submits  the  following  values  as  those  which  should  be  obtained  with  materials  and  work- 
manship in  accordance  with  the  recommendations  of  this  report. 

Although  occasional  tests  may  show  higher  results  than  those  here  given,  the  Committee  recommends  that 
these  values  should  be  the  maximum  used  in  design. 

Table  of  Compressive  Strengths  of  Different  Mixtures  of  Concrete 
(In  Pounds  per  Square  Inch) 


Aggregate 

1  :  3* 

1  :  4U* 

1  :  G* 

1  -.IVi* 

1  :  9* 

Granite,  trap  rock  

3,300 

2,800 

2,200 

1,800 

1,400 

Gravel,  hard  limestone  and  hard 

3,000 

2,500 

2,000 

1,000 

1,300 

Soft  limestone  and  sandstone.  .  .  . 

2,200 

1,800 

1,500 

1,200 

1,000 

800 

700 

600 

500 

400 

Note. — For  variations  in  the  moduli  of  elasticity  see  Sect.  8. 

*  Combined  volume  fine  and  coarse  aggregate  measured  separately. 


2.  Bearing. — When  compression  is  applied  to  a  surface  of  concrete  of  at  least  twice  the  loaded  area,  a  stress 
of  35%  of  the  compressive  strength  may  be  allowed  in  the  area  actually  under  load. 

3.  Axial  Compression. —  (a)  For  concentric  compression  on  a  plain  concrete  pier,  the  length  of  which  does 
not  exceed  4  diameters,  or  on  a  column  reinforced  with  longitudinal  bars  only,  the  length  of  which  does  not  exceed 
12  diameters,  22.5%  of  the  compressive  strength  may  be  allowed. 

(6)  Columns  with  longitudinal  reinforcement  to  the  extent  of  not  less  than  1  %  and  not  more  than  4  % 
and  with  lateral  ties  of  not  less  than  \i  in.  in  diameter,  12  in.  apart,  nor  more  than  16  diameters  of  the  longitudinal 
bar:  the  unit  stress  recommended  for  (a). 

(c)  Columns  reinforced  with  not  less  than  1%  and  not  more  than  4%  .  of  longitudinal  bars  and  with 
circular  hoops  or  spirals  not  less  than  1  %  of  the  volume  of  the  concrete  and  as  hereinafter  specified  :3  a  unit 
stress  55%  higher  than  given  for  (a),  provided  the  ratio  of  unsupported  length  of  column  to  diameter  of  the 
hooped  core  is  not  more  than  10. 

4.  Compression  in  Extreme  Fiber. — The  extreme  fiber  stress  of  a  beam,  calculated  on  the  assumption  of  a 
constant  modulus  of  elasticity  for  concrete  under  working  stresses  may  be  allowed  to  reach  32.5%  of  the  compres- 
sive strength.    Adjacent  to  the  support  of  continuous  beams,  stresses  15%  higher  may  be  used. 

5.  Shear  and  Diagonal  Tension. — In  calculations  on  beams  in  which  the  maximum  shearing  stress  in  a  sec- 
tion is  used  as  the  means  of  measuring  the  resistance  to  diagonal  tension  stress,  the  following  allowable  values  for 
the  maximum  vertical  shearing  stress  in  concrete,  calculated  by  the  method  given  in  formula  (22)^  are  recommended: 

1  From  Final  Report  of  the  Special  Committee  on  Concrete  and  Reinforced  Concrete  of  the  American  Society 
of  Civil  Engineers,  presented  before  the  Society,  Jan.  17,  1917. 

2  The  materials  should  be  mixed  wet  enough  to  produce  a  concrete  of  such  a  consistency  as  will  flow  sluggishly 
into  the  forms  and  about  the  metal  reinforcement  when  used,  and  which,  at  the  same  time,  can  be  conveyed  from 
the  mixer  to  the  forms  without  separation  of  the  coarse  aggregate  from  the  mortar.  The  quantity  of  water  is  of 
the  greatest  importance  in  securing  concrete  of  maximum  strength  and  density;  too  much  water  is  as  objectionable 
as  too  little. 

3  Sec  Art.  7,  Sect.  8. 

T 


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(a)  For  beams  with  horizontal  bare  only  and  without  web  reinforcement,  2%  of  the  compressive 
strength. 

(6)  For  beams  with  web  reinforcement  consisting  of  vertical  stirrups  looped  about  the  longitudinal  reinforcing 
bars  in  the  tension  side  of  the  beam  and  spaced  horizontally  not  more  than  one-half  the  depth  of  the  beam;  or  for 
beams  in  which  longitudinal  bars  are  bent  up  at  an  angle  of  not  more  than  45  deg.  or  less  than  20  deg.  with  the 
axis  of  the  beam,  and  the  points  of  bending  are  spaced  horizontally  not  more  than  three-quarters  of  the  depth  of  the 
beam  apart,  not  to  exceed  of  the  compressive  strength. 

(c)  For  a  combination  of  bent  bars  and  vertical  stirrups  looped  about  the  reinforcing  bars  in  the  tension 
side  of  the  beam  and  spaced  horizontally  not  more  than  one-half  of  the  depth  of  the  beam,  5%  of  the  compressive 
strength. 

id)  For  beams  with  web  reinforcement  (either  vertical  or  inclined)  securely  attached  to  the  longitudinal 
bars  in  the  tension  side  of  the  beam  in  such  a  way  as  to  prevent  slipping  of  bar  past  the  stirrup,  and  spaced  hori- 
zontally not  more  than  one-half  of  the  depth  of  the  beam  in  case  of  vertical  stirrups  and  not  more  than  three- 
fourths  of  the  depth  of  the  beam  in  the  case  of  inclined  members,  either  with  longitudinal  bars  bent  up  or  not, 
6%  of  the  compressive  strength. 

The  web  reinforcement  in  case  any  is  used  should  be  proportioned  by  using  two-thirds  of  the  external  vertical 
shear  in  formulas  (24) i  or  (25). 2  The  effect  of  longitudinal  bars  bent  up  at  an  angle  of  from  20  to  45  deg.  with  the 
axis  of  the  beam,  may  be  taken  at  sections  of  the  beam  in  which  the  bent-up  bars  contribute  to  diagonal  tension 
resistance,  as  defined  under  Chap.  VII,  Sect.  8,  as  reducing  the  shearing  stresses  to  be  otherwise  provided  for. 
The  amount  of  reduction  of  the  shearing  stress  by  means  of  bent-up  bars  will  depend  upon  their  capacity,  but  in 
no  case  should  be  taken  as  greater  than  4J4%  of  the  compressive  strength  of  the  concrete  over  the  effective  cross- 
section  of  the  beam  (formula  22). 3  The  limit  of  tensile  stress  in  the  bent-up  portion  of  the  bar  calculated  by 
formula  (25), 2  using  in  this  formula  an  amount  of  total  shear  corresponding  to  the  reduction  in  shearing  stress 
assumed  for  the  bent-up  bars,  may  be  taken  as  specified  for  the  working  stress  of  steel,  but  in  the  calculations 
the  stress  in  the  bar  due  to  its  part  as  longitudinal  reinforcement  of  the  beam  should  be  considered.  The  stresses 
in  stirrups  and  inclined  members  when  combined  with  bent-up  bars  are  to  be  determined  by  finding  the  amount 
of  the  total  shear  which  may  be  allowed  by  reason  of  the  bent-up  bars,  and  subtracting  this  shear  from  the  total 
external  vertical  shear.  Two-thirds  of  the  remainder  will  be  the  shear  to  be  carried  by  the  stirrups,  using  formulas 
(24)1  or  (25)2. 

Where  punching  shear  occurs,  provided  the  diagonal  tension  requirements  are  met,  a  shearing  stress  of  6% 
of  the  compressive  strength  may  be  allowed. 

6.  Bond. — The  bond  stress  between  concrete  and  plain  reinforcing  bars  may  be  assumed  at  4%  of  the  com- 
pressive strength,  or  2  %  in  the  case  of  drawn  wire.  In  the  best  types  of  deformed  bar,  the  bond  stress  may  be 
increased,  but  not  to  exceed  5  %  of  the  compressive  strength  of  the  concrete. 

7.  Reinforcement. — The  tensile  or  compressive  stress  in  steel  should  not  exceed  16,000  lb.  per  sq.  in. 

In  structural  steel  members,  the  working  stresses  adopted  by  the  American  Railway  Engineering  Association 
are  recommended. 

8.  Modulus  of  Elasticity. — The  value  of  the  modulus  of  elasticity  of  concrete  has  a  wide  range,  depending 
on  the  materials  used,  the  age,  the  range  of  stresses  between  which  it  is  considered,  as  well  as  other  conditions. 
It  is  recommended  that,  in  computations  for  the  position  of  the  neutral  axis,  and  for  the  resisting  moment  of  beams, 
and  for  compression  of  concrete  in  columns,  it  be  assumed  as: 

(a)  One-fortieth  that  of  steel,  when  the  strength  of  the  concrete  is  taken  as  not  more  than  800  lb.  per  sq.  in. 

(b)  One-fifteenth  that  of  steel,  when  the  strength  of  the  concrete  is  taken  as  greater  than  800  lb.  per  sq.  in. 
and  less  than  2200  lb.  per  sq.  in. 

(c)  One-twelfth  that  of  steel,  when  the  strength  of  the  concrete  is  taken  as  greater  than  2200  lb.  per  sq.  in 
and  less  than  2900  lb.  per  sq.  in.,  and 

{d)  One-tenth  that  of  steel,  when  the  strength  of  the  concrete  is  taken  as  greater  than  2900  lb.  per  sq.  in. 

Although  not  rigorously  accurate,  these  assumptions  will  give  safe  results.  For  the  deflection  of  beams 
which  are  free  to  move  longitudinally  at  the  supports,  in  using  formulas  for  deflection  which  do  not  take  into  account 
the  tensile  strength  developed  in  the  concrete,  a  modulus  of  one-eighth  of  that  of  steel  is  recommended. 

1  Vertical  web  reinforcement, 

jd 

2  Bars  bent  up  at  angles  between  20  and  45  deg.  with  the  horizontal  and  web  members  inclined  at  45  deg., 

A  jd 

(See  Standard  Notation,  Appendix  D.) 
V 

~  bjd' 


APPENDIX  C 


RULINGS  PERTAINING  TO  FLAT-SLAB  DESIGN 

Rulings  have  been  adopted  by  the  Cities  of  Pittsburgh  and  Chicago,  by  a  Special  Committee  of  the  American. 
Society  of  Civil  Engineers,  and  by  the  American  Concrete  Institute,  for  the  regulation  of  the  design  of  fiat-slab 
floors.  These  rulings  are  given  below.  Rulings  have  been  adopted  by  other  cities  which  are  of  merit,  but  those 
of  Pittsburgh  and  Chicago  have  been  most  widely  used  and  properly  applied  have  given  satisfactory  results. 

The  ruling  of  the  American  Concrete  Institute  is  in  many  respects  similar  to  that  of  the  City  of  Chicago, 
while  the  Report  of  the  Special  Committee  of  the  American  Society  is  similar  as  to  method  but  more  conservative 
as  to  reinforcement,  and  in  the  light  of  all  the  test  data  available  would  seem  to  be  in  some  respects  ultra  conservative. 

For  the  method  of  application  and  a  comparison  of  designs,  the  reader  is  referred  to  Art,  20,  Sect,  11,  page 

487. 

RULING  ON  THE  DESIGN  OF  CANTILEVER  FLAT-SLAB  CONSTRUCTION  IN 
THE  CITY  OF  PITTSBURGH 

General. — The  design  and  construction  of  reinforced-concrete  flat  slabs  shall  be  carried  out  strictly  in  accord- 
ance with  all  the  provisions  of  the  ordinance  "Authorizing  and  Regulating  the  Use  of  Concrete  and  Reinforced 
Concrete  in  the  City  of  Pittsburgh,"  with  special  reference  to  Sect.  2,  heading  "Special  Systems  not  Covered  by 
this  Ordinance." 

Reason  for  Ruling. — Since  there  has  been  a  number  and  are  likely  to  be  more  applications  for  building  per- 
mits, in  which  it  is  proposed  to  employ  the  flat-slab  construction,  and  since  there  have  been  proposed  several  differ- 
ent proprietary  systems,  it  has  become  advisable  to  set  forth  a  ruling  with  which  each  one  must  conform,  and  which 
will  state  the  interpretation  of  the  ordinance  and  all  its  clauses  which  might  relate  to  flat-slab  construction  as 
made  by  this  Bureau. 

The  ruling  is  expected  to  provide  uniformity  of  the  requirements  among  the  several  systems  and  equity 
between  them  in  preparing  designs,  and  to  so  regulate  their  design  and  construction  that  they  will  be  conducted 
under  correct  principles  and  in  conformity  with  the  spirit  of  the  ordinance. 

Statement. — Inasmuch  as  the  above-mentioned  clause  of  the  ordinance  specified  that  the  tests  shall  be  made 
to  a  breaking  load  in  order  to  determine  a  factor  of  safety  of  4,  for  loads  for  which  the  structure  is  planned,  a  state- 
ment should  be  made  to  explain  the  reason  for  placing  the  ruling  in  its  following  form. 

On  account  of  the  practical  impossibility  of  so  conducting  a  breaking  load  test  that  it  would  provide  a  basis 
for  a  complete  analysis  which  will  prove  the  above  required  factor  for  safety  and  at  the  same  time  serve  as  a  con- 
vincing guide  in  the  proper  analysis  for  safe  design  and  construction,  as  well  as  omitting  to  require  a  severe, 
expensive  and  improper  test  which  would  not  afford  sufficient  or  consistent  information,  it  has  been  formally 
decided  that: 

First. — The  tests  shall  have  been  conducted  in  such  a  manner  as  to  demonstrate  what  are  the  actual  strains 
in  the  materials  at  the  time  working  conditions  are  imposed  upon  the  structure.  This  should  also  demonstrate 
clearly  the  effect  of  an  uneven  or  partial  distribution  of  design  loading,  and  that  such  loads  will  not  cause  the  strains 
in  the  materials  to  become  substantially  greater  than  those  allowed  for  ordinary  working  conditions,  and  that  an 
unusual  load  or  uncertainties  of  manufacture  and  installation  of  building  materials  will  not  result  in  weakness 
or  unsatisfactory  result. 

Second. — The  test  should  be  conducted  in  such  a  manner  as  to  bring  to  light  the  relation  which  exists  between 
the  strength  of  construction  designed  according  to  the  provisions  of  the  ordinance,  and  according  to  the  provisions 
of  this  ruling,  and  to  show  that  all  proper  considerations  have  been  provided  for,  therein. 

Further,  it  is  being  understood  that  it  is  the  intention  of  the  ordinance  to  provide  for  safety  of  building  con- 
struction and  equity  among  the  different  systems,  it  is  decided  that  the  requirements  for  all  special  systems  as  to 
strains  in  the  materials  shall  be  the  same  as  for  ordinary  construction  as  provided  in  the  ordinance. 

In  view  of  the  above  reasoning,  reports  of  strain-gage  tests  made  by  disinterested  laboratories  and  testing 
engineers  from  which  it  is  possible  to  derive  formulas,  have  been  accepted  and  studied  as  they  were  submitted  by 
applicants.  Inasmuch  as  the  tests  herein  submitted  have  been  conducted  upon  structures  varying  somewhat 
from  those  designed  and  built  under  this  ruling,  in  the  matter  of  strength,  and  as  there  are  matters  to  be  deter- 
mined under  this  ruling,  which  have  so  far  not  been  determined  under  this  ruling,  which  have  so  far  not  been  de- 
termined by  test,  it  is  sufficient  that  tests  be  conducted  to  determine: 

First,  the  bending  strains  to  which  columns  are  subject  within  the  interior  of  the  structure  as  well  as  at  the 

walls. 

Second,  the  proper  percentage  of  increase  in  strength  which  should  be  provided  in  outer  floor  panels  or  wall 
columns  over  that  for  interior  construction,  and  for  the  effect  upon  the  structure  of  uneven  or  partial  distribution 
of  floor  loading,  such  as  placing  the  load  between  two  rows  of  columns  stretching  clear  across  the  structure  than  on 

847 


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CONCRETE  ENGINEERS'  HANDBOOK 


interior  or  exterior  panels.  If  it  should  be  disclosed  by  such  test  that  any  provision  of  this  ruling  is  too  severe  or 
not  severe  enough,  the  ruling  will  be  promptly  revised  only  in  so  far  as  thus  indicated. 

Finally,  it  is  herein  determined  that  all  systems  admitted  under  this  ruling  shall  have  passed  a  strain-gage 
test  to  demonstrate  its  abihty  to  conform  to  the  requirements  of  this  ruling  before  any  further  construction  work 
can  be  passed  to  a  permit. 

If  it  should  be  decided  by  all  parties  interested  to  conduct  jointly  one  complete  loading  test  which  will  also 
be  in  all  respects  satisfactory  to  this  Bureau,  this  test  would  be  considered  sufficient  to  allow  all  systems  to  be  con- 
structed without  further  test. 

It  being  noted  that  the  only  additional  information  necessary  will  concern  especially  the  points  of  uncertainty 
described  immediately  preceding.  And  that  additional  tests  will  not  be  requested  by  this  Bureau  of  those  whose 
systems  are  now  approved.  Tests  by  those  whose  systems  are  now  approved  will  only  be  considered  necessary 
whenever  these  requirements  are  objected  to  by  applicants  as  being  too  severe  in  the  above-mentioned  points. 

Flat  slabs  as  understood  by  this  ruling  shall  consist  of  reinforced-concrete  columns  with  enlarged  capitals 
on  which  is  supported  a  flat  reinforced  slab  floor  with  or  without  plates  or  depressed  panels  at  the  column  cap. 
The  construction  may  be  such  as  to  admit  the  use  of  hollow  panels  in  the  ceiling  or  smooth  ceiling  with  depressed 
panel  in  the  floor  at  the  column  cap. 

The  column  capital  shall  be  defined  as  the  gradual  flaring  out  of  the  column  without  any  marked  offset  in 
the  concrete. 

The  depressed  panel  shall  be  defined  as  a  square,  rectangular  or  approximately  circular  depression  around 
the  column  capital  extending  below  the  adjacent  slab. 

The  panel  length  shall  be  defined  as  the  distance  center  to  center  of  column  of  the  side  of  a  square  panel, 
and  the  panel  length  and  breadth  of  a  rectangular  panel  as  the  distance  center  to  center  of  column  in  the  long  and 
short  directions  respectively.  The  span  length  being  defined  as  the  distance  in  the  clear  from  edge  to  edge  of 
column  cap  where  it  intersects  either  the  floor  slab  or  the  depressed  panel,  measured  on  the  length  or  breadth  of 
the  panel  as  the  case  may  be. 

Requirements 

Stresses. — All  unit  stresses  shall  be  as  specified  in  the  ordinance  governing  the  use  of  concrete  and  reinforced 
concrete.  The  resisting  moment  and  coincident  stresses  shall  be  computed  under  the  assumption  set  forth  in 
the  ordinance. 

W  U 

Moments. — The  negative  bending  moment  at  the  support  shall  be  taken  — jj—  in  which  W  equals  the  total 

load  on  one  panel  exclusive  of  any  load  within  the  area  of  the  column  capital,  and  L'  is  the  clear  span  between 
column  capitals  measured  along  the  side  of  the  panel. 

WL 

The  positive  moment  at  the  center  of  the  panel  shall  be  taken  as  -jg-  in  which  W  is  the  total  load  on  a  panel 
and  L  the  distance  center  to  center  of  columns  measured  along  the  side  of  the  panel. 

Resisting  Sections. — The  negative  moment  at  the  support  shall  be  considered  as  acting  on  a  vertical  section 
passing  through  the  slab  along  the  periphery  of  the  column  capital.  The  compressive  stress  in  the  concrete  on 
this  section  shall  be  calculated  by  the  ordinary  straight  line  assumptions  of  stress  distribution,  by  the  formulas 
given  in  the  ordinance,  taking  the  periphery  of  the  column  capital,  as  the  width  of  the  section  and  the  depth  from 
the  lower  face  of  the  concrete  adjoining  the  column  capital  to  the  center  of  gravity  of  the  slab  steel  as  the  depth 
of  the  section. 

The  area  of  slab  steel  resisting  the  negative  moment  of  — —  at  the  support  shall  be  taken  as  the  total  section 
of  all  slab  rods  cutting  a  conical  critical  section  starting  at  the  periphery  of  the  column  capital  and  flaring  outwards 
at  a  45-deg.  angle  with  the  vertical.  The  spacing  of  rods  thus  determined  for  the  width  of  the  critical  section  shall 
be  maintained  for  the  full  width  of  the  bands. 

The  positive  moment  at  the  center  shall  be  resisted  by  the  steel  and  concrete  cut  by  a  vertical  critical  section 
through  the  slab  having  its  center  at  the  column  center  and  its  diameter  equal  to  the  main  dimension  of  the  sides 
of  the  panel. 

Drop  Construction. — The  thickness  of  the  slab  adjacent  to  the  column  capital  may  be  increased,  if  necessary, 
by  means  of  a  depending  concrete  drop  panel  centered  on  the  column  center.  Where  this  drop  panel  is  used  the 
resisting  nioment^f  the  slab  at  the  periphery  of  the  drop  shall  be  not  less  than  that  calculated  from  the  formula 

(lY     2L'  "~  which  W  and  L'  are  as  defined  above  and  X  is  the  distance  between  the  edge  of  the  column 

capital  and  circle  of  area  equal  to  that  of  the  drop  used.  This  drop  panel  may  be  diminished  in  thickness  at  greater 
distance  from  the  column  capital  if  desired  provided  the  resisting  moment  at  any  section  shall  not  fall  below  the 
value  determined  by  the  above  formula  applied  to  that  particular  section. 

Columns. — The  columns  shall  be  calculated  for  the  unbalanced  moment  of  the  live  floor  load  when  the  entire 
area  in  one  side  of  a  fine  through  the  column  center  is  considered  as  loaded  and  the  area  on  the  other  side  unloaded. 
The  live-load  reaction  producing  this  moment  shall  be  considered  as  uniformly  distributed  along  the  periphery 
of  the  column  capital. 

Distribution  of  Slab  Steel. — The  computed  area  of  steel  per  unit  width  of  band  determined  from  the  moment 
at  the  support  shall  be  maintained  the  same  for  the  entire  width  of  each  band.  Width  of  bands  shall  be  sufficient 
to  cause  the  whole  area  of  the  panel  to  be  covered  by  reinforcing  bars.    The  total  steel  area  as  determined  from  the 


APPENDIX  C 


849 


computations  may  be  distributed  equally  between  all  the  bands  or  somewhat  more  than  one-half  may  be  placed 
in  the  direct  bands.  In  no  case,  however,  shall  the  steel  area  of  direct  bands  exceed  that  in  diagonal  bands  by 
more  than  one-third  for  square  panels. 

Rectangular  Panels. — The  slab  thicknesses  and  the  steel  area  in  the  various  bands  shall  be  determined  in 
rectangular  panels  by  computations  based  on  a  square  panel  of  the  same  dimensions.  The  steel  area  in  the  long 
direct  band  shall  be  that  required  in  the  same  band  if  situated  on  the  edge  of  a  square  panel  of  the  long  dimensions 
in  size.  The  steel  area  in  the  short  direct  band  shall  be  that  required  in  the  same  band  if  situated  on  the  edge  of 
a  square  panel  of  the  short  dimension  in  size. 

The  steel  area  in  the  diagonal  bands  shall  be  that  required  in  the  same  band  if  situated  diagonally  in  a  square 
panel  whose  size  will  be  the  average  of  the  long  and  short  dimensions. 

W'L' 

Profile  of  Column  Capital. — The  profile  of  the  column  capital  shall  satisfy  the  moment  of  at  any  con- 

centric vertical  section  through  it  and  the  slab,  the  value  of  TF'  and  L'  being  taken  for  the  particular  section 
considered. 

Moments  in  Wall  Panels. — The  bending  moment  to  be  resisted  by  any  band  of  reinforcing  extending  into 
an  exterior  panel  shall  be  increased  by  20%  if  concrete  column  supports  are  present  at  the  wall,  and  by  40%  if 
the  slab  rests  on  a  brick  wall  at  its  exterior  edge. 

Concentrated  Loads. — Girders  and  beams  shall  be  provided  where  necessary  to  carry  concentrated  loads 
in  excess  of  the  safe  capacity  of  the  floor  slab.  Such  girders  and  beams  shall  be  calculated  to  carry  the  full  con- 
centrated load.  * 

Openings  Cut  in  Floors. — Girders  and  beams  shall  be  provided  on  all  sides  of  the  opening  wherever  there  are 
openings  or  holes  in  the  slab.    They  shall  be  calculated  to  carry  the  reaction  of  the  floor  on  all  sides  of  the  openings. 

RULING  COVERING  DESIGN  OF  FLAT-SLAB  CONSTRUCTION  IN  THE 

CITY  OF  CHICAGO 

(For  ruling  as  amended  Jan.  1,  1918,  see  page  851.) 

1.  Definitions. — Flat  slabs  as  understood  by  this  ruling  are  reinforced-concrete  slabs  supported  directly 
on  reinforced  columns  with  or  without  plates  or  capitals  at  the  top,  the  whole  coastruction  being  hingeless  and  mono- 
lithic without  any  visible  beams  or  girders.  The  construction  may  be  such  as  to  admit  the  use  of  hollow  panels 
in  the  ceiling  or  smooth  ceiling  with  depressed  panels  in  the  floor. 

2.  The  column  capital  shall  be  defined  as  the  gradual  flaring  out  of  the  top  of  the  column  without  any  marked 

offset. 

3.  The  drop  panel  shall  be  defined  as  a  square  or  rectangular  depression  around  the  column  capital  extending 
below  the  slab  adjacent  to  it. 

4.  The  panel  length  shall  be  defined  as  the  distance  center  to  center  of  columns  of  the  side  of  a  square  panel, 
or  the  average  distance  center  to  center  of  columns  of  the  long  and  short  sides  of  a  rectangular  panel. 

6.  Columns. — The  least  dimensions  of  any  concrete  column  shall  be  not  less  than  one-twelfth  the  panel 
length,  or  one-twelfth  the  clear  height  of  the  column. 

6.  Slab  Thickness. — The  minimum  total  thickness  of  the  slab  in  inches  shall  be  determined  by  the  formula: 

t  =  0.023L\/w 

where 

t  =  total  thickness  of  slab  in  inches. 
L  =  panel  length  in  feet. 

w  =  total  live  and  dead  load  in  pounds  per  square  foot. 

7.  In  no  case  shall  the  slab  thickness  be  less  than  one-thirty-second  of  the  panel  length  for  floors,  and  one- 
fortieth  of  the  panel  length  for  roofs,  and  also  not  less  than  6  in. 

8.  Column  Capital. — The  diameter  of  the  column  capital  shall  be  measured  where  its  vertical  thickness  is  at 
least  VA  in.,  and  shall  be  at  least  0.225  of  the  panel  length. 

9.  The  slope  of  the  column  capital  shall  nowhere  make  an  angle  with  the  vertical  of  more  than  45  deg.  Spe- 
cial attention  shall  be  given  to  the  design  of  the  column  capital  in  considering  eccentric  loads,  and  the  effect  of  wind 
upon  the  structure. 

10.  Drop  Panel. — The  depth  of  the  drop  shall  be  determined  by  computing  it  as  a  beam,  using  the  negative 
bending  moment  specified  elsewhere  in  this  ruling.  The  width  and  length  shall  be  determined  by  the  allowable 
unit  shearing  stresses  on  the  perimeter,  given  below. 

11.  Shearing  Stresses. — The  allowable  unit  punching  shear  on  the  perimeter  of  the  column  capital  shall  be 
three-fiftieths  of  the  ultimate  compressive  strength  of  the  concrete  as  given  in  Sect.  546  of  the  building  ordinance. 
The  allowable  unit  shear  on  the  perimeter  of  the  drop  panel  shall  be  three  one-hundredths  of  the  ultimate  compres- 
sive strength  of  the  concrete.  In  computing  shearing  stress  for  the  purpose  of  determining  the  resistance  to  diag- 
onal tension  the  method  specified  by  the  ordinance  shall  be  used. 

12.  Panel  Strips. — For  the  purpose  of  establishing  the  bending  moments  and  the  resisting  moments  of  a 
square  panel,  the  panel  shall  be  divided  into  strips  known  as  strip  A  and  strip  B.  Strip  A  shall  include  ihe  rein- 
forcement and  slab  in  a  width  extending  from  the  center  line  of  the  columns  for  a  distance  each  side  of  this  center 
line  equal  to  one-fourth  of  the  panel  length.    Strip  B  shall  include  the  reinforcement  and  slab  in  the  half  width  re- 

54 


850 


CONCRETE  ENGINEERS'  HANDBOOK 


maining  in  the  center  of  the  panel.  At  right  angles  to  these  strips,  the  panel  shall  be  divided  into  similar  strips  A 
and  B,  having  the  same  widths  and  relations  to  the  center  line  of  the  columns  as  the  above  strips.  These  strips 
shall  be  for  designing  purposes  only,  and  are  not  intended  as  the  boundary  lines  of  any  bands  of  steel  used. 

13.  These  strips  shall  apply  to  the  system  of  reinforcement  in  which  the  reinforcing  bars  are  placed  parallel 
and  at  right  angles  to  the  center  line  of  the  columns,  hereinafter  known  as  the  two-way  system,  and  also  to  the  sys- 
tem of  reinforcement  in  which  the  reinforcing  bars  are  placed  parallel,  at  right  angles  to  and  diagonal  to  the  center 
line  of  the  columns  hereinafter  known  as  the  four-way  system. 

Bending  Moment  Coefficients,  Interior  Panel,  Two-way  System 

14.  The  negative  bending  moment  taken  at  a  cross-section  of  each  strip  A  at  the  edge  of  a  column  capital  or 
over  it,  shall  be  taken  as  The  positive  bending  moment  taken  at  a  cross-section  of  each  strip  A,  midway 
between  column  centers  shall  be  taken  as  WL^/30.  The  positive  bending  moment  taken  at  a  cross-section  of  each 
strip  B  in  the  middle  of  the  panel  shall  be  taken  at  WL'^/60.  The  negative  bending  moment  taken  at  a  cross-sec- 
tion of  each  strip  B  on  the  center  line  of  the  columns  shall  be  taken  at  WL^/QO,    In  the  formulas  hereinabove  given 

W  =  total  live  and  dead  load  per  lineal  foot  of  each  strip. 
L   =  panel  length  in  feet. 

Bending  Moment  Coefficients,  Interior  Panel,  Four-way  System 

15.  The  negative  bending  moment  taken  at  a  cross-section  of  each  strip  A  at  the  edge  of  the  column  capital  or 
over  it,  shall  be  taken  as  WL^/ 15.  The  positive  bending  moment  taken  at  a  cross-section  of  each  strip  A,  midway 
between  column  centers  shall  be  taken  as  WL^/4:0.  The  positive  bending  moment  taken  at  a  cross-section  of  each 
strip  B  in  the  middle  of  the  panel  shall  be  taken  as  WL^/60,  The  negative  bending  moment  taken  at  a  cross-section 
of  each  strip  B  on  the  center  line  of  the  column  shall  be  taken  at  WL'^/GO. 

Bending  Moment  Coefficients,  Wall  Panels 

16.  Wherever  the  coefficients  Ms,  Ho,  Mo  or  \io  appear  in  the  moments  given  for  interior  panels  in  either  the 
two-way  or  the  four- way  systems,  the  coefficients  M2,  }/25,  Vzz  and  Ybo  respectively  shall  be  used  in  the  moments 
for  wall  panels  supported  on  concrete  columns  and  girders. 

17.  When  brick  walls  are  used  partly  to  support  wall  panels,  these  walls  shall  be  stiffened  by  pilasters  or  piers 
as  directed  by  the  Commissioner  of  Buildings.  Wherever  the  coefficients  Hs,  J^o,  Vio  or  Y^o  appear  in  the  mo- 
ments given  for  interior  panels  in  either  the  two-way  or  the  four-way  systems,  the  coefficients  Mo,  }^o,  Vii  and  Mq 
respectively  shall  be  used  in  the  moments  for  such  panels  resting  on  brick  walls. 

Point  of  Inflection 

18.  For  the  purpose  of  making  the  calculations  of  the  bending  moment  at  the  sections  away  from  the  column 
capital,  the  point  of  inflection  shall  be  considered  as  being  one-quarter  the  distance  center  to  center  of  columns,  both 
crosswise  and  diagonally,  from  the  center  of  the  column. 

Tensile  Stress  in  Steel  and  Compressive  Stress  in  Concrete 

19.  The  tensile  stress  in  steel  and  the  compressive  stress  in  the  concrete  to  resist  the  bending  moment  shall 
be  calculated  on  the  basis  of  the  reinforcement  and  slab  in  the  width  included  in  a  given  strip,  and  according  to  the 
assumptions  and  requirements  given  in  Sects.  545  to  548  inclusive  of  the  building  ordinance. 

20.  The  steel  shall  be  considered  as  being  concentrated  at  the  center  of  gravity  of  all  the  bands  of  steel  in  a 
given  strip. 

21.  For  the  four-way  system  of  reinforcement  the  amount  of  steel  to  resist  the  negative  bending  moment  ovei 
the  support  in  each  strip  A  shall  be  taken  as  the  sum  of  the  areas  of  steel  in  one  cross  band  and  one  diagonal  band 
The  amount  of  steel  to  resist  the  positive  bending  moment  of  each  strip  B  shall  be  considered  as  the  area  of  the  steel 
in  a  diagonal  band.  The  amount  of  steel  to  resist  the  positive  bending  moment  in  each  strip  A  shall  be  considered 
as  the  area  of  the  steel  in  a  cross-band,  and  the  amount  of  steel  to  resist  the  negative  moment  in  each  strip  B  shall  be 
the  steel  included  in  the  width  of  strip  B. 

22.  For  the  two-way  system  of  reinforcement  the  amount  of  steel  to  resist  the  bending  moment  in  any  strip 
shall  be  considered  as  the  area  of  steel  included  in  the  width  of  the  strip. 

23.  In  both  systems  of  reinforcement  the  compressive  stress  in  the  concrete  in  any  strip  shall  be  calculated  by 
taking  the  area  of  steel  considered  for  each  strip,  and  applying  it  in  a  beam  formula  based  on  the  principles  of  Sect. 
548  of  the  building  ordinance. 

24.  When  the  length  of  a  panel  does  not  exceed  the  breadth  by  more  than  5  %,  all  computations  shall  be  made 
on  the  basis  of  a  square  with  sides  equal  to  the  mean  of  the  length  and  breadth.  In  no  rectangular  panel  shall  the 
length  exceed  four-thirds  the  breadth. 

25.  For  panels  with  length  more  than  5  %  in  excess  of  the  breadth,  the  slab  shall  first  be  designed  for  a  bending 
moment  based  on  an  assumed  square  panel  with  sides  equal  to  the  mean  of  the  length  and  breadth  of  the  rectangu- 
lar panel. 


APPENDIX  C 


851 


26.  For  the  four-way  system  of  reinforcement  the  amount  of  steel  found  for  the  positive  moment  of  each 
strip  B  by  designing  in  this  manner  shall  be  that  used  in  the  diagonal  band.  For  the  positive  moment  in  each 
strip  A,  the  required  amount  of  steel  in  the  cross-band  shall  be  obtained  by  multiplying  the  steel  used  in  the  design 
of  the  assumed  square  panel  by  the  cube  of  the  ratio  found  by  dividing  the  length  or  breadth  of  the  rectangular  panel 
by  the  side  of  the  assumed  square  panel,  for  the  long  and  short  sides  of  the  panel  respectively.  The  compressive 
stresses  shall  be  calculated  on  the  basis  of  a  width  equal  to  one-half  of  the  side  of  the  assumed  square  panel,  and  on 
the  assumptions  used  in  the  calculations  of  compressive  stresses  in  square  panels.  In  no  case  shall  the  amount  of 
steel  in  the  short  side  be  less  than  two-thirds  of  that  required  for  the  long  side. 

27.  For  the  two-way  system  of  reinforcement,  the  amount  of  steel  found  for  the  positive  and  negative  moment 
of  each  strip  B  by  designing  in  this  manner  shall  be  obtained  by  multiplying  the  steel  used  in  the  design  of  the 
assumed  square  panel  by  the  cube  of  the  ratio  found  by  dividing  the  length  or  breadth  of  the  rectangular  panel  by 
the  side  of  the  assumed  square  panel,  for  the  short  and  long  side  of  the  panel  respectively.  The  mfethod  of  obtaining 
the  amount  of  steel  required  for  each  strip  A,  shall  be  the  same  as  that  given  above  for  the  four-way  system. 

28.  Walls  and  Openings. — Girders  or  beams  shall  be  constructed  under  walls,  and  around  openings  and  to 
carry  concentrated  loads. 

29.  Computations. — Complete  computations  of  interior  and  wall  panels  and  such  other  portions  of  the  build- 
ing as  may  be  required  by  the  Commissioner  of  Buildings  shall  be  left  in  the  office  of  the  Commissioner  of  Buildings 
when  plans  are  presented  for  approval. 

30.  Placing  of  Steel. — In  order  that  the  slab  bars  shall  be  maintained  in  the  position  shown  in  the  design  dur- 
ing the  work  of  pouring  the  slab,  spacers  and  supports  shall  be  provided  satisfactory  to  the  Commissioner  of  Build- 
ings. All  bars  shall  be  secured  in  place  at  intersections  by  wire  or  other  metal  fastenings.  In  no  case  shall  the 
spacing  of  the  bars  exceed  9  in.  The  steel  to  resist  the  negative  moment  in  each  strip  B  shall  extend  one-fourth  of 
the  panel  length  beyond  the  center  line  of  the  columns  in  both  directions. 

31.  All  splices  in  bars  shall  be  made  over  the  column  head.  The  length  of  the  splice  beyond  the  center  line 
of  the  column  in  both  directions  shall  be  at  least  2  ft.  nor  less  than  that  necessary  for  the  full  development  of  the 
strength  of  the  bar  as  limited  by  the  unit  bond  stresses  given  by  the  ordinance.  The  splicing  of  adjacent  bars  shall 
be  avoided  as  far  as  possible. 

32.  Slab  bars  which  are  lapped  over  the  column,  the  sectional  area  of  both  being  included  in  the  calculations 
for  negative  moment,  shall  extend  not  less  than  0.25  of  the  panel  length  for  cross-bands,  and  0.35  of  the  panel 
length  for  diagonal  bands,  beyond  the  column  center. 

33.  Test  of  Workmanship. — The  Commissioner  of  Buildings  or  his  representative  may  choose  any  two  adja- 
cent panels  in  the  building  for  the  purpose  of  ascertaining  the  character  of  workmanship.  The  test  shall  not  be 
made  sooner  than  the  time  required  for  the  cement  to  set  thoroughly,  nor  less  than  6  weeks  after  the  concrete  had 
been  poured. 

34.  All  deflections  under  test  load  shall  be  taken  at  the  center  of  the  slab,  and  shall  be  measured  from  the  nor- 
mal unloaded  position  of  the  slab.  The  two  panels  selected  shall  be  uniformly  loaded  over  their  entire  area  with  a 
load  equal  to  the  dead  load  plus  twice  the  live  load,  thus  obtaining  twice  the  total  design  load.  The  load  shall  remain 
in  place  not  less  than  24  hr.  If  the  total  deflection  in  the  center  of  the  panel  under  the  test  load  does  not  exceed  one 
eight-hundredth  of  the  panel  length,  the  slab  may  be  placarded  to  carry  the  full  design  live  load.  If  it  exceeds  this 
amount  of  deflection,  and  recovers  not  less  than  80%  of  the  total  deflection  within  7  days  after  the  load  is  removed, 
the  slab  may  be  placarded  to  carry  the  full  design  live  load.  If  the  deflection  exceeds  the  allowable  amount  above 
specified,  and  the  recovery  is  less  than  80%  in  7  days  after  the  removal  of  the  test  load,  other  tests  shall  be  made  on 
the  same  or  other  panels,  the  results  of  which  will  determine  the  amount  of  live  load  the  slabs  will  be  permitted  to 
carry. 

35.  General. — The  design  and  execution  of  the  work  shall  conform  to  the  provisions  of  the  Chicago  building 
ordinances,  and  to  correct  principles  of  construction. 

CHICAGO  REINFORCED -CONCRETE  FLAT-SLAB  RULING  AMENDED 

(New  ordinance  adopted  Jan.  1,  1918,  while  this  book  was  in  press) 

1.  Definitions. — Flat  slabs  as  understood  by  this  ruling  are  reinforced-concrete  slabs,  supported  directly  on 
reinforced  columns  with  or  without  plates  or  capitals  at  the  top,  the  whole  construction  being  hingeless  and  mono- 
lithic without  any  visible  beams  or  girders.  The  construction  may  be  such  as  to  admit  the  use  of  hollow  panels  in 
the  ceiling  or  smooth  ceiling  with  depressed  panels  in  the  floor. 

2.  The  column  capital  shall  be  defined  as  the  gradual  flaring  out  of  the  top  of  the  column  without  any  marked 

offset. 

3.  The  drop  panel  shall  be  defined  as  a  square  or  rectangular  depression  around  the  column  capital  extending 
below  the  slab  adjacent  to  it. 

4.  The  panel  length  shall  be  defined  as  the  distance  c.  to  c.  of  columns  of  the  side  of  a  square  panel,  or  the 
average  distance  c.  to  c.  of  columns  of  the  long  and  short  sides  of  a  rectangular  panel. 

6.  Columns. — The  least  dimension  of  any  concrete  column  shall  be  not  less  than  one-twelfth  the  panel  length, 
nor  one-twelfth  the  clear  height  of  the  column. 

6.  Slab  Thickness. — The  minimum  total  thickness  of  the  slab  in  inches  shall  be  determined  by  the  formula: 
Vi 

t  =  W  /44  ( =  square  root  of  W  divided  by  44),  where  t  =  total  thickness  of  slab  in  inches,  W  =  total  live  load  and 
dead  load  in  pounds  on  the  panel,  measured  c.  to  c.  of  columns. 


852 


CONCRETE  ENGINEERS'  HANDBOOK 


7.  In  no  case  shall  the  thickness  be  less  than  of  the  panel  length  (I//32)  for  floors,  nor  >io  of  the  panel 
length  (L/40)  for  roofs  {L  being  the  distance  c,  to  c.  of  columns). 

8.  In  no  case  shall  the  thickness  of  slab  be  less  than  6  in.  for  floors  or  roofs. 

9.  Column  Capital. — When  used  the  diameter  of  the  column  capital  shall  be  measured  where  its  vertical 
thickness  is  at  least       in.  and  shall  be  at  least  0.225  of  the  panel  length. 

The  slope  of  the  column  capital  shall  nowhere  make  an  angle  with  the  vertical  of  more  than  45  deg.  Special 
attention  shall  be  given  to  the  design  of  the  column  capital  in  considering  eccentric  loads,  and  the  effect  of  wind 
upon  the  structure. 

10.  Drop  Panel. — When  used,  the  drop  panel  shall  be  square  or  circular  for  square  panels  and  rectangular  or 
elliptical  for  oblong  panels. 

11.  The  length  of  the  drop  shall  not  be  less  than  one-third  of  the  panel  length  (L/3)  if  square,  and  not  less  than 
one-third  of  the  long  or  short  side  of  the  panel  respectively,  if  rectangular, 

12.  The  depth  of  the  drop  panel  shall  be  determined  by  computing  it  as  a  beam,  using  the  negative  moment 
over  the  column  capital  specified  elsewhere  in  this  ruling. 

13.  In  no  case,  however,  shall  the  dimensions  of  the  drop  panel  be  less  than  required  for  punching  shear  along 
its  perimeter,  using  the  allowable  unit  shearing  stresses  specified  below. 

14.  Shearing  Stresses. — The  allowable  unit  punching  shear  on  the  perimeter  of  the  column  capital  shall  be 
%o  of  the  ultimate  compressive  strength  of  the  concrete  as  given  in  Sect.  533  of  the  building  ordinance.  The 
allowable  unit  shear  on  the  perimeter  of  the  drop  panel  shall  be  0.03  of  the  ultimate  compressive  strength  of  the 
concrete.  In  computing  shearing  stress  for  the  purpose  of  determining  the  resistance  to  diagonal  tension  the 
method  specified  by  the  ordinance  shall  be  used. 

16.  Panel  Strips. — For  the  purpose  of  establishing  the  bending  moments  and  the  resisting  moments  of  a  square 
panel,  the  panel  shall  be  divided  into  strips  known  as  strip  A  and  strip  B.  Strip  A  shall  include  the  reinforcement 
and  slab  in  a  width  extending  from  the  center  line  of  the  columns  for  a  distance  each  side  of  this  center  line  equal  to 
one-quarter  of  the  panel  length.  Strip  B  shall  include  the  reinforcement  and  slab  in  the  half  width  remaining  in  the 
center  of  the  panel.  At  right  angles  to  these  strips,  the  panel  shall  be  divided  into  similar  strips  A  and  B,  having 
the  same  widths  and  relations  to  the  center  line  of  the  columns  as  the  above  strips.  These  strips  shall  be  for  design- 
ing purposes  only,  and  are  not  intended  as  the  boundary  lines  of  any  bands  of  steel  used. 

16.  These  strips  shall  apply  to  the  system  of  reinforcement  in  which  the  reinforcing  bars  are  placed  parallel 
and  at  right  angles  to  the  center  line  of  the  columns,  hereinafter  known  as  the  two-way  system,  and  also  to  the  system 
of  reinforcement  in  which  the  reinforcing  bars  are  placed  parallel,  at  right  angles  to  and  diagonal  to  the  center  line 
of  the  columns  hereinafter  known  as  the  four-way  system. 

17.  Any  other  system  of  reinforcement  in  which  the  reinforcing  bars  are  placed  in  circular,  concentric  rings  and 
radial  bars,  or  systems  with  steel  rods  arranged  in  any  manner  whatsoever,  shall  comply  with  the  requirements  of 
either  the  two-way  or  the  four-way  system  herein  specified. 

18.  Bending  Moment  Coefficients,  Interior  Panel,  Two-way  System. — In  panels  where  standard  drops  and 
column  capitals  are  used  as  above  specified,  the  negative  bending  moment,  taken  at  a  cross-section  of  each  strip  A  at 
the  edge  of  the  column  capital  or  over  it,  shall  be  taken  as  PFZ//30. 

19.  The  positive  bending  moment  taken  at  a  cross-section  of  each  strip  A  midway  between  column  centers 
shall  be  taken  as  WL/m. 

20.  The  positive  bending  moment  taken  at  a  cross-section  of  each  strip  B  in  the  middle  of  the  panel  shall  be 
taken  as  WL/ 120. 

21.  The  negative  bending  moment  taken  at  a  cross-section  of  each  strip  B  on  the  center  line  of  the  columns 
shall  be  taken  as  TFL/120, 

22.  In  the  formulas  hereinabove  given  W  =  total  live  and  dead  load  on  the  whole  panel  in  pounds,  L  =  panel 
length,  c.  to  c.  of  columns. 

23.  Bending  Moment  CoeflScients,  Interior  Panel,  Four-way  System. — In  panels  where  standard  drops  and 
column  capitals  are  used  as  above  specified,  the  negative  bending  moment,  taken  at  a  cross-section  of  each  strip  A 
at  the  edge  of  column  capital  or  over  it,  shall  be  taken  as  WL /30. 

24.  The  positive  bending  moment,  taken  at  a  cross-section  of  each  strip  A,  midway  between  column  centers, 
shall  be  taken  as  WL/80. 

25.  The  positive  bending  moment,  taken  at  a  cross-section  of  each  strip  B,  taken  in  the  middle  of  the  panel, 
shall  be  taken  as  PFL/120. 

26.  The  negative  bending  moment,  taken  at  a  cross-section  of  each  strip  B  on  the  center  line  of  the  columns, 
shall  be  taken  as  WL/120. 

27.  Bending  Moment  Coefficients,  Wall  Panels. — Where  wall  panels  with  standard  drops  and  capitals  are 
carried  by  columns  and  girders  built  in  walls,  as  in  skeleton  construction,  the  same  coefficients  shall  be  used  as  for 
an  interior  panel,  except  as  follows:  The  positive  bending  moments  on  strips  A  and  B  midway  between  wall  and 
first  line  of  columns  shall  be  increased  25%, 

28.  Where  wall  panels  are  carried  on  new  brick  walls,  these  shall  be  laid  in  Portland  cement  mortar  and  shall 
be  stiffened  with  pilasters  as  follows:  If  a  16-in.  wall  is  used,  it  shall  have  a  4-in.  pilaster.  If  a  12-in.  wall  is  used,  it 
shall  have  an  8-in.  pilaster.  The  length  of  pilasters  shall  be  not  less  than  the  diameter  of  the  column,  nor  less  than 
one-eighth  of  the  distance  between  pilasters.  The  pilasters  shall  be  located  opposite  the  columns  as  nearly  as  prac- 
ticable, and  shall  be  corbeled  out  4  in.  at  the  top,  starting  at  the  level  of  the  base  of  the  column  capital.  Not  less 
than  8-in.  bearing  shall  be  provided  for  the  slab,  the  full  length  of  wall. 


APPENDIX  C 


853 


The  coefficients  of  bending  moments  required  for  these  panels  shall  be  the  same  as  those  for  the  interior  panels 
except  as  provided  herewith:  The  positive  bending  moments  on  strips  A  and  B  midway  between  the  wall  and  first 
line  of  columns  shall  be  increased  50%. 

29.  Where  wall  panels  are  supported  on  old  brick  walls,  there  shall  be  columns  with  standard  drops  and  capi- 
tals built  against  the  wall,  which  shall  be  tied  to  the  same  in  an  approved  manner,  and  at  least  an  8-in.  bearing 
provided  for  the  slab,  the  full  length.  Where  this  is  impracticable,  there  shall  be  built  a  beam  on  the  underside  of 
slab  adjacent  to  the  wall  between  columns,  strong  enough  to  carry  25%  of  the  panel  load. 

The  coefficients  of  bending  moments  for  the  two  cases  of  slab  support  herein  described  shall  be  the  same  as 
those  specified  in  Sect.  27  and  Sect.  28  for  skeleton  and  wall  bearing  condition,  respectively. 

30.  Nothing  specified  above  shall  be  construed  as  applying  to  a  case  of  slabs  merely  resting  on  walls  or  ledges, 
without  any  condition  of  restraint.  These  shall  be  figured  as  in  ordinary  beam-and-girder  construction  specified  in 
the  ordinances. 

31.  Bending  Moment  Coefficients,  Wall  and  Interior  Columns. — Wall  columns  in  skeleton  construction  shall 
be  designed  to  resist  a  bending  moment  of  WL/GO  at  floors  and  WL/30  at  roof.  The  amount  of  steel  required  for 
this  moment  shall  be  independent  of  that  required  to  carry  the  direct  load.  It  shall  be  placed  as  near  the  surfaces 
of  the  column  as  practicable  on  the  tension  sides,  and  the  rods  shall  be  continuous  in  crossing  from  one  side  to 
another.  The  length  of  rods  below  the  base  of  the  capital  and  above  the  floor  line  shall  be  sufficient  to  develop 
their  strength  through  bond,  but  not  less  than  40  diameters,  nor  less  than  one-third  the  clear  height  between  the 
floor  line  and  the  base  of  the  column  capital. 

32.  The  interior  columns  must  be  analyzed  for  the  worst  condition  of  unbalanced  loading.  It  is  the  intention 
of  this  ruling  to  cover  ordinary  cases  of  eccentric  loads  on  the  columns  by  the  requirement  of  Sect.  5.  Where  the 
minimum  size  of  column  therein  specified  is  found  insufficient,  however,  the  effect  of  the  resulting  bending  moment 
shall  be  properly  divided  between  the  adjoining  slab  and  the  columns  above  and  below  according  to  best  principles 
of  engineering,  and  the  columns  enlarged  sufficiently  to  carry  the  load  safely. 

33.  Bending  Moment  Coefficients,  Panels  Without  Drops,  or  Capitals,  or  Both. — In  square  panels  where  no 
column  capital  or  no  depressions  are  used,  the  sum  total  of  positive  and  negative  bending  moments  shall  be^qual 
to  that  computed  by  the  following  formula 

B.M.  =  (WL/8)  (1.53  -  4^-  +  4.18A;3) 
where  B.M.  —  Numerical  sum  of  positive  and  negative  bending  moments,  regardless  of  algebraic  signs; 
W  =  Total  live  and  dead  load  on  the  whole  panel; 
L  =  Length  of  side  of  a  square  panel,  c.  to  c.  of  columns; 
k  =  Ratio  of  the  radius  of  the  column  or  column  capital  to  panel  length,  L. 
This  total  bending  moment  shall  be  divided  between  the  positive  and  the  negative  moments  in  the  same  pro- 
portion as  in  the  typical  square  panels  for  two-way  or  four-way  systems  specified  above  for  interior  and  wall  panels 
respectively. 

34.  Point  of  Inflectiori. — For  the  purpose  of  making  the  calculations  of  the  bending  moment  at  the  sections 
away  from  the  column  capital,  the  point  of  inflection  shall  be  considered  as  being  one-quarter  the  distance  c.  to  c. 
of  columns,  both  crosswise  and  diagonally,  from  the  center  of  the  column. 

35.  Tensile  Stress  in  Steel  and  Compressive  Stress  in  Concrete. — The  tensile  stress  in  steel  and  the  compres- 
sive stress  in  the  concrete  to  resist  the  bending  moment  shall  be  calculated  on  the  basis  of  the  reinforcement  and  slab 
in  the  width  included  in  a  given  strip,  and  according  to  the  assumptions  and  requirements  given  in  Sects.  532  to  535 
inclusive  of  the  building  ordinance.  The  steel  shall  be  considered  as  being  concentrated  at  the  center  of  gravity  of 
all  the  bands  of  steel  in  a  given  strip. 

36.  For  the  four-way  system  of  reinforcement  the  amount  of  steel  to  resist  the  negative  bending  moment  over 
the  support  in  each  strip  A  shall  be  taken  as  the  sum  of  the  areas  of  steel  in  one  cross  band  and  one  diagonal  band. 
The  amount  of  steel  to  resist  the  positive  bending  moment  of  each  strip  B  shall  be  considered  as  the  area  of  the 
steel  in  a  diagonal  band.  The  amount  of  steel  to  resist  the  positive  bending  moment  in  each  strip  A  shall  be  con- 
sidered as  the  area  of  the  steel  in  a  cross  band,  and  the  amount  of  steel  to  resist  the  negative  moment  in  each  strip 
B  shall  be  the  steel  included  in  the  width  of  strip  B. 

37.  For  the  two-way  system  of  reinforcement  the  amount  of  steel  to  resist  the  bending  moment  in  any  strip 
'shall  be  considered  as  the  area  of  steel  included  in  the  width  of  the  strip. 

38.  In  both  systems  of  reinforcement  the  compressive  stress  in  the  concrete  in  any  strip  shall  be  calculated  by 
taking  the  area  of  steel  considered  for  each  strip  and  applying  it  in  a  beam  formula  based  on  the  principles  of  Sect. 
535  of  the  building  ordinance. 

39.  Where  drop  panels  are  used,  the  width  of  beam  assumed  to  resist  the  compressive  stresses  over  the  column 
capital  shall  be  the  width  of  the  drop. 

40.  The  width  of  beam,  where  no  drop  panels  are  used,  shall  be  the  width  of  steel  bands.  Where  this  is  found 
insufficient,  the  area  shall  be  increased  by  introducing  compression  steel  in  the  bottom  of  slab. 

41.  Rectangular  Panels. — When  the  length  of  panel  in  either  two-way  or  four-way  system  does  not  exceed  the 
breadth  by  more  than  5%,  all  computations  shall  be  based  on  a  square  panel  whose  side  equals  the  mean  of  the 
length  and  breadth,  and  the  steel  equally  distributed  among  the  strips  according  to  the  coefficients  above  specified. 

42.  In  no  rectangular  panel  shall  the  length  exceed  the  breadth  by  more  than  one-third  of  the  latter. 

43.  Rectangular  Panels,  Four-way  System. — In  the  four-way  system  of  reinforcement,  where  length  exceeds 
breadth  by  more  than  5  %,  the  amount  of  steel  required  in  strip  A,  long  direction,  both  positive  and  negative,  shall  be 


854 


CONCRETE  ENGINEERS'  HANDBOOK 


the  same  as  that  required  for  the  same  strip  in  a  square  panel  whose  length  is  equal  to  the  long  side  of  the  rectangu- 
lar panel. 

44.  The  amount  of  steel,  strip  A,  short  direction,  positive  and  negative,  shall  be  the  same  as  that  required  for 
the  same  strip  in  a  square  panel,  whose  length  is  equal  to  the  short  side  of  the  rectangular  panel. 

46.  The  amount  of  steel  in  strip  B,  positive  and  negative,  shall  be  the  same  as  that  required  for  similar  strip  in 
a  square  panel  whose  length  is  equal  to  the  mean  of  the  long  and  the  short  side  of  the  rectangular  panel. 

46.  In  no  case  shall  the  amount  of  steel  in  the  short  side  be  less  than  two-thirds  of  that  required  for  the  long 

side. 

47.  Rectangular  Panels,  Two-way  System. — In  the  two-way  system  of  reinforcement  the  amount  of  steel 
required  for  the  positive  and  the  negative  moment  of  each  strip  A  shall  be  determined  in  the  same  manner  as  indi- 
cated for  the  four-way  system  above. 

48.  The  amount  of  steel  in  strip  B,  positive  and  negative,  running  in  short  direction,  shall  be  equal  to  that 
required  for  the  same  strip  in  a  square  panel  whose  length  equals  the  long  side  of  the  rectangular  panel. 

49.  The  amount  of  steel  in  strip  B,  long  direction,  positive  and  negative,  shall  be  equal  to  that  required  for 
the  same  strip  in  a  square  panel,  whose  length  equals  the  short  side  of  the  rectangular  panel. 

50.  In  no  case  shall  the  amount  of  steel  in  strip  B,  long  direction,  be  less  than  two-thirds  of  that  in  the  short 
direction. 

61.  Walls  and  Openings. — Girders  and  beams  shall  be  constructed  under  walls,  around  openings  and  to  carry 
concentrated  loads. 

62.  Spandrel  Beams. — The  spandrel  beams  or  girders  shall,  in  addition  to  their  own  weight  and  the  weight  of 
the  spandrel  wall,  be  assumed  to  carry  20%  of  the  wall  panel  load  uniformly  distributed  upon  them. 

63.  Placing  of  Steel. — In  order  that  the  slab  bars  shall  be  maintained  in  the  position  shown  in  the  design  dur- 
ing the  work  of  pouring  the  slab,  spacers  and  supports  shall  be  provided  satisfactory  to  the  Commissioner  of  Build- 
ings. All  bars  shall  be  secured  in  place  at  intersections  by  wire  or  other  metal  fastenings.  In  no  case  shall  the 
spacing  of  the  bars  exceed  9  in.  The  steel  to  resist  the  negative  moment  in  each  strip  B  shall  extend  one-quarter  of 
the  panel  length  beyond  the  center  line  of  the  columns  in  both  directions. 

54.  Splices  in  bars  may  be  made  wherever  convenient,  but  preferably  at  points  of  minimum  stress.  The 
length  of  splice  beyond  the  center  point,  in  each  direction,  shall  not  be  less  than  40  diameters  of  the  bars,  nor  less 
than  2  ft.    The  splicing  of  adjacent  bars  shall  be  avoided  as  far  as  possible. 

65.  Slab  bars  which  are  lapped  over  the  column,  the  sectional  area  of  both  being  included  in  the  calculations 
for  negative  moment,  shall  extend  not  less  than  0.25  of  the  panel  length  for  cross  bands  and  0.35  of  the  panel  length 
for  diagonal  bands,  beyond  the  column  center. 

56.  Computations. — Complete  computations  of  interior  and  wall  panels  and  such  other  portions  of  the  build- 
ing as  may  be  required  by  the  Commissioner  of  Buildings  shall  be  left  in  the  office  of  the  Commissioner  of  Buildings 
when  plans  are  presented  for  approval. 

57.  Test  of  Workmanship. — The  Commissioner  of  Buildings  or  his  representative  may  choose  any  two  adja-  . 
cent  panels  in  the  building  for  the  purpose  of  ascertaining  the  character  of  workmanship.    The  test  shall  not  be 
made  sooner  than  the  time  required  for  the  cement  to  set  thoroughly,  nor  less  than  6  weeks  after  the  concrete  had 
been  poured. 

68.  All  deflections  under  test  load  shall  be  taken  at  the  center  of  the  slab,  and  shall  be  measured  from  the  nor- 
mal unloaded  position  of  the  slab.  The  two  panels  selected  shall  be  uniformly  loaded  over  their  entire  area  with  a 
load  equal  to  the  dead  load  plus  twice  the  live  load,  thus  obtaining  twice  the  total  design  load.  The  load  shall 
remain  in  place  not  less  than  24  hours.  If  the  total  deflection  in  the  center  of  the  panel  under  the  test  load  does  not 
exceed  ^oo  of  the  panel  length,  the  slab  may  be  placarded  to  carry  the  full  design  live  load.  If  it  exceeds  this 
amount  of  deflection,  and  recovers  not  less  than  80%  of  the  total  deflection  within  7  days  after  the  load  is 
removed,  the  slab  may  be  placarded  to  carry  the  full  design  live  load.  If  the  deflection  exceeds  the  allowable 
amount  above  specified,  and  the  recovery  is  less  than  80%  in  7  days  after  the  removal  of  the  test  load,  other 
tests  shall  be  made  on  the  same  or  other  panels,  the  results  of  which  will  determine  the  amount  of  live  load  the  slabs 
will  be  permitted  to  carry. 

59.  General. — The  design  and  the  execution  of  the  work  shall  conform  to  the  general  provisions  and  the 
spirit  of  the  Chicago  Building  Ordinances  in  points  not  covered  by  this  Ruling  and  to  the  best  engineering  practice 
in  general. 

60.  Enforcement. — This  Ruling  shall  go  into  effect  on  and  after  Jan.  1,  1918.    All  previous  rulings  on  flat 
slabs  are  hereby  rescinded. 

FINAL  REPORT  OF  SPECIAL  COMMITTEE  OF  THE  AMERICAN  SOCIETY  OF 

CIVIL  ENGINEERS 
PART  PERTAINING  TO  FLAT-SLAB  DESIGN 

The  continuous  flat  slab  reinforced  in  two  or  more  directions  and  built  monolithically  with  the  supporting 
columns  (without  beams  or  girders)  is  a  type  of  construction  which  is  now  extensively  used  and  which  has  recog- 
nized advantages  for  certain  types  of  structures  as,  for  example,  warehouses  in  which  large,  open  floor  space  is 
desired.  In  its  construction,  there  is  excellent  opportunity  for  inspecting  the  position  of  the  reinforcement.  The 
conditions  attending  depositing  and  placing  of  concrete  are  favorable  to  securing  uniformity  and  soundness  in 
the  concrete.  The  recommendations  in  the  following  paragraphs  relate  to  flat  slabs  extending  over  several  rows 
of  panels  in  each  direction.  Necessarily  the  treatment  is  more  or  less  empirical. 
The  coefficients  and  moments  given  relate  to  uniformily  distributed  loads. 


APPENDIX  C 


855 


(a)  Column  Capital. — It  is  usual  in  flat-slab  construction  to  enlarge  the  supporting  columns  at  their  top, 
thus  forming  column  capitals.  The  size  and  shape  of  the  column  capital  affect  the  strength  of  the  structure  in 
several  ways.  The  moment  of  the  external  forces  which  the  slab  is  called  upon  to  resist  is  dependent  upon  the  size 
of  the  capital;  the  section  of  the  slab  immediately  above  the  upper  periphery  of  the  capital  carries  the  highest 
amount  of  punching  shear;  and  the  bending  moment  developed  in  the  column  by  an  eccentric  or  unbalanced  load- 
ing of  the  slab  is  greatest  at  the  under  surface  of  the  slab.  Generally,  the  horizontal  section  of  the  column  capital 
should  be  round  or  square  with  rounded  corners.  In  oblong  panels  the  section  may  be  oval  or  oblong,  with  dimen- 
sions proportional  to  the  panel  dimensions.  For  computation  purposes,  the  diameter  of  the  column  capital  will 
be  considered  to  be  measured  where  its  vertical  thickness  is  at  least  lli  in.,  provided  the  slope  of  the  capital  below 
this  point  nowhere  makes  an  angle  with  the  vertical  of  more  than  45  deg.  In  case  a  cap  is  placed  above  the  column 
capital,  the  part  of  this  cap  within  a  cone  made  by  extending  the  lines  of  the  column  capital  upward  at  the  slope  of 
45  deg.  to  the  bottom  of  the  slab  or  dropped  panel  may  be  considered  as  part  of  the  column  capital  in  determining 
the  diameter  for  design  purposes.  Without  attempting  to  limit  the  size  of  the  column  capital  for  special  cases, 
it  is  recommended  that  the  diameter  of  the  column  capital  (or  its  dimension  parallel  to  the  edge  of  the  panel) 
generally  be  made  not  less  than  one-fifth  of  the  dimension  of  the  panel  from  center  to  center  of  adjacent  columns. 
A  diameter  equal  to  0.225  of  the  panel  length  has  been  used  quite  widely  and  acceptably.  For  heavy  loads  or 
large  panels,  especial  attention  should  be  given  to  designing  and  reinforcing  the  column  capital  with  respect  to 
compressive  stresses  and  bending  moments.  In  the  case  of  heavy  loads  or  large  panels,  and  where  the  conditions 
of  the  panel  loading  or  variations  in  panel  length  or  other  conditions  cause  high  bending  stresses  in  1;he  column, 
and  also  for  column  capitals  smaller  than  the  size  herein  recommended,  especial  attention  should  be  given  to  design- 
ing and  reinforcing  the  column  capital  with  respect  to  compression  and  to  rigidity  of  connection  to  floor  slab. 

(6)  Dropped  Panel. — In  one  type  of  construction  the  slab  is  thickened  throughout  an  area  surrounding  the 
column  capital.  The  square  or  oblong  of  thickened  slab  thus  formed  is  called  a  dropped  panel  or  a  drop.  The 
thickness  and  the  width  of  the  dropped  panel  may  be  governed  by  the  amount  of  resisting  moment  to  be  provided 
(the  compressive  stress  in  the  concrete  being  dependent  upon  both  thickness  and  width),  or  its  thickness  may  be 
governed  by  the  resistance  to  shear^required  at  the  edge  of  the  column  capital  and  its  width  by  the  allowable  com- 
pressive stresses  and  shearing  stresses  in  the  thinner  portion  of  the  slab  adjacent  to  the  dropped  panel.  Generally, 
however,  it  is  recommended  that  the  width  of  the  dropped  panel  be  at  least  four-tenths  of  the  corresponding  side 
of  the  panel  as  measured  from  center  to  center  of  columns,  and  that  the  off'set  in  thickness  be  not  more  than  five- 
tenths  of  the  thickness  of  the  slab  outside  the  dropped  panel. 

(c)  Slab  Thickness. — In  the  design  of  a  slab,  the  resistance  to  bending  and  to  shearing  forces  will  largely 
govern  the  thickness,  and,  in  the  case  of  large  panels  with  light  loads,  resistance  to  deflection  may  be  a  controlling 
factor.  The  following  formulas  for  minimum  thicknesses  are  recommended  as  general  rules  of  design  when  the 
diameter  of  the  column  capital  is  not  less  than  one-fifth  of  the  dimension  of  the  panel  from  center  to  center  of 
adjacent  columns,  the  larger  dimension  being  used  in  the  case  of  oblong  panels.    For  notation,  let 


t  =  total  thickness  of  slab,  in  inches. 
L  =  panel  length,  in  feet. 

w  =  sum  of  live  load  and  dead  load,  in  pounds  per  square  foot. 
Then,  for  a  slab  without  dropped  panels. 


minimum  t 
for  a  slab  with  dropped  panels, 

minimum  t 


0.024  L\/w  +  IH 


Position  ofresuH-an) 
oF  shear  on  quarter 
peripheries  of  fwo 
coturnn  capihjis 

 .7° 

'^Cerrfer  of  gravity 
of  load  on  half 
panel 


Fig.  1. 


0.02  L^w  +  1 

for  a  dropped  panel  whose  width  is  four-tenths  of  the  panel  length, 

minimum  t  =  0.03  L\/ w  +  IH 

In  no  case  should  the  slab  thickness  be  made  less  than  6  in.,  nor  should 
the  thickness  of  a  floor  slab  be  made  less  than  one  thirty-second  of  the  panel 
length,  nor  the  thickness  of  a  roof  slab  less  than  one-fortieth  of  the  panel 
length. 

(d)  Bending  and  Resisting  Moments  in  Slabs. — If  a  vertical  section  of  a  slab  be  taken  across  a  panel  along  a  line 
midway  between  columns,  and  if  another  section  be  taken  along  an  edge  of  the  panel  parallel  to  the  first  section, 
but  skirting  the  part  of  the  periphery  of  the  column  capitals  at  the  two  corners  of  the  panels,  the  moment  of  the 
couple  formed  by  the  external  load  on  the  half  panel,  exclusive  of  that  over  the  column  capital  (sum  of  dead  and 
live  loads)  and  the  resultant  of  the  external  shear  or  reaction  at  the  support  at  the  two  column  capitals  (see  Fig.  1), 
may  be  found  by  ordinary  static  analysis.  It  will  be  noted  that  the  edges  of  the  area  here  considered  are  along 
lines  of  zero  shear,  except  around  the  column  capitals.  This  moment  of  the  external  forces  acting  on  the  half 
panel  will  be  resisted  by  the  numerical  sum  of  (a)  the  moment  of  the  internal  stresses  at  the  section  of  the  panel 
midway  between  columns  (positive  resisting  moment)  and  (b)  the  moment  of  the  internal  stresses  at  the  section 
referred  to  at  the  end  of  the  panel  (negative  resisting  moment).  In  the  curved  portion  of  the  end  section  (that 
skirting  the  column),  the  stresses  considered  are  the  components  which  act  parallel  to  the  normal  stresses  on  the 
straight  portion  of  the  section.  Analysis  shows  that,  for  a  uniformly  distributed  load,  and  round  columns,  and 
square  panels,  the  numerical  sum  of  the  positive  moment  and  the  negative  moment  at  the  two  sections  named  is 
given  quite  closely  by  the  equation 

ilf«  =  Hwl  (Z  -  Hey 


856 


CONCRETE  ENGINEERS'  HANDBOOK 


In  this  formula  and  in  those  which  follow  relating  to  oblong  panels, 
w  =  sum  of  the  live  and  dead  loads  per  unit  of  area. 
I  =  side  of  a  square  panel  measured  from  center  to  center  of  columns. 
h  =  one  side  of  the  oblong  panel  measured  from  center  to  center  of  columns. 
h  =  other  side  of  oblong  panel  measured  in  the  same  way. 
c  =  diameter  of  the  column  capital. 
Mx  =  numerical  sum  of  positive  moment  and  negative  moment  in  one  direction. 
My  =  numerical  sum  of  positive  moment  and  negative  moment  in  the  other  direction,  i 

For  oblong  panels,  the  equation  for  the  numerical  sum  of  the  positive  moment  and  the  negative  moment  at  the 
two  sections  named  becomes 

My  =^  wli  (I2  -  |c)  ^ 

where  Mx  is  the  numerical  sum  of  the  positive  moment  and  the  negative  moment  for  the  sections  parallel  to  the 
dimension,  h,  and  My  is  the  numerical  sum  of  the  positive  moment  and  the  negative  moment  for  the  sections  parallel 
to  the  dimension,  h. 

What  proportion  of  the  total  resistance  exists  as  positive  moment  and  what  as  negative  moment  is  not  readily 
determined.  The  amount  of  the  positive  moment  and  that  of  the  negative  moment  may  be  expected  to  vary  some- 
what with  the  design  of  the  slab.  It  seems  proper,  however,  to  make  the  division  of  total  resisting  moment  in  the 
ratio  of  three-eighths  for  the  positive  moment  to  five-eighths  for  the  negative  moment. 

With  reference  to  variations  in  stress  along  the  sections,  it  is  evident  from  conditions  of  flexure  that  the  resist- 
ing moment  is  not  distributed  uniformly  along  either  the  section  of  positive  moment  or  that  of  negative  moment.  As 
the  law  of  the  distribution  is  not  known  definitely,  it  will  be  necessary  to  make  an  empirical  apportionment  along  the 
sections;  and  it  will  be  considered  sufficiently  accurate  generally  to  divide  the  sections  into  two  parts  and  to  use  an 
average  value  over  each  part  of  the  panel  section. 

The  relatively  large  breadth  of  structure  in  a  flat  slab  makes  the  effect  of  local  variations  in  the  concrete  less 
than  would  be  the  case  for  narrow  members  like  beams.  The  tensile  resistance  of  the  concrete  is  less  affected  by 
cracks.  Measurements  of  deformations  in  buildings  under  heavy  load  indicate  the  presence  of  considerable  tensile 
resistance  in  the  concrete,  and  the  presence  of  this  tensile  resistance  acts  to  decrease  the  intensity  of  the  com- 
pressive stresses.  It  is  believed  that  the  use  of  moment  coefficients  somewhat  less  than  those  given  in  a  preceding 
paragraph  as  derived  by  analysis  is  warranted,  the  calculations  of  resisting  moment  and  stresses  in  concrete  and  re- 
inforcement being  made  according  to  the  assumptions  specified  in  this  report  and  no  change  being  made  in  the 
^  ^  ^  ^,         ^      values  of  the  working  stresses  ordinarily  used.    Accordingly,  the  values  of 

CtAimn  heiod.       HkJ-SecHon  .  Mumn-head  ,  ,  .  ,  ,    ,  ,  ,         ,  ,  , 

Section p    C  D    ^  Section     the  moments  which  are  recommended  for  use  are  somewhat  less  than  those 

derived  by  analysis.  The  values  given  may  be  used  when  the  column 
capitals  are  round,  oval,  square,  or  oblong. 

(e)  Names  for  Moment  Sections. — For  convenience,  that  portion  of 
the  section  across  a  panel  along  a  line  midway  between  columns  which  lies 
within  the  middle  two  quarters  of  the  width  of  the  panel  (HI,  Fig.  2)  will  be 
called  the  inner  section,  and  that  portion  in  the  two  outer  quarters  of  the 
!  "  '°"  \        width  of  the  panel  (GH  and  IJ,  Fig.  2)  will  be  called  the  outer  sections. 

I  1         Of  the  section  which  follows  a  panel  edge  from  column  capital  to  column 

1<_...^/ .  —  >/  ^t...^/^...-^         capital  and  which  includes  the  quarter  peripheries  of  the  edges  of  two 

^         column  capitals,  that  portion  within  the  middle  two  quarters  of  the  panel 
/  width  (CD,  Fig.  2)  will  be  called  the  mid-section,  and  the  two  remaining 

~Fig~'2  portions  (ABC  and  DEF,  Fig.  2),  each  having  a  projected  width  equal 

to  one-fourth  of  the  panel  width,  will  be  called  the  column-head  sections. 
(/)  Positive  Moment. — For  a  square  interior  panel,  it  is  recommended  that  the  positive  moment  for  a  section 

in  the  middle  of  a  panel  extending  across  its  width  be  taken  as  2^  wl  (j  —  |-c^  .     Of  this  moment,  at  least  25% 

should  be  provided  for  in  the  inner  section;  in  the  two  outer  sections  of  the  panel  at  least  55%  of  the  specified 
moment  should  be  provided  for  in  slabs  not  having  dropped  panels,  and  at  least  60  %  in  slabs  having  dropped 
panels,  except  that  in  calculations  to  determine  necessary  thickness  of  slab  away  from  the  dropped  panel  at  least 
70  %  of  the  positive  moment  should  be  considered  as  acting  in  the  two  outer  sections. 

(g)  Negative  Moment. — For  a  square  interior  panel,  it  is  recommended  that  the  negative  moment  for  a  section 
which  follows  a  panel  edge  from  column  capital  to  column  capital  and  which  includes  the  quarter  peripheries  of  the 
edges  of  the  two  column  capitals  (the  section  altogether  forming  the  projected  width  of  the  panel)  be  taken  as 
1      /      2  \2 

Y^wl [I  —  g-c j  .    Of  this  negative  moment,  at  least  20 %  should  be  provided  for  in  the  mid-section  and  at  least 

65  %  in  the  two  column-head  sections  of  the  panel,  except  that  in  slabs  having  dropped  panels  at  least  80  %  of  the 
specified  negative  moment  should  be  provided  for  in  the  two  column-head  sections  of  the  panel. 

1  See  paper  and  closure,  "Statical  Limitations  upon  the  Steel  Requirement  in  Reinforced  Concrete  Flat 
Slab  Floors,"  by  John  R.  Nichols,  Jun.  Am.  Soc.  C.  E.,  Trans.  Am.  Soc.  C.  E.,  vol.  77. 


\ 


APPENDIX  C 


857 


(^i)  Moments  for  Oblong  Panels. — When  the  length  of  a  panel  does  not  exceed  the  breadth  by  more  than  5  % , 
computation  may  be  made  on  the  basis  of  a  square  panel  with  sides  equal  to  the  mean  of  the  length  and  the  breadth. 
When  the  long  side  of  an  interior  oblong  panel  exceeds  the  short  side  by  more  than  one-twentieth  and  by  not 


more  than  one-third  of  the  short  side,  it  is  recommended  that  the  positive  moment  be  taken  as  -^wh  (h  —  5-' 


on  a  section  parallel  to  the  dimension,  h,  and  -Kn^h  (h  —  o"<^)        a  section  parallel  to  the  dimenison,  h;  and  that 


the  negative  moment  be  taken  as  y^wh  (h  —  o  a  section  at  the  edge  of  the  panel  corresponding  to  the  dimen- 


sion, Z-2,  and  j^wZi  —  ^cj  at  a  section  in  the  other  direction.  The  limitations  of  the  apportionment  of  moment 
between  inner  section  and  outer  section  and  between  mid-section  and  column-head  sections  may  be  the  same  as  for 
square  panels. 

(i)  Wall  Panels. — The  coefficient  of  negative  moment  at  the  first  row  of  columns  away  from  the  wall  should  be 
increased  20%  over  that  required  for  interior  panels,  and  likewise  the  coefficient  of  positive  moment  at  the  section 
half  way  to  the  wall  should  be  increased  by  20%.  If  girders  are  not  provided  along  the  wall,  or  the  slab  does  not 
project  as  a  cantilever  beyond  the  column  line,  the  reinforcement  parallel  to  the  wall  for  the  negative  moment  in  the 
column-head  section  and  for  the  positive  moment  in  the  outer  section  should  be  increased  by  20%.  If  the  wall  is 
carried  by  the  slab,  this  concentrated  load  should  be  provided  for  in  the  design  of  the  slab.  The  coefficient  of  nega- 
tive moments  at  the  wall  to  take  bending  in  the  direction  perpendicular  to  the  wall  line  may  be  determined  by  the 
conditions  of  restraint  and  fixedness  as  found  from  the  relative  stiffness  of  columns  and  slab,  but  in  no  case  should 
it  be  taken  as  less  than  one-half  of  that  for  interior  panels. 

0)  Reinforcement. — In  the  calculation  of  moments,  all  the  reinforcing  bars  which  cross  the  section  under  con- 
sideration and  which  fulfill  the  requirements  given  under  paragraph  (Z)  of  this  chapter  may  be  used.  For  a  column- 
head  section,  reinforcing  bars  parallel  to  the  straight  portion  of  the  section  do  not  contribute  to  the  negative  resisting 
moment  for  the  column-head  section  in  question.  In  the  case  of  four-way  reinforcement,  the  sectional  area  of  the 
diagonal  bars  multiplied  by  the  sine  of  the  angle  between  the  diagonal  of  the  panel  and  the  straight  portion  of  the 
section  under  consideration  may  be  taken  to  act  as  reinforcement  in  a  rectangular  direction. 

(k)  Point  of  Inflection. — For  the  purpose  of  making  calculations  of  moments  at  sections  away  from  the  sections 
of  negative  moment  to  act  integrally  for  a  width  equal  to  the  width  of  the  column-head  section. 

(o)  Provision  for  Diagonal  Tension  and  Shear. — In  calculations  for  the  shearing  stress  which  is  to  be  used  as 
the  means  of  measuring  the  resistance  to  diagonal  tension  stress,  it  is  recommended  that  the  total  vertical  shear 
on  two  column-head  sections  constituting  a  width  equal  to  one-half  the  lateral  dimension  of  the  panel,  for  use  in 
the  formula  for  determining  critical  shearing  stresses,  be  considered  to  be  one-fourth  of  the  total  dead  and  live 
loads  on  a  panel  for  a  slab  of  uniform  thickness,  and  to  be  three-tenths  of  the  sum  of  the  dead  and  live  loads  on  a 
panel  for  a  slab  with  dropped  panels.    The  formula  for  shearing  unit  stress  given  in  the  Appendix  to  this  report 

0.25  IF  0.30  PF 

may  then  be  written  v  =  -^-^j^ior  slabs  of  uniform  thickness,  and  v  =    '^j^  ■  for  slabs  with  dropped  panels, 

where  W  is  the  sum  of  the  dead  and  live  loads  on  a  panel,  b  is  half  the  lateral  dimension  of  the  panel  measured 
from  center  to  center  of  columns,  and  jd  is  the  lever  arm  of  the  resisting  couple  at  the  section. 

The  calculation  of  what  is  commonly  called  punching  shear  may  be  made  on  the  assumption  of  a  uniform 
distribution  over  the  section  of  the  slab  around  the  periphery  of  the  column  capital  and  also  of  a  uniform  distribu- 
tion over  the  section  of  the  slab  around  the  periphery  of  the  dropped  panel,  using  in  each  case  an  amount  of  vertical 
shear  greater  by  25  %  than  the  total  vertical  shear  on  the  section  under  consideration. 

The  values  of  working  stresses  should  be  those  recommended  for  diagonal  tension  and  shear  in  Appendix  B. 

(p>  Walls  and  Openings. — Girders  or  beams  should  be  constructed  to  carry  walls  and  other  concentrated 
loads  which  are  in  excess  of  the  working  capacity  of  the  slab.  Beams  should  also  be  provided  in  case  openings  in 
the  floor  reduce  the  working  strength  of  the  slab  below  the  required  carrying  capacity. 

(g)  Unusual  Panels. — The  coefficients,  apportionments,  and  thicknesses  recommended  are  for  slabs  which 
have  several  rows  of  panels  in  each  direction,  and  in  which  the  size  of  the  panels  is  approximately  the  same.  For 
structures  having  a  width  of  one,  two,  or  three  panels,  and  also  for  slabs  having  panels  of  markedly  different  sizes, 
an  analysis  should  be  made  of  the  moments  developed  in  both  slab  and  columns,  and  the  values  given  herein  modi- 
fied accordingly.  Slabs  with  paneled  ceiling  or  with  depressed  paneling  in  the  floor  are  to  be  considered  as  coming 
under  the  recommendations  herein  given. 

(r)  Bending  Moments  in  Columns. — Provision  should  be  made  in  both  wall  columns  and  interior  columns  for 
the  bending  moment  which  will  be  developed  by  unequally  loaded  panels,  eccentric  loading,  or  uneven  spacing  of 
columns.  The  amount  of  moment  to  be  taken  by  a  column  will  depend  upon  the  relative  stiffness  of  columns  and 
slab,  and  computations  may  be  made  by  rational  methods,  such  as  the  principle  of  least  work,  or  of  slope  and  de- 
flection. Generally,  the  larger  part  of  the  unequalized  negative  moment  will  be  transmitted  to  the  columns,  and 
the  column  should  be  designed  to  resist  this  bending  moment.  Especial  attention  should  be  given  to  wall  columns 
and  corner  columns. 


2 


858 


CONCRETE  ENGINEERS'  HANDBOOK 


STANDARD  BUILDING  REGULATIONS  FOR  THE  USE  OF  REINFORCED  CONCRETE, 
AMERICAN  CONCRETE  INSTITUTE,  1917,  PART  PERTAINING  TO  FLAT-SLAB 

FLOORS 


Continuous  flat-slab  floors,  reinforced  with  steel  rods  or  mesh  and  supported  on  spaced  columns  in  orderly 
arrangement,  shall  conform  to  the  following  requirements: 
(a)  Notation  and  Nomenclature. — In  the  formulas  let: 

w  =  total  dead  and  live  load  in  pounds  per  square  foot  of  floors. 

li  =  span  in  feet  center  to  center  of  columns  parallel  to  sections  on  which  moments  are  considered. 
h  =  span  in  feet  center  to  center  of  columns  perpendicular  to  sections  at  which  moments  are  considered. 
c  =  average  diameter  of  column  capital  in  feet  at  point  where  its  thickness  is  l^-i  in. 
Q  =■  distance  from  center  line  of  the  capital  to  the  center  of  gravity  of  the  periphery  of  the  half  capital 
divided  by  V2C.    For  round  capitals  q  may  be  considered  as  two-thirds  and  for  square  capitals  as 
three-quarters. 
t  =  total  slab  thickness  in  inches. 

L  =  average  span  in  feet  center  to  center  of  columns,  but  not  less  than  0.9  of  the  greater  span. 
The  column-head  section,  mid-section,  outer  section,  and  inner  section,  are  located  and  dimensioned  as 
shown  in  Fig.  3.    Corresponding  moments  shall  be  figured  on  similar  sections  at  right  angles  to  those  shown  in 
Fig.  3. 


head  sedio" 


""  sect  ion 


Mid,  section  ^!l9!(p°j!J'T!r>.~ 

head  section 


#  •  IH 


Fig.  3. 


L  >  V": ....  / 

r  ~''W'less  than  aSL  drop  H 


(o)  Drop  construction 
I 


(b)  Cap  construction 


.-Not  over  J  of  slab  thickness 


j^..„  tiPl°yer_pf>L-Ceiling  panel _ . 


Cc>  PaneHed  ceiling  consfrnxjtion 
Fig.  4. 


(b)  Structural  Variations. — Flat-slab  floors  may  be  built  with  or  without  caps,  drops  or  paneled  ceilings. 
These  terms  are  illustrated  in  Fig.  4. 

Where  caps  are  employed  they  shall  be  considered  a  part  of  the  columns  and  the  column  capital  dimension 
c  shall  be  found  by  extending  the  lines  of  the  capital  below  to  an  intersection  with  the  plane  of  the  under  surface 
of  the  slab  as  indicated  in  Fig.  46.    The  cap  shall  be  large  enough  to  enclose  this  extension  of  the  capital  lines. 

The  column  capital  profile  shall  not  fall  at  any  point  inside  an  inverted  cone  drawn,  as  shown  in  Fig.  4a, 
from  the  periphery  of  the  designed  capital  of  diameter  c  and  with  a  base  angle  of  45  deg.  The  diameter  of  the  de- 
signed capital  c  shall  be  taken  where  the  vertical  thickness  of  the  column  capital  is  at  least  1}^  in. 

The  drop,  where  used,  shall  not  be  less  than  0.3  of  L  in  width. 

Where  paneled  ceilings  are  used  the  paneling  shall  not  exceed  one-third  of  the  slab  thickness  in  depth  and 
the  dimension  of  the  paneling  shall  not  exceed  0.6  of  the  paneled  dimension  (see  Fig.  4c). 

(c)  Slab  Thickness. — The  slab  thickness  shall  not  be  less  than  t  =  0.02L\/ w  -\-  I  io.. 

In  no  case  shall  the  slab  thickness  be  less  that      L  for  the  floor  slabs  nor  less  than  —  L  for  the  roof  slabs. 

(d)  Design  Moments. — The  numerical  sum  of  the  positive  and  negative  moments  in  foot-pounds  shall  not 
be  less  than  0.09  wh  (h  —  gc)2.  Of  this  total  amount  not  less  than  40%  shall  be  resisted  in  the  column-head  sec- 
tions.   Where  a  drop  is  used  not  less  than  50  %  shall  be  resisted  in  the  column-head  sections. 

Of  the  total  amount  not  less  than  10%  shall  be  resisted  in  the  mid-section. 
Of  the  total  amount  not  less  than  18%  shall  be  resisted  in  the  outer  sections. 
Of  the  total  amount  not  less  than  12  %  shall  be  resisted  on  the  inner  sections. 

(e)  Exterior  Panels. — The  negative  moments  at  the  first  interior  row  of  columns  and  the  positive  moments  at 
the  center  of  the  exterior  panel  on  sections  parallel  to  the  wall,  shall  be  increased  20  %  over  those  specified  above 
for  interior  panels.    If  girders  are  not  provided  along  the  column  line,  the  reinforcement  parallel  to  the  wall  for 


APPENDIX  C 


859 


negative  moment  in  the  column-head  section  and  for  positive  moment  in  the  outer  section  adjacent  to  the  wall, 
shall  be  altered  in  accordance  with  the  change  in  the  value  of  c.  The  negative  moment  on  sections  at  the  wall  and 
parallel  thereto  should  be  determined  by  the  conditions  of  restraint,  but  must  never  be  taken  less  than  50%  of 
those  for  the  interior  panels. 

(/)  Reinforcement. — In  the  calculation  of  moments  all  the  reinforcing  bars  which  cross  the  section  under 
consideration  and  which  fulfil  the  requirements  given  under  "Arrangement  of  Reinforcement"  may  be  used.  For 
a  column-head  section  reinforcing  bars  parallel  to  the  straight  portion  of  the  section  do  not  contribute  to  the  negative 
resisting  moment  for  the  column-head  section  in  question.  The  sectional  area  of  bars,  crossing  the  section  at  an 
angle  multiplied  by  the  sine  of  the  angle  between  those  bars  and  the  straight  portion  of  the  section  under  considera- 
tion may  be  taken  to  act  as  reinforcement  in  a  rectangular  direction. 

(g)  Point  of  Inflection. — For  the  purpose  of  making  calculations  of  moment  at  sections  away  from  the  sec- 
tions of  negative  moment  and  positive  moment  already  specified,  the  point  of  inflection  shall  be  taken  at  a  distance 
from  center  line  of  columns  equal  to  Hih  —  qc)  -f-  J-^gc.  This  becomes  %{h  +  c)  where  capital  is  circular.  For 
slabs  having  drop  panels  the  coefficient  of  li  should  be  used  instead  of  Ya. 

(h)  Arrangement  of  Reinforcement. — The  design  should  include  adequate  provision  for  securing  the  reinforce- 
ment in  place  so  as  to  take  not  only  the  maximum  moments  but  the  moments  of  intermediate  sections.  If  bars 
are  extended  beyond  the  column  capital  and  are  used  to  take  the  bending  moment  on  the  opposite  side  of  the  column, 
they  must  extend  to  the  point  of  inflection.  Bars  in  diagonal  bands  used  as  reinforcement  for  negative  moment 
should  extend  on  each  side  of  the  line  drawn  through  the  column  center  at  right  angles  to  the  direction  of  the  band 
a  distance  equal  to  0.35  of  the  panel  length,  and  bars  in  the  diagonal  bands  used  as  reinforcement  for  positive 
moment,  should  extend  on  each  side  of  the  diagonal  through  the  center  of  the  panel  a  distance  equal  to  0.35  of  the 
panel  length.  Bars  spliced  by  lapping  and  counted  as  only  one  bar  in  tension  shall  be  lapped  not  less  than  80 
diameters  if  splice  is  made  at  point  of  maximum  stress  and  not  more  than  50  %  of  the  rods  shall  be  so  spliced  at 
any  point  in  any  single  band  or  in  any  single  region  of  tensile  stress.  Continuous  bars  should  not  all  be  bent  up 
at  the  same  point  of  their  length,  but  the  zone  in  which  this  bending  occurs  should  extend  on  each  side  of  the 
assumed  point  of  inflection. 

(i)  Tensile  and  Compressive  Stresses. — The  usual  method  of  calculating  the  tensile  and  compressive  stresses 
in  the  concrete  and  in  the  reinforcement,  based  on  the  assumptions  for  internal  stresses,  should  be  followed.  In 
the  case  of  the  drop  panel,  the  section  of  the  slab  and  drop  panel  may  be  considered  to  act  integrally  for  a  width 
equal  to  the  width  of  the  column-head  section.  Within  the  column-head  section  the  allowable  compression  may 
be  increased  by  10%  over  that  prescribed  in  Sect.  41.i 

1  Section  41. — Reinforced-concrete  structures  shall  be  so  designed  that  the  stresses,  figured  in  accordance  with 
these  regulations,  in  pounds  per  square  inch,  shall  not  exceed  the  following: 

Extreme  fiber  stress  in  concrete  in  compression — 37}^  %  of  the  minimum  compressive  strength  given  in  the 
table  below.  Adjacent  to  the  support  of  continuous  members,  41  %,  provided  the  member  frames  into  a  mass  of 
concrete  projecting  at  least  50  %  of  the  least  dimension  of  the  member  on  all  sides  of  the  compression  area  of  the 
member. 

Concrete  in  direct  compression — 25%  of  the  minimum  compressive  strength  given  in  the  table. 

Shearing  stress  in  concrete  when  main  steel  is  not  bent  and  when  steel  is  not  provided  to  resist  diagonal  ten- 
sion— 2%  of  the  minimum  compressive  strength  given  in  the  table. 

Punching  shear  in  concrete,  7}^  %  of  the  minimum  compressive  strength  given  in  the  table. 

Shearing  stress  in  concrete  when  steel  to  assist  in  resisting  diagonal  tension  is  provided — %  of  the  minimum 
compressive  strength  given  in  the  table  providing  that  sufficient  web  reinforcement  is  supplied  to  carry  the  stresses 
in  excess  of  the  value  allowed  for  the  unreinforced  concrete;  and  providing  further,  that  this  web  reinforcement 
extends  from  top  to  bottom  of  beam  and  is  adequately  anchored  to  the  horizontal  reinforcement.  If  main  rein- 
forcing bars  are  bent  up  and  anchored,  they  may  be  considered  as  part  of  the  web  reinforcement. 

Bond  stress  between  concrete  and  plain  reinforcing  bars — 4%  of  the  compressive  strength. 

Bond  stress  between  concrete  and  approved  deformed  bars — 5%  of  the  compressive  strength. 

Bearing  upon  a  surface  of  concrete  at  least  twice  the  loaded  area — 50%  of  the  compressive  strength  of  the 
concrete. 

Tensile  stress  in  steel — 16,000  lb.  per  sq.  in.,  except  that  for  steel  having  an  elastic  limit  of  at  least  50,000  lb.,  a 
working  stress  of  18,000  lb.  per  sq.  in.  will  be  allowed. 


Tablk  of  Strengths  of  Different  Mixtures  of  Concrete 
(In  Pounds  per  Square  Inch) 


Aggregate 

1  :  3 

1  :m 

1  :  6 

1  :  7H 

1  :9 

3,300 

2,800 

2,200 

1,800 

1,400 

Gravel,    hard    limestone,  hard 

sandstone  and  approved  slag  .  . 

3,000 

2,500 

2,000 

1,600 

1,300 

Soft  limestone  and  sandstone .... 

2,200 

1,800 

1,500 

1,200 

1,000 

Cinders  

800 

700 

600 

500 

400 

860 


CONCRETE  ENGINEERS'  HANDBOOK 


0)  Provision  for  Diagonal  Tension  and  Shear. — In  calculations  for  the  shearing  stress  which  is  to  be  used  as  the 
means  of  measuring  the  resistance  to  diagonal  tension  stress,  it  shall  be  assumed  that  the  total  vertical  shear  on  a 
column-head  section  constituting  a  width  equal  to  one-half  of  the  lateral  dimension  of  the  panel,  for  use  in  deter- 
mining critical  shearing  stresses,  shall  be  considered  to  be  one-fourth  of  the  total  dead  and  live  load  on  a  panel  for  a 
slab  of  uniform  thickness,  and  to  be  0.3  of  the  sum  of  the  dead  and  live  loads  on  a  panel  for  a  slab  with  drop  panels. 

The  formula  for  shearing  unit  stress  shall  hev  =    '  .  ,—  for  slabs  of  uniform  thickness  and  v  =  -  for  slabs  with 

oja  bjd 

drop  panels,  where  W  is  the  sum  of  the  dead  and  live  load  on  a  panel,  b  is  half  the  lateral  dimension  of  the  panel 

measured  from  center  to  center  of  columns,  and     is  the  lever  arm  of  the  resisting  couple  at  the  section. 

The  calculation  for  punching  shear  shall  be  made  on  the  assumption  of  a  uniform  distribution  over  the  section 
of  the  slab  around  the  periphery  of  the  column  capital  and  also  of  a  uniform  distribution  over  the  section  of  the  slab 
around  the  periphery  of  the  drop  panel,  using  in  each  case  an  amount  of  vertical  shear  greater  by  50  %  than  the 
total  vertical  shear  on  the  section  under  consideration. 

The  values  of  working  stresses  should  be  those  recommended  for  diagonal  tension  and  shear  in  Sect.  41. 

(k)  Walls  and  Openings. — Girders  or  beams  shall  be  constructed  to  carry  walls  and  other  concentrated  loads 
which  are  in  excess  of  the  working  capacity  of  the  slab.  Beams  should  also  be  provided  in  case  openings  in  the  floor 
reduce  the  working  strength  of  the  slab  below  the  reqmred  carrying  capacity. 

(0  Unusual  Panels. — The  coefficients,  steel  distribution,  and  thicknesses  recommended  are  for  slabs  which  have 
three  or  more  rows  of  panels  in  each  direction  and  in  which  the  sizes  of  the  panels  are  approximately  the  same.  For 
structures  having  a  width  of  one  or  two  panels  and  also  for  slabs  having  panels  of  markedly  different  size,  an  analy- 
sis should  be  made  of  the  moments  developed  in  both  slab  and  columns  and  the  values  given  herein  modified 
accordingly. 

(m)  Bending  Moments  in  Columns. — Provision  shall  be  made  in  both  wall  columns  and  interior  columns  for  the 
bending  moment  which  will  be  developed  by  unequally  loaded  panels,  eccentric  loading,  or  uneven  spacing  of 
columns.  The  amount  of  moment  to  be  taken  by  a  column  will  depend  on  the  relative  stiffness  of  columns  and  slab, 
and  computations  may  be  made  by  rational  methods  such  as  the  principle  of  least  work  or  of  slope  and  deflection. 
Generally  the  largest  part  of  the  unequalled  negative  moment  will  be  transmitted  to  the  columns  and  the  columns 
should  be  designed,  and  reinforced  where  necessary,  with  these  conditions  in  mind. 

The  resistance  of  any  column  to  bending  in  a  direction  parallel  to  h  shall  not  be  less  than  0 . 022  wih {h  —  qz)  2,  in 
which  wi  is  the  designed  live  load  per  square  foot.  In  determining  the  resistance  to  be  provided  in  exterior  columns 
in  a  direction  perpendicular  to  the  wall  the  full  dead  and  live  load  w  shall  be  used  in  the  above  formula  in  place  of 
w\.  The  moment  in  such  exterior  column  may  be  reduced  by  the  balancing  moment  of  the  weight  of  the  structure 
which  projects  beyond  the  supporting  wall-column  center  line. 

Where  the  column  extends  through  the  story  above,  the  resisting  moment  shall  be  divided  between  the  upper 
and  the  lower  columns  in  proportion  to  their  stiffness.  The  calculations  of  combined  stresses  due  to  bending  and 
direct  load  shall  not  exceed  by  more  than  50  %  the  stresses  allowed  for  direct  load. 


APPENDIX  D 
STANDARD  NOTATION 

(tt)  Rectangular  Beams. 

fs  =  tensile  unit  stress  in  steel. 
fc  =  compressive  unit  stress  in  concrete. 
Es  =  modulus  of  elasticity  of  steel. 
Ec  =  modulus  of  elasticity  of  concrete. 
Es 

"^^^ 

M  =  moment  of  resistance,  or  bending  moment  in  general. 
As  =  steel  area. 

b  —  breadth  of  beam. 

d  =  depth  of  beam  to  center  of  steel. 

k  =  ratio  of  depth  of  neutral  axis  to  depth,  d. 

z  =  depth  below  top  to  resultant  of  the  compressive  stresses. 

j  —  ratio  of  lever  arm  of  resisting  couple  to  depth,  d. 
jd  =  d  —  z  =  arm  of  resisting  couple. 

p  =  steel  ratio  = 

{b)T -beams. 

b  =  width  of  flange. 
b'  =  width  of  stem. 
t  =  thickness  of  flange. 

(c)  Beams  Reinforced  for  Compression. 

A'  =  area  of  compressive  steel. 

p'  =  steel  ratio  for  compressive  steel. 
//  =  compressive  unit  stress  in  steel. 

C  =  total  compressive  stress  in  concrete. 
C  =  total  compressive  stress  in  steel 

d'  =  depth  of  center  of  compressive  steel, 
r  =  depth  to  resultant  of  C  and  C. 

(d)  Shear,  Bond  and  Web  Reinforcement. 

V  =  total  shear. 

V  =  total  shear  producing  stress  in  reinforcement. 
V  =  shearing  unit  stress. 

u  =  bond  stress  per  unit  area  of  bar. 
o  =  circumference  or  perimeter  of  bar. 
So  =  sum  of  the  perimeters  of  all  bars. 
T  =  total  stress  in  single  reinforcing  member, 
s  =  horizontal  spacing  of  reinforcing  members. 

(e)  Columns. 

A  =  total  net  area. 
As  =  area  of  longitudinal  steel. 
Ac  —  area  of  concrete. 

P  =  total  safe  load. 


861 


APPENDIX  E 


CONCRETE  BARGES  AND  SHIPS 

EXTRACT  FROM  REPORT  OF  THE  JOINT  COMMITTEE  OF  THE  AMERICAN 
CONCRETE  INSTITUTE  AND  PORTLAND  CEMENT  ASSOCIATION 

The  idea  of  building  ships  or  other  floating  vessels  of  reinforced  concrete  is  not  new.  For  many  years  and  in 
several  different  countries,  attempts  have  been  made  from  time  to  time  to  build  small  boats  and  barges  of  reinforced 
concrete.  From  the  information  at  hand,  apparently  some  of  these  attempts  have  been  successful  and  the  vessels 
thus  built  have  been  in  use  for  considerable  periods.  However,  no  definite  information  regarding  boats  built 
prior  to  the  war  is  at  hand  which  would  assist  your  Committee  in  solving  the  general  problem  of  the  concrete  ship. 

Since  the  beginning  of  the  war,  however,  owing  to  the  loss  of  the  world's  tonnage  due  to  submarine  sinkings, 
the  attention  of  many  naval  architects,  concrete  engineers  and  others  has  been  drawn  to  the  question  of  concrete 
ships  to  replace  those  sunk.  The  scarcity  of  steel,  wood,  and  labor,  and  the  length  of  time  necessary  to  construct 
ships  of  steel  or  wood  directs  attention  generally  to  the  substitution  of  reinforced  concrete.  Norway  appears  to 
have  taken  the  lead  in  this  work  and  two  different  companies  are  already  building  ships  of  concrete.  The  Porsgrund 
Cement  Works,  whose  Vice  President  and  General  Manager,  Jens  Hauland,  has  recently  been  in  this  country, 
has  already  launched  one  or  more  ships  of  100-tons  cargo  capacity  and  is  reported  to  have  under  construction  a 
ship  of  1000-tons  cargo  capacity.  The  general  design  of  these  ships  follows  generally  that  of  a  framed  steel  ship, 
and  your  Committee  has  been  informed  by  Mr.  Hauland  that  the  weight  compares  very  favorably  with  that  of  a 
steel  ship.    No  definite  information  is  available,  however,  by  which  this  statement  can  be  verified. 

The  Fougner  Steel  Concrete  Shipbuilding  Company  of  Christiania,  Norway,  has  been  building  vessels  since 
June,  1916.  About  eighteen  in  all  have  been  launched  up  to  the  present  time.  Several  others  are  under  con- 
struction. The  "  Namsenfjord"  about  400  tons  displacement  launched  some  time  ago  has  made  a  round  trip 
between  Norway  and  England.  No  detailed  information  is  available  at  the  present  time  regarding  these  vessels 
that  would  throw  light  on  the  general  problem. 

On  this  side  of  the  Atlantic,  at  least  two  ships  are  under  construction.  At  San  Francisco,  a  large  ship  about 
5000-tons  capacity  is  being  built  and,  from  information  at  hand,  will  be  shortly  launched.  Your  Committee 
learns  that  this  ship  is  320  ft.  long,  44  ft.  6  in.  beam  and  30  ft.  0  in.  deep.  At  24-ft.  draft  the  displacement  is 
said  to  be  8000  tons.  The  weight  of  the  hull  is  said  to  be  2200  tons.  At  Montreal,  Canada,  a  small  concrete  ship 
which  will  have  about  300  tons  carrying  capacity  has  already  been  launched  and  is  now  being  equipped.  This 
vessel  is  being  constructed  by  the  Atlas  Construction  Co.,  Ltd.,  of  which  Chas.  M.  Morssen  is  President.  Your 
Committee  is  indebted  to  Mr.  Morssen  for  considerable  data  relating  to  this  ship  and  it  takes  this  opportunity  of 
acknowledging  the  very  courteous  treatment  shown  its  representatives  by  Mr.  Morssen  and  the  freedom  with  which 
he  discussed  the  details  of  the  design  and  construction.  This  ship  is  126  ft.  0  in.  long,  between  perpendiculars,  22  ft. 
6  in.  beam,  with  a  depth  of  12  ft.  6  in.  The  displacement  is  about  650  tons.  The  ship  will  be  self-propelled  and 
is  now  being  equipped  with  boilers  and  engines.  She  will  shortly  make  her  first  trip.  No  estimate  of  cost  is  at 
present  available. 

With  the  exception  of  the  two  ships  noted  above,  little  information  has  been  gained  from  the  ships  now  under 
construction  which  will  assist  in  the  solution  of  the  concrete  ship  problem. 

The  present  report  will  confine  itself  to  a  general  statement  of  the  several  elements  which  make  up  the  concrete 
ship  problem  and  a  discussion  of  the  information  obtained  from  the  tentative  design  of  a  concrete  ship. 

In  order  to  make  any  advance  toward  the  solution  of  the  concrete  ship  problem,  information  must  be  obtained 
concerning  several  points  regarding  which  only  meager  information  is  now  available.  These  points  taken  together 
constitute  the  concrete  ship  problem. 

1.  The  Relation  Between  Carrying  Capacity  and  Displacement. — The  displacement  of  a  ship  is  the  weight  of 
the  water  she  displaces,  and  is  therefore,  the  sum  of  the  weight  of  the  ship  itself  and  its  cargo  capacity  expressed  in 
tons.  The  cargo  capacity  will  hereafter  be  spoken  of  as  the  "dead  weight" — following  the  usual  practice  with 
naval  architects.  Wherever  displacement,  dead  weight  or  weight  of  ship  is  spoken  of,  it  will  be  in  terms  of  long 
tons  (2240  Ib^.y^which  is  the  usual  practice. 

It  is  apparent  that  the  efficiency  of  a  ship  as  a  cargo  carrier  depends  upon  the  relationship  between  dead  weight 
and  displacem,ent.  Expressed  in  terms  of  %,  in  the  average  cargo  ship  built  of  steel,  the  dead  weight  is  from  70  to 
75  %  of  the  displacement — taking  into  account  as  weight  of  ship  all  spars,  fittings,  deck  houses,  anchors  and  chains, 
auxilia^3J^  engipes  and  tanks,  but  not  boilers,  engines  or  coal.  In  a  wooden  ship,  the  dead  weight  is  from  60  to  65% 
-  W'  5s*^'v-   863 


864 


CONCRETE  ENGINEERS'  HANDBOOK 


of  the  displacement.  It  is  quite  evident  that  from  the  difference  in  weight  of  materials,  it  will  be  difficult  to  design 
a  ship  of  concrete  that  will  give  a  relationship  between  dead  weight  and  displacement  approaching  that  of  steel. 
However,  if  ships  are  to  be  built  of  concrete  for  commercial  use,  the  weight  of  the  ship  must  be  such  as  to  provide 
a  reasonable  dead  weight  or  cargo  capacity  for  the  displacement. 

2.  Transverse  Strength. — The  stresses  in  the  transverse  members  of  a  ship  are,  in  still  water,  functions  of  the 
draft  and  the  stiffness,  and  may  be  computed  by  mathematical  processes,  although  the  computations  are  long  and 
laborious.  When  the  material  is  reinforced  concrete,  the  problem  becomes  much  more  complicated.  Experience 
has  shown,  however,  that  numerous  elements  other  than  draft  effect  the  transverse  strength  of  a  ship,  such  as  the 
effect  of  rolling  in  a  sea  way,  impact  with  docks  or  other  ships  and  stresses  incident  to  going  into  dry-dock.  The 
transverse  members  of  cargo  ships  of  today  are,  therefore,  not  designed  to  withstand  computed  stresses,  but  are 
designed  in  accordance  with  various  rules  which  embody  the  result  of  long  experience  in  the  construction  and  use 
of  ships.    It  should  be  noted  in  this  connection  that  granting  of  insurance  depends  on  compliance  with  these  rules. 

Steel  ships  are  of  two  different  types  (a)  framed  ships  in  which  transverse  ribs  or  frames  are  spaced  from  18  to 
24  in.  on  centers,  the  plating  being  rivetted  to  these  ribs  without  intermediate  longitudinal  members,  excepting 
in  the  bottom,  and  (6)  longitudinally  framed  ships  (Isherwood)  in  which  heavy  frames  are  spaced  from  10  to  15  ft. 
on  centers  with  intermediate  longitudinals  to  which  the  plating  is  rivetted. 

From  a  comparison  with  the  ordinary  steel  ship  design,  it  would  appear  to  be  not  difficult  to  design  transverse 
members  of  reinforced  concrete  of  equivalent  strength  to  steel  members — the  question  of  strength  only  being 
considered. 

3.  Longitudinal  Strength. — A  ship  must  be  able  to  meet  conditions  which  are  unlike  any  to  which  land  structures 
are  subject. 

In  determining  the  longitudinal  strength  of  a  ship,  it  is  customary  to  assume  two  conditions.  Under  the  first 
condition,  the  ship  is  assumed  to  be  suspended  between  two  wave  crests,  the  length  between  crests  being  equal  to 
the  length  of  the  ship  between  perpendiculars,  the  height  of  the  wave  being  equal  to  one-twentieth  of  that  length. 
In  this  case,  the  ship  as  a  whole,  is  acting  as  a  simple  beam  supported  at  the  ends.  This  condition  is  termed  "sag- 
ging. "  Under  the  second  condition  the  ship  is  assumed  to  be  supported  amidships  on  one  crest  of  the  same  wave. 
Under  this  condition,  the  ship  as  a  whole  acts  as  a  cantilever.  This  condition  is  termed  "hogging."  It  is  ap- 
parent therefore,  that  when  a  ship  is  riding  the  waves  both  the  deck  and  the  bottom  of  the  ship  will  be  required  to 
withstand  tensile  and  compressive  stresses  alternately — the  maximum  tensile  stress  following  the  maximum  com- 
pressive stress  at  very  short  intervals.  In  a  steel  ship  the  entire  cross-sectional  area  of  the  midship  section  acts 
to  resist  these  stresses,  taking  into  account,  in  determining  the  moment  of  inertia,  all  of  the  continuous  members 
such  as  continuous  scantlings  and  deck,  side  and  bottom  plates.  In  the  concrete  ship,  equivalent  strength  must 
be  provided.  In  the  case  of  the  concrete  ship,  however,  only  the  steel  reinforcement  can  be  relied  upon  to  take 
tensile  stresses.    The  concrete,  assisted  by  the  steel,  will  take  the  compressive  stresses. 

The  effect  of  the  rapid  change  of  the  character  of  the  stress  in  either  the  deck  or  the  bottom  is  much  more  serious 
in  the  case  of  concrete  ship  than  in  the  steel  ship  for  the  reason  that  owing  to  the  low  tensile  stress  of  concrete, 
cracks  will  occur  at  the  extreme  fiber  under  relatively  low  tensile  stresses  in  the  steel.  These  cracks,  if  any,  alter- 
nately opening  and  closing,  may  tend  to  cause  disintegration,  with  resulting  leaks  or  impairment  of  the 
reinforcement. 

At  the  present  time,  little  information  is  available  as  to  the  effect  of  such  reversal  of  stress,  and  but  little  can 
be  hoped  for  until  an  actual  trial  has  been  made  of  a  concrete  ship  in  a  sea. 

4.  Elasticity. — There  is  an  almost  unanimous  opinion  among  naval  architects  and  seafaring  men  generally 
that  a  concrete  ship  will  be  so  inelastic  that  she  will  tear  herself  to  pieces  in  a  sea.  While  it  is  doubtless  true  that  in 
a  concrete  ship  there  will  not  be  the  same  readjustment  of  stresses  as  in  a  steel  ship  when  subject  to  the  action  of  a 
heavy  sea,  experience  with  reinforced  concrete  structures  generally  has  shown  that  such  structures  have  consider- 
able elasticity  and  there  is  ample  reason  for  the  hope  that  reinforced  concrete  will  prove  a  suitable  material  for 
ship  building  purposes. 

6.  Effects  of  Sea  Water  on  Concrete  and  Reinforcing  Steel. — Until  very  recently  little  information  has  been 
available  as  to  the  effect  of  sea  water  on  concrete.  The  recent  work  of  the  Bureau  of  Standards,  acting  in  co- 
operation with  the  Portland  Cement  Association,  has  thrown  considerable  light  on  what  may  be  expected  from  the 
action  of  sea  water.  The  result  of  their  investigation  tends  to  show  that  inferior  concrete  or  concrete  of  which 
the  surface  skin  has  been  impaired  suffers  serious  disintegration  when  in  contact  with  sea  water.  Inasmuch  as  in 
most  instances  the  structures  examined,  which  form  the  basis  of  the  report  of  the  Bureau  of  Standards,  were  built 
without  thought  as  to  the  action  of  sea  water  (it  being  assumed  that  there  would  be  no  deleterious  action)  there  is 
every  reason  to  hope  that  where  the  effect  of  sea  water  is  appreciated,  and  where  steps  are  taken  in  the  way  of 
selected  materials  and  adequate  workmanship,  assuring  a  good  mix  and  a  satisfactory  surface  skin,  the  concrete 
will  not  so  deteriorate. 

With  regard  to  the  effect  of  sea  water  on  the  reinforcing  steel,  there  is  some  question  as  to  whether  a  thin  layer 
of  concrete  can  be  relied  upon  to  protect  the  steel  from  corrosion.  To  provide  a  thick  protective  layer  of  concrete 
outside  of  the  reinforcing  steel  is  practically  out  of  the  question,  owing  to  the  large  increase  in  weight.  If  the 
reinforcement,  therefore,  is  to  be  maintained  in  perfect  condition,  the  steel  must  be  protected  by  galvanization 
and  by  increasing  the  efficiency  of  the  protective  concrete  by  means  of  additional  care  in  materials  and  workman- 
ship and  by  a  surface  coating  of  a  waterproofing  character. 

6.  Relative  Cost. — Just  at  the  present  time,  the  demand  for  tonnage  is  so  great  that  any  ship  of  reasonable 
capacity  that  can  be  used  for  carrying  cargo  will  prove  financially  successful.    The  relative  costs  of  ships  of  concrete 


APPENDIX  E 


865 


and  steel,  or  concrete  and  wood,  is  not  therefore  as  important  a  consideration  as  it  will  be  after  the  war  when  condi- 
tions again  approach  the  normal.  However,  it  is  necessary  to  have  an  adequate  idea  of  the  probable  cost  of  a 
concrete  ship  as  well  as  a  comparison  with  the  cost  of  steel  and  wooden  ships. 

7.  Speed  of  Construction. — Speed  of  construction  is  of  vital  importance  in  the  ship  building  program  today 
owing  to  the  immediate  requirements  for  tonnage.  If  it  shall  be  found  that  the  concrete  ship  can  be  constructed 
in  much  less  time  than  a  steel  or  wood  ship,  this  fact  will  contribute  largely  to  the  success  of  the  concrete  ship. 

Although  there  are  some  questions  regarding  the  concrete  ship  which  can  only  be  answered  by  actual  experiment, 
the  studies  which  your  Committee  has  made  point  to  the  commercial  success  of  the  concrete  ship. 

Your  Committee  suggests  that  specifications  for  a  concrete  vessel  should  embody  the  following  principles: 

(a)  Both  cement  and  aggregates  should  be  selected  with  great  care  to  insure  a  concrete  of  maximum  efficiency. 

(b)  The  concrete  should  be  placed  in  one  continuous  operation  to  insure  monolithic  construction.  The  concrete 
mixture  should  be  such  as  will  develop  a  crushing  strength  in  excess  of  3000  lb.  per  sq.  in.  when  tested  in  standard 
cylinders  at  28  days.  A  concrete  consisting  of  one  part  Portland  cement,  one  part  sand  and  two  parts  H-in. 
aggregate  may  be  expected  to  give  such  a  concrete.  The  mixture  and  workmanship  in  placing  must  be  such  as  will 
assure  impermeability. 

(c)  The  reinforcing  steel  should  be  in  the  form  of  deformed  bars  and  should  be  galvanized. 

(d)  In  parts  of  the  vessel  where  cracks  in  the  concrete  would  tend  to  cause  leaks,  the  stress  in  the  steel  should 
be  kept  low  (preferable  less  than  12,000  lb.). 

(e)  Some  form  of  elastic  waterproofing  coating  should  be  applied  to  the  hull  below  the  deck. 


65 


INDEX 


Aberthaw  Construction  Co.,  108,  110,  120,  122,  123, 

131,  256,  823 
Abrasive  resistance  of  mortars,  255 
Absorptive  properties  of  concrete,  262 
Abutments  for  steel  bridges,  645-649 

buried-pier,  648 

care  in  constructing,  649 

cellular,  647 

pier  abutments,  645 

skeleton  and  arched,  648 

T-abutments,  647 

U-abutments,  647 

wing  abutments,  646 
Abutments  in  arch  bridges,  702 

of  arches,  653 
Acids,  effect  on  concrete,  257 
Adhesive  strength  of  mortars  and  concretes,  246 
Adjustable  beam  saddles,  145 
Aggregates,  12-31 

blast-furnace  slag,  17 

cinders,  17 

classification,  12 

coarse,  12,  13 
requirements,  20 

colored,  92 

cost  affected  by  grading,  23 
crushed  stone,  19 
density  and  strength,  22 

effect  on  strength  of  mortar  and  concrete,  218-222 
fine,  12,  13 

materials  suitable  for,  17 

requirements,  19 
for  concrete  products  manufacture,  152 
grading  of  mixtures,  22 
granite,  13 
gravel,  16 
impurities,  21 
limestone,  15 
mechanical  analysis,  23 
metamorphic  rocks,  16 

mica,  clay,  and  loam,  effect  on  strength,  224 
mineral  character,  effect  on  strength  of  concrete, 
219 

N.  Y.  Public  Service  Commission  test,  27-30 
physical  characteristics,  67 
plums,  21 
preheating,  77 
preparation  of,  171-173 
quality  of  sands,  19 
sand,  18 
sandstone,  15 
screenings,  19 
sea  sand,  19 
sedimentary  rocks,  14 
shape  and  size  of,  221 
particles  of  sand,  19 


Aggregates,  size  and  gradation  of  particles,  22 
specific  gravity,  tests  for,  25 

specifications  of  N.  Y.  Public  Service  Commission, 
30 

standard  sand,  19 

test  of  sand  used  in  N.  Y.  City,  23 

testing,  219 
on  the  job,  68 

tests  of,  27-30 

trap  rock  or  diabase,  14 

voids  in,  25-27 
Air  bubbles  on  concrete  surface,  167 

entrained,  75 
Akme  flat-slab  system,  467 

computations  for,  488 

tables,  505,  506 
Alaska-Gastineau  Mining  Co.,  739 
Alkali,  action  on  concrete,  257 
Allen,  L.  H.,  823 
Ambursen  dam,  743 

type  of  dam  apron,  741 
American  bars,  44 

American  Concrete  Institute,  computations  for  Corr- 
plate  floors,  489 
loading  tests  for  floors,  483-486 
paper  on  form  design,  123 

recommendations  on  design  of  exterior  columns, 
470 

on  natural  and  steam  curing  of  concrete,  156,  158 
report  on  bridges,  655 

on  concrete  ships,  863 

on  design  of  flat-slab  floors,  487 
ruling  on  flat  slab  floors,  495 

on  flat-slab  design,  858 
specifications  for  concrete  pavement,  24 

for  concrete  stone,  168 
American  Concrete  Steel  Co.,  479 
American  Society  for  Testing  Materials,  10,  27 
field  testings  of  concrete,  79 
specifications  for  reinforcement  bars,  38,  41 

for  strength  of  mortar,  248 
American  Society  of  Civil  Engineers,  28 
on  remixing  of  concrete,  232 
rulings  on  flat-slab  design,  854 

See  also  Joint  Committee  on  Concrete  and  Rein- 
forced Concrete. 
American  Steel  and  Wire  Co.,  47 
American  System  of  Reinforcing,  44,  48,  58 
American  wire  clamp,  119 
Ames  gage,  266 

Analysis  of  aggregates,  mechanical,  23 
of  beams,  314 

of  the  arch  by  elastic  theory,  660-668 
Anderson,  A.  O.,  778,  782 
Anti-freezing  mixtures,  78 
Aprons  of  dams,  741 

867 


868 


INDEX 


Arch  bridges,  details  of,  691-702 

piers  and  abutments,  702 

railing  and  ornamental  details,  702 

spandrel  details,  691,  694 
culverts,  796-799 
ring  construction,  702 

thickness  of,  656,  658 
Arched  abutments  for  bridges,  648 

dams,  design  of,  736 
Arches,  651-721 

analysis  by  elastic  theory,  660-668 
arch  ring,  thickness  of,  656,  658 
arrangement  of  spandrels,  653 
axis,  shape  of,  658 
classification  of  arch  rings,  660 

Cochrane's  formulas  for  designing  symmetrical 

arches,  669-691 
construction  of,  702-715 
curve  of  the  intrados,  651 
dead  loads  and  their  action  lines,  658 
definitions  of  terms,  651 
designing  an  arch  ring,  665 
details  of  arch  bridges,  691-702 
filling  at  crown,  depth  of,  654 
formulas  for  thrust,  shear,  and  moment,  663 
internal  temperature  investigations,  664 
line-of-thrust  theories,  659 
loads,  654 
parabola,  653 
piers  and  abutments,  653 
reinforcement  of  concrete,  660 

report  on  bridges,  of  American  Concrete  Institute, 
655 

semi-ellipse,  652 

temporary  hinges,  use  in  erection,  659 
testing  trial  arch,  658 

thickness  of  arch  ring,  rules  for,  656,  658 
three-centered  curve,  652 
three-hinged,  715-721 

See  also  Elastic  theory  of  stability  of  the  arch. 
Areas  of  rods,  table,  354 
Arrow  Rock  Dam,  236 

tests  on  concrete,  261 
Association  of  American  Steel   Manufacturers,  steel 

specifications,  37,  40 
Atlas  Construction  Co.,  Ltd.,  863 
Austin  dam,  743 
Autoclave  test,  11 
Axial  compression,  845 
Ayres  (F.  C.)  Mercantile  Co.,  810 

Bach,  Prof.,  475 

Backfilling  of  retaining  wall,  601 
Backwater  curve  of  a  dam,  726 
Bailey,  F.  S.,  290 

Bank-run  gravel,  proportioning,  70 

Bankers  for  concrete  stone  manufacture,  156 

Bar  bender,  140 

Bar-chairs,  145 

Barges,  concrete,  863-865 

Barney,  Prof.,  225 

Barrett  Co.,  517 

Barrows  for  concrete,  193 

Bars,  bent,  for  web  reinforcement,  296 

Bars,  reinforcement,  36-45 


Bars,  reinforcement,  American  bars,  44 
corrugated  bars,  43 
deformed  bars,  42 
diamond  bars,  42 
factors  affecting  cost,  42 
Havermeyer  bars,  43 
inland  bars,  44 
rib  bars,  44 
size  extras,  42 

steel  specifications,  37,  38,  40,  41 
Barton  Spider  Web  flat-slab  system,  461 
Basement  floors,  438 

walls,  545 
Bates,  R.  H.,  87 
Bazin,  750,  753 

Beam-and-girder   construction,   compared   with  flat- 
slab,  457 

moments  at  columns  in,  416-425 

monoUthic,  439-456 

forms,  103 
Beam  concentrations,  331 

spacers,  143 

tests  on  reinforced  concrete,  269 
Beams  and  slabs,  273-370 

designing  tables,  341-359 
diagrams,  360-370 
rectangular  beams,  273-307 

shear  and  moment  in  restrained  and  continuous 
beams,  318-341 

slabs,  306,  307 

special  beams,  314-317 

T-beams,  307-313 

tables,  354-359 
Beams,  continuous  and  restrained,  shear  and  moment 
in,  318-341 

deflection  formulas  for  curved,  660 

in  flat-slab  floors,  497 
Beams,  rectangular,  273-307 

Beard  and  Schuler's  charts,  350 

bending  points  of  horizontal  reinforcement,  297 

bent  bars  and  vertical  stirrups  for  web  reinforce- 
ment, 296 

bond  stress,  284 

deflection  of  rectangular  beams,  304 

depth  of  concrete  below  rods,  300 

designing,  341-344  i 

diagrams,  360,  366-369 

distribution  of  stress  in  homogeneous  beams,  273 
economical  proportions,  302 
flexure  formulas,  276-280 

formulas  for  percentages  of  steel  in  reinforced 

beams,  304 
Leffler's  chart  for  designing,  348,  370 
lengths  of  beams,  280 
moment  and  diagonal-tension  tests,  281 
placing  stirrups  from  the  moment  diagram,  291 
plain  concrete  beams,  275 

purpose  and  location  of  steel  reinforcement,  275 

ratio  of  length  to  depth  of  beam,  301 

shear  reinforcement,  286 

shearing  stresses,  280 

steel  in  compressive  side  of  beam,  302 

strength  in  moment  and  shear,  301 

strengthening  against  failure  in  diagonal  tension. 


INDEX 


869 


Beams,  rectangular,  tables,  354-356,  359 

tensile  stress  lines,  275 

theory  of  flexure,  275 

transverse  spacing  of  reinforcement,  300 

vertical  stirrups,  289 

web  reinforcement,  285 
Beams,  reinforcement  of,  table  of  rods  and  area  for,  357 

restrained,  shear  and  moment  in,  318-341 
Beams,  special,  314-317 

analysis,  314 

designing  double-reinforced,  317 
moment  of  inertia,  of  complex  sections,  317 
neutral  axis,  location  of,  315,  316 
of  complex  sections,  314 
resisting  moment  of  beams,  316 
Beams,  T-beams,  307-313 
analysis,  315 

bonding  of  web  and  flange,  308 
conditions  met  in  design  of,  310 
continuous,  at  the  supports,  design  of,  311 
deflection  formulas,  306,  313 
designing,  345,  352 

by  Beard  and  Schuler's  chart,  350 

for  shear,  310 
economical  considerations,  310 
flange  width,  308 
flexure  formulas,  308 

formulas  for  percentages  of  steel  in  reinforced 

beams,  313 
Leffler's  chart  for  designing,  349,  370 
proportions,  310 

steel  in  double-reinforced,  formulas,  313 

tables  for  designing,  364,  365 
for  formulas,  359 

tests,  307 
Beams,  wedge-shaped,  314 

diagrams,  361 
Beard,  R.  S.,  304,  309,  403 

Beard  and  Schuler's  charts  for  designing  beams  and 

slabs,  350 
Bearing  capacity  of  soils,  557 
table,  583 

walls,  532 
Belt  conveyors,  177 
Bending  and  direct  stress,  385-409 
Bending  and  placing  reinforcement,  139-146 

bar  bender,  140 

care  necessary,  141 

hand  devices,  139 

placing  of  reinforcement,  142 

power-operated  benders,  141 

slab  reinforcement,  142 

types  of  bends,  139 

Universal  bar  bender,  140 
Bending-moment  curves  for  beams,  335 

moments  in  slabs,  diagrams,  362,  363 
Berger  Mfg.  Co.,  57 
Berry,  Prof,  H.  C,  254 

Billet-steel  reinforcement  bars,  specifications,  37,  38 
Bins,  deep  grain,  805-810 
shallow,  810-815 

designing,  data  for,  812 

friction  angles  of  various  materials,  813 

pressure  on  sides,  811,  812 

submerged  storage  for  coal,  813 


Bins,  shallow,  weights  and  angle  of  repose  of  materials, 
812 

See  also  Grain  bins. 
Bitumens  applied  to  concrete,  88 
Blast-furnace  slag,  6 

as  an  aggregate,  17 

proportioning  in  concrete,  71 
Blaw  Steel  Construction  Co.,  110,  136,  713 
Block,  concrete,  146-169 
Bond  between  concrete  and  steel,  265 

stress  of  steel  beams,  284 

stresses,  in  column  footings,  561 
Bonding  set  and  new  concrete,  75 
Boom  plants,  203 
Boussinesque,  751,  753 
Bouvier,  M.,  733 
Box  culverts,  783-796 
Brackets,  column,  530 
Bradley  Knitting  Co.,  571 
Brick,  concrete,  146-169 

exterior  wall  supports  for  floors,  498 

parapet  walls,  522 

veneer,  539 
Bridges,  arch,  details  of,  691-702 

arches,  651-721 

cantilever,  639-641 

concrete  floors  and  abutments  for,  643-649 

continuous-girder,  622-638 

girder,  613-622 

slab,  603-612 

See  also  Arches. 
Brown  Hoisting  Machinery  Co.,  57 
Brushing  concrete  surfaces,  92 

stone  surfaces,  165 
Bucket,  clam-shell,  176 

unloaders  and  conveyors,  177 
Buckets  for  concrete,  194 

for  concrete  products  manufacture,  154 
Building  Codes,  Rochester,  and  Seattle,  431 

frames,  moments  in,  411-430 

tests,  480 
Buildings,  431-555 

columns,  527-532 

construction  methods  and  safeguards,  506 

contraction  and  expansion,  provision  for,  554 

elevator  shafts,  552-554 

floors,  concrete,  431-512 

roofs,  512-527 

stairs,  549-552 

steel-frame  construction,  511 

unit  construction,  508-511 

walls  and  partitions,  532-549 
Buried-pier  abutments,  648 
Bush  Stores,  182 

Buttresses  of  reinforced-concrete  dams,  740 

Cableways  for  transporting  concrete,  195 

Caissons  for  dams,  728 

Calcium  chloride,  effect  on  concrete,  236 

quicklime,  2 
California  R.  R.  Commission,  745 
Candlot,  233 

Cantilever  bridges,  639-641 

flat-slab  construction,  463,  481 
of  bridges,  612 


870 


INDEX 


Cantilever  footings,  568 

walls  of  reinforced  concrete,  587-592 
Carton  molds  for  concrete  tests,  81 
Carts,  concrete,  193 
Casey,  John  F.,  Co.,  763 
Casting  concrete  in  sand,  161 
Catskill  Reservoir,  N.  Y.,  763 
Cellular  abutments,  647 
Cement,  1-62 

bulk,  use  of,  12 

chemical  analysis,  11 

common  lime,  1 

consistency,  9 

containers  for,  11 

fineness,  8 

grappier,  2 

grouting,  88 

gypsum  plasters,  1 

handling  in  sacks,  177 

hydraulic  and  non-hydraulic,  1 

hydraulic  lime,  2 

manufacture,  6-8 

natural  cement,  3 

non-hydraulic,  1 

Portland  and  natural  cement,  4 

puzzolan,  2 

rock,  6 

sacks,  bundling  and  storage,  178 
sand,  4 
seasoning,  12 
slag,  2 

soundness,  10 
specifications  for,  11 
specific  gravity,  11 

storage  and  conveying  for  concrete  products,  151 

storing,  11,  173 

strength,  10 

testing,  8 

time  of  setting,  9 

tufa,  4 

weight,  12 

See  also  Portland  cement. 
Cement  mortar,  properties,  215-263 
aggregates,  218-222 

compressive  and  tensile  strengths  compared,  227 
consistency,  relation  to  strength,  225 
contraction  and  expansion,  252-254 
curing  conditions,  effect  on  strength,  234 
durability,  254-259 
effect  of  freezing,  236 

of  method  of  placing,  on  strength,  231 
of  mica  clay,  and  loam  in  aggregates,  224 
of  size  of  sand  on  strength  of,  221 
elastic  properties,  250-252 
laboratory  tests  of  strength,  215 
method  of  mixing,  effect  on  strength,  230 
permeability,  and  absorptive  properties,  262 
porosity,  261 
regaging,  232 

relation  between  density  and  strength,  222 
rise  of  temperature  in  setting,  259 
salts,  effect  of,  236  • 
strength,  215-250 

compared  with  neat  cement,  217 
weight,  263 


Centering  arches,  704 
Centering  fabrics,  55 

See  also  Self-centering  fabrics. 
Chair  lock,  146 

pinchers,  146 

spacers,  145 
Chalk,  for  cement  manufacture,  7 
Chambers,  S.  H.,  258 
Chanelath,  56 
Chapman,  C.  M.,  82,  238 
Charging  hoppers,  190 
Charts,  Beard  and  Schuler's,  350 

Leffler's  comprehensive  beam,  348,  370 
Checking  materials  on  the  job,  69 
Chemical  analysis  of  cements,  11 

hardeners  for  concrete  floors,  210 
Chezy  formula,  727 

Chicago  Building  code,  460,  462,  465,  483-486 
cube  mixer,  230 

flat-slab  design  rulings,  847,  849 
Chicago,  Milwaukee  &  St.  Paul  Railway,  box  cul- 
vert, 785 

bridges,  625 
Chicago  ruling  for  flat-slab  construction,  494 

for  flat-slab  panels,  501-503 
Chile  Exploration  Co.,  768 
Chimneys,  reinforced-concrete,  816-821 

bases,  820 

construction,  820 

dead-load  stresses,  816 

eccentric  load,  407 

longitudinal  shear,  819 

stresses  on  annular  sections  in  flexure,  816 

temperature  stresses,  819 

wind  stresses,  818 

without  vertical  reinforcement,  818 
China-wood  oil,  on  concrete  floors,  210 
Churn  drills,  171 

Chutes  for  transporting  concrete,  195 
Cinder-concrete  insulation  for  roofs,  514 

concrete,  strength  of,  248 

fill  for  roofs,  514 
Cinders,  as  an  aggregate,  17 

proportioning  in  concrete,  71 
Circumferential  flat-slab  system,  461,  471 
Clam-shell  buckets,  176 
Clay  cement  in  a  sandstone,  18 

for  cement  manufacture,  6 

in  aggregates,  21,  224 
Cleveland  Building  Code,  462,  477,  478 

Railway  Co.,  476 

reservoir,  763 
Cline,  A.  E.,  158 
Clinton  Wire  Cloth  Co.,  46 
Coal  bins,  see  Bins,  shallow. 

submerged  storage  for,  813 
Coarse  aggregates,  12,  20 
Cochrane,  V.  H.,  658 

Cochrane's  formulas  for  designing  arches,  669-691 
Coefl&cient  of  expansion  of  steel,  37 
Cold,  effect  on  concrete  floors,  209 
Cold-weather  concreting,  77 
Colored  aggregates,  92 
Colors,  adding  to  concrete,  93 
for  concrete  floors,  206 


INDEX 


871 


Colors  of  concrete  products,  164 

Columbia  Univ.,  tests,  250 

Column  footings,  see  Footings,  concrete. 

forms,  96-103 

heads,  forms  for,  108 

moment,  486 

reinforcement,  table  of  rods  and  area  for^  357 
Columns,  concrete,  371-384,  527-532 

bracket  loads,  stress  in  columns  supporting,  381 

brackets,  530 

combined  stresses  in,  426 

definition  by  Joint  Committee,  371 

design,  details  of,  527 

diagram  for  designing,  374,  382 

formula  for  bending  stress,  371 

hooped  and  longitudinal  reinforcement,  372 

in  flat-slab  construction,  497 

load  tables,  374-381 

loading,  530 

long,  reduction  formula,  381 
longitudinally  reinforced,  371 
maximum  combined  stresses,  426 
modulus  of  elasticity,  371 
moments  at,  415,  416-425,  486 
plain,  371 

reduction  formula,  381 

reinforced  with  structural-steel  shapes,  372 
strength  of,  229 

stresses  for  hollow  and  solid,  407-409 
supporting  bracket  loads,  stress  in,  381 
types,  371 

working  stresses,  373 
Combined  column  footings,  565 

stresses  in  columns,  maximum,  426 
Common  lime,  1  ' 
Composite  wood  and  concrete  piles,  573 
Compression  of  beams,  steel  reinforcement  for,  302 
Compressive  strength  of  cement,  10 

of  mortar  and  concrete,  227,  845 
Concrete  Appliances  Co.,  Inc.,  23 
Concrete  barges  and  ships,  863-865 

bonding  set  and  new,  75 

cinder,  strength  of,  248 

columns,  371-384,  527-532 

cost  of,  823-826 

curbing,  212 

depositing,  73-78 

electrolysis  in,  258 
Concrete  Engineering  Co.,  138 
Concrete,  field  tests  of,  78-82 

finishing  surfaces,  90 

floors,  205-210,  431-512 

and  abutments,  for  steel  bridges,  643-649 
forms  for,  93-139 

freezing,  78 

grading  of  sands  for,  23 
hardening  rate  in  warm  weather,  77 
impervious,  rules  for,  89 
machine  vs.  handmixing,  186 
Concrete  materials,  1-62 
aggregates,  12-31 
cement,  1-12 
reinforcements,  36-62 
water,  31-36 

See  also  Handling  concrete  materials. 


Concrete,  mixing,  72,  186 

parapet  walls,  522 

piles,  572 

placing,  73-78 
Concrete,  plain,  properties  of,  215-263 

contraction  and  expansion,  252-254 

durabihty,  254-259 

elastic  properties,  250-252 

permeability  and  absorptive  properties,  262 

porosity,  261 

protection  of  embedded  steel  from  corrosion,  262 
rise  of  temperature  in  setting,  259 
strength,  215-250 
weight,  263 

Concrete  products,  see  Concrete  stone,  manufacture 
and  use  of. 

proportioning,  63-72 

quality  for  reservoir  masonry,  760 

reinforced,  see  Reinforced  concrete. 

remixed  and  retempered,  76 

removing  entrained  air,  75 

roadways,  213-214 

roof  surfaces,  516 

sea  water,  action  on,  256,  864 

ships  and  barges,  863-865 

sidewalks,  210-212 

spading,  puddling,  and  tamping,  75 

specifications  to  prevent  excess  of  water,  36 
Concrete  Steel  Co.,  N.  Y.,  143,  145,  465 
Concrete  Steel  Engineering  Co.,  42,  43 
Concrete  Steel  Products  Co.,  Chicago,  463,  480 
Concrete  stone,  manufacture  and  use  of,  146-169 

aggregates,  kind  and  quality,  152 

agitation  after  mixing,  153 

air  bubbles,  167 

bankers,  156 

brushing,  165 

buckets  and  hoppers,  154 

casting  in  sand,  161 

cement  storage  and  conveying,  151 

colors,  164 

combination  molds,  161 
commercial  molds,  149 
consistency,  148 
crazing,  167  v 
curing,  156 

development  of  industry,  146 

dry-tamp  method,  147 

efflorescence,  167 

face  design  in  standard  units,  162 

facing  materials,  163 

gang  molds  for  wet-cast  products,  151 

materials,  151 

methods  of  manufacture,  147 
mixing,  152 
molds,  159 
mosaics,  167 
natural  curing,  156 
operation  of  machines,  150 
pallets,  155 
placing,  154 
•  plaster  molds,  159 
pressure  method,  148 
rubbing  surface,  166 
sand  molds,  161 


872 


INDEX 


Concrete    stone,   manufacture    of,  specifications  of 
American  Concrete  Inst.,  168 

spraying,  165 

steam  curing,  157 

surfaces,  162 

tamping,  150 

tooling,  166 

waste  molds,  161 

wet-cast  method,  148 

wheelbarrows,  155 

wood  molds,  159 
Concrete,  strength  of,  64,  215-250 

transporting,  72 

waterproofing,  82-90 

weakness,  cause  of,  64 

work,  measurement  of,  830 

working  stresses,  845 
Concreting  in  hot  and  cold  weather,  76-78 

effect  of  weather,  76 

preheating  aggregates  and  water,  77 
Concreting  plant,  181-203 

balancing  the  plant,  181 

cost,  181 

machine  vs.  handmixing,  186 

spouting  plants,  203 

time  of  mixer  operations,  189 

transporting  and  placing  of  concrete,  193-203 

types  of  mixers,  187 

typical  plants,  181 
Condensation  on  roof  slabs,  prevention  of,  513 
Condron,  T.  L.,  483 
Condron  Co.,  467,  488 
Conductivity  of  concretes,  254 
Conduits  and  sewers,  799-803 

construction,  802 

external  earth  pressure,  799 

forms  for  sewers,  803 

longitudinal  reinforcement,  802 

non-circular,  799 

reinforced  pipe,  examples,  803 

stresses  due  to  internal  pressure,  799 
Consistency  of  concrete  stone,  148 

of  mortar  and  concrete,  225 
Consolidated  Expanded  Metal  Cos.,  51,  60 
Constant-angle  dams,  738 
Construction,  methods,  63-169,  506 

bending  and  placing  reinforcement,  139-146 

field  tests  of  concrete,  78-82 

finishing  concrete  surfaces,  90-93 

flat-slab,  457-508 

floor,  monolithic  beam-and-girder,  439-456 
forms,  93-139 
hollow-tile,  447 

manufacture  and  use  of  concrete  stone,  block,  and 

brick,  146-169 
mixing,  transporting,  and  placing  concrete,  72-78 
proportioning  concrete,  63-72 
waterproofing  concrete,  82-90 
See  also  Forms. 
Construction  of  arches,  702-715 
arch-ring  construction,  702 
centering,  704 
sand  boxes,  710 
steel  centers,  712 
three-hinged  arches,  717 


Construction  of  arches,  timber  centers,  704 
Construction  plant,  171-203 

concreting  plant,  181-203 

handling  and  storage  of  materials,  173-179 

preparation  of  concrete  aggregates,  171-173 

typical  installation,  179 
Containers  for  cement,  11 

Continuous  beams,  shear  and  moment  in,  318-341 
Continuous-girder  bridges,  622-638 

analysis  of  stresses,  625 

effect  of  fixed  bases,  638 

examples  of  types,  623 

expansion  joints,  622 

four-span  viaduct  frame,  629,  633 

monolithic  construction,  622 

one-span  frame,  unequal  columns,  636 

one-span  viaduct  frame,  633 

temperature  stresses,  636 

three-span  viaduct  frame,  631,  634 

two-span  viaduct  frame,  632,  634 

viaduct  bent,  638 
frames,  628 
Continuous  slab  spacers,  145 
Contraction  in  buildings,  provision  for,  554 

of  cement  mortar  and  concrete,  252-254 
coefficient  of  expansion,  252 
Conveyances  for  concrete  materials,  174 
Cooper's  Standard  Loadings,  for  railroad  bridges,  656 
Core  drill  test  specimens,  79 
Cornell  University,  mortar  tests,  222 

tests  of  strengths  of  concrete,  229 
on  expansion  of  concretes,  252 
Corr-mesh,  56 
Corr-plate  floors,  470 

computations  for,  489 

tables,  503-505 
Corr  reinforcing  system,  60 
Corr-X-metal,  52 

Corrosion  of  steel  reinforcement,  protection  by  concrete, 
262 

Corrugated  Bar  Co.,  43,  52,  56,  60,  470,  480,  481,  489 
Corrugated  bars,  43 

sheets,  dovetailed,  57 
Costs  of  concrete,  estimating,  823-826 

concreting  plant,  181 

conveying  concrete  materials,  174 

forms,  94,  826-828 

steel  reinforcement,  828 

surface  finish,  829 
Coulomb's  wedge  of  maximum  earth  pressure,  577 
Counterforted  walls,  design  of,  592-600 

back  floor  slab,  593 

cantilever  toe  slab,  596 

methods  of  reinforcing,  596 

thickness  and  spacing  of  counterforts,  592 

vertical  or  face  wall,  593 
Cracks  in  concrete  surfaces,  167 
Cramp  &  Co.,  182 
Crazing  of  concrete  surfaces,  167 
Creager,  W,  P.,  730 
Cream  of  lime,  1 
Crushed  limestone,  172  . 

stone,  19 

aggregate,  preparation  of,  171-173 
screening,  grading,  and  washing,  172 


INDEX 


873 


Crusher-run  stone,  proportioning,  71 
Crushers,  stone,  172 
Culverts,  775-799 

arch,  796-799 

box,  783-796 

circular,  cast  in  place,  782 
construction  of  box  culverts,  794 
design  of  cross-section  of  arch  culverts,  796 
of  box  culverts,  785 

of  ends,  777 
diagrams  of  box  culverts,  794 
efficiency,  776 
factors  in  design,  776 
forms  for  arch  culverts,  797 

for  box  culverts,  795 
length,  776 

loading  of  box  culverts,  785 

loads  on  pipes  in  ditches,  table,  779 

pipe,  777 

pressure  in  trenches,  778 

strength  of  pipe,  781 

waterway  required,  776 
Cumming's  reinforcing  system,  58 
Curbing,  concrete,  212 

Curing  in  concrete  products  manufacture,  156 
Curry  tyer,  143 
Curtain  walls,  533 

Dams,  723-759 
apron,  741 
arched,  design,  736 
automatically  operating,  759 
backwater  curve,  726 
bracing,  741 
buttresses,  740 
caissons,  728 
capacity  of  reservoir,  726 
constant-angle,  738 
constant-radius,  736 
cut-off  walls,  728,  740 
design  of  foundation,  728 
discharge  capacity  of  spillway,  749 
Dunning's  dam,  758 
earthen,  with  concrete  core  wall,  745 
Edge  dam,  743 
final  calculation,  734 
fish  ladders,  759 
foundation  mattress,  740 
Gatun  dam,  754 
geological  investigations,  723 
gravity  section,  design  of,  729 
grouting,  728 
height  of  structure,  724 
hollow  reinforced,  743 
hydrographic  inivestigations,  725 
hydrostatic  pressure,  729 
ice  thrust,  732 
initial  stress,  732 
Kensico  dam,  236 
locating,  723 
Morton  dam,  743 
movable,  758 
multiple  arch,  743 
operation  of  movable  dams,  759 
overflow  dams,  753 
passing  the  discharge,  748 


Dams,  pilings,  728 

preliminary  studies,  723 
profiles,  729 

of  spillways,  749 
Ransome  dam,  743 

reinforced-concrete,  design  of,  739-745 

selecting  suitable  type,  724 

shearing  stresses,  734 

sheet  piling,  728 

siphonic  spillways,  755 

sluices,  754 

spillway,  form  of,  748 

stresses  in  masonry  and  on  foundation,  733 

temperature  stresses,  732 

uplift,  731 

wind  pressure,  732 
Davis,  R.  P.,  222 
Day's  work  planes,  34 
Dead  loads  of  arches,  658 

of  floors,  432 

stresses  on  chimneys,  816 
Decanville  Automobile  Co.,  571 
Deck  girders  for  bridges,  613 
Deere  Webber  Building  Co.,  479,  480 
Defects  in  concrete  floors,  207-210 
Deflection  formulas  for  curved  beams,  660 

of  rectangular  beams,  304 

of  T-beams,  306,  313 
Deformed  bars  for  reinforcement,  42 
Delaware,  Lackawanna,  and  Western  R.  R.  bridge,  715 
Density  of  aggregates,  22 

of  concrete,  maximum,  68 

of  mortars  and  concretes,  222 
Depositing  concrete  in  forms,  73,  74 

through  water,  76 
Designing  columns,  tables  and  diagrams,  374-382 

double-reinforced  beams,  317 

floor  construction,  problem,  440 

forms  for  concrete,  120 

drafting-room  methods,  123 

formulas,  125 

tables  and  diagrams,  124 

hollow-tile  floors,  problem,  453 

retaining  walls,  584,  587-600 

T-beams,  310 

tables  and  diagrams  for  beams,  341-370 
Beard  and  Schuler's  charts,  350 
diagrams,  360-370 

effler's  comprehensive  beam  chart,  348,  370 

tables,  354-359 
Deslaurier's  Column  Mold  Co.,  110 
Detroit  river  tunnel,  232 
Diabase,  14 

Diagonal  tensile  stress  in  beams,  281 
tension  in  column  footings,  562 

Diagrams  for  beams  and  slabs,  341-370 

for  designing  symmetrical  arches,  669-691 

for  stress,  bending  and  direct,  388-402,  404,  405 

Diamond  bars,  42 

Direct  stress,  385-409 

Dock  pockets,  815 

Dolomitic  quicklime,  2 

Door  openings,  543 

Douglas,  W.  J.,  656 

Dovetailed  corrugated  sheets,  57 

Dow,  A.  W.,  248 


874 


INDEX 


Drainage  of  retaining  wall,  601 

of  roofs,  518 
Drills  for  quarrying,  171 
Drum,  J.  L.,  479 
Drum  mixers,  187 

Dry-tamp  method  of  making  concrete  stone,  147 
Duchemin's  formula  for  wind  pressure,  513 
Dunning's  dam,  758 

Durability  of  cement  mortar  and  concrete,  254-259 

abrasive  resistance,  255 

action  of  acids,  oils,  and  sewage,  257 
of  alkali,  257 
of  sea  water,  256 

electrolysis  in  concrete,  258 

fire-resistance  properties,  254 

manure,  effect  of,  259 

weathering  qualities,  255 
Dusting  of  concrete  floors,  206 

Earth  pressure,  575 

coefficients  of  internal  friction,  576 

Coulomb's  wedge  of  maximum  pressure,  577 

Rankine's  formula,  576 

results  of  theories,  interpretation  of,  580 
Earthern  dams,  745 
Easel-chairs,  145 
Eastwood,  743 
Easy  chairs,  143 
Econo  expanded  metal,  53 
Edge,  W.  S.,  457 
Edge  dam,  743 

EflBorescence  of  concrete  surface,  167 
Elastic  properties  of  cement  mortar  and  concrete,  250- 
252 

modulus  of  elasticity,  251 
stress-strain  curves,  250 
yield  point,  251 
Elastic  theory  of  stability  of  the  arch,  659,  660-668 
analysis,  procedure,  661 
arch-ring  design,  665 

arch  structure  of  two  spans  with  elastic  pier,  667 
Cochrane's  formulas  for  designing  arches,  669-691 
correcting  maximum  moments  when  axis  deviates, 
686 

deflection  at  any  point,  664 

deflection  of  curved  beams,  660 

diagrams,    for   moments,   thrusts,    and  average 

stresses,  681 
difficulties  in  applying,  669 
division  of  arch  ring,  663 

formulas  for  thrust,  shear,  and  moment,  663 
influence-line  diagrams,  673 
internal  temperature  investigations,  664 
loadings,  664 

origin  of  coordinates  at  crown,  etc,  665-667 

shape  of  arch  axis,  669 

shrinkage  stresses,  664 

skew  arches,  665 

unsymmetrical  arches,  665 

use  of  influence  lines,  664 

variation  in  thickness  of  arch  ribs,  670 
Electric  Welding  Co.,  58,  146 
Electrolysis  in  concrete,  258 
Elephant  Butte  Dam,  191 
Elevated  tanks,  771-775 
Elevator  shafts,  552-554 


Elevator,  pent  houses,  553 

pits,  552 
Emperger  columns,  529 

Empirical  rules  for  thickness  of  arch  ring,  656 
Entrained  air,  removal  of,  75 
Estimating,  823-832 

concrete,  cost  of,  823-826 

costs,  823-830 

forms,  unit  cost  of,  826-828 

formwork,  831 

labor,  cost  of,  824,  827 

materials,  cost,  823,  827 

measurement  of  concrete  work,  830 

plant,  cost  of,  825 

quantities,  830-832 

steel,  amount  of,  832 

steel  reinforcement,  cost  of,  828 

surface  finish,  amount  of,  832 
cost  of,  829 

unit  costs,  823 
Expanded  metal,  50-54 

Corr-X-metal,  52 

econo,  53 

GF,  53 

Kahn  mesh,  52 

steel  Crete,  51 
Expanded  Metal  Cos.,  546 
Expansion  in  buildings,  provision  for,  554 

joints,  86 

of  cement  mortar  and  concrete,  252-254 
moisture  changes,  253 

Facing  materials  of  concrete  stone,  162 

Factor  of  limita,tion  of  retaining  walls,  584 

Feret,  R.,  243,  244 

Fiber  stresses  of  forms,  124 

Field  tests  of  concrete,  78-82 

carton  molds,  81 

core  drill  specimens,  79 

field-molded  specimens,  79 

limitations,  78 

methods  of  American  Society  for  Testing  materials, 
79 

pre-use  tests,  82 

transverse  tests  on  beam  specimens,  79 
Fine  aggregates,  12,  17,  19 
Fineness  of  cement,  8 
Finishing  concrete  surfaces,  90 

addition  of  colors  to  concrete,  93 

brushing,  92 

colored  aggregates,  92 

plaster  finishes,  93 

removing  form  marks,  90 

rubbing,  91 

sand-blasting,  92 

specification  for  rubbed  surface,  93 
tooling,  90 

Fire  protection,  depth  of  concrete  below  rods,  300 

resistance  properties  of  concrete,  254 

-resisting  windows,  541 
Fish  ladders  in  dams,  759 
Flange  width  of  T-beams,  308 
Flat-slab  bridges,  612 
Flat-slab  construction,  457-508 

advantages  over  beam-and-girder,  457 

Akme  system,  467,  488 


INDEX 


875 


Flat-slab  construction,  Akme  system,  tables,  505,  506 
Barton  Spider  Web  system,  461 
beams  in  floors,  497 
brick  exterior  wall  supports,  498 
buildings  to  which  adapted,  458 
cantilever  system,  463 
Chicago  ruling,  tables,  501-503 
columns,  497 

computations  on  Chicago  ruling,  494 

on  Pittsburgh  ruling,  492 

on  ruling  of  American  Concrete  Inst.,  495 
Corr-plate  floors,  470,  489 

tables,  503-505 
designing,  methods,  459,  487 

rulings  pertaining  to,  847-860 
foundations,  571 

four-way  system,  461-466,  480,  494,  495 
loading  tests,  480 

methods  and  safeguards,  506 
moments  in  columns  in,  425 
mushroom  system,  465 
Pittsburgh  ruling,  tables,  498-501 
roof  design,  496 
simplex  system,  465 

systems  of  designing  and  reinforcing,  461 

tables  for  flat-slab  panels,  498-506 
of  moments,  483,  484,  485 

tests,  discussion  of,  482 

three-way  system,  476 

Watson  system,  466 

See  also  Floors,  concrete. 
Flat  Slab  Patents  Co.,  461,  465 
Fleming,  Prof.  B.  P.,  254 

Flexure  formulas  for  reinforced-concrete  beams,  276- 
280 

assumptions  in  calculations,  276 
for  T-beams,  308 
ultimate  loads,  279 

working  and  ultimate  loads  compared,  280 

working  loads,  straight-line  theory,  276 
Flexure,  theory  of,  275 
Floors,  concrete,  205-210,  431-508 

attaching  shaft-hangers  and  sprinkler  pipes,  434 

basement  floors,  438 

bedding  machinery,  437 

causes  of  defects,  207 

chemical  hardeners,  210 

coatings  and  paints,  210 

dead  load,  432 

defects,  207-210 

designing   monolithic   beam-and-girder  construc- 
tion, problem,  440 
dusting,  206 

economic  considerations,  432 
effect  of  excess  water,  35 

of  freezing,  209 
flat-slab  construction,  457-508 

rulings,  847 
for  reservoirs,  762 
for  steel  bridges,  643-649 
grinding,  surface,  206 
hardeners  and  surface  compounds,  207 
hollow-tile  construction,  447 
loads,  431 

making  good  floors  and  surfaces,  206 

monolithic  beam-and-girder  construction,  439-456 


Floors,,  concrete,  openings,  433 
paints,  210 
patents,  479 
pigments,  206 
problems,  205 
remedies  for  defects,  209 
slabs,  support  of,  307 
surface  finishes,  206 
surfaces,  93,  432 
tests,  438,  480 
tiles,  433 

top  coat  separating  from  base,  209 
types,  431 
use  of  oils,  210 
waterproof,  438 
wood  surfaces,  432 
See  also  Flat-slab  construction. 
Footings,  concrete,  558 
bond  stresses,  561 
cantilever  footings,  568 
column,  559 
combined,  565 
diagonal  tension,  562 
examples,  571 

four-way  reinforcement,  562 
single,  559 

stepped  and  sloping,  562 
wall,  559 

width,  in  flexure  computations,  561 
Form  marks,  removal  of,  90 
Forms  for  concrete,  93-139 

beam-and-girder  forms,  103 

Blaw  light  wall  forms,  137 

calculating  floor  forms,  121 

clamp  of  Sterling  Wheelbarrow  Co.,  100 
of  Universal  Form  Clamp  Co.,  102 

column  forms,  96-103 
heads,  108 

construction  notes,  138 

cost,  94,  826-828 

curved  pier  forms,  119 

depositing  concrete  in,  73,  74 

design  of,  120 

drafting-room  methods  of  design,  123 
estimating  amount  of,  831 

unit  cost  of,  826-828 
examples  of  design,  96 
for  retaining  walls,  602 
Gemco  adjustable  steel  shoring,  107 

column  clamp,  99,  101 
Hodges  system,  105 
hydraulic  steel  column  forms,  137 
K.  &  W.  clamp,  100 
lumber  for,  94 
Meyer  steelforms,  138 
New  England  column  clamp,  99 
number  of  sets  in  building  work,  96 
pier,  103,  111 

pressure  of  concrete  against,  121 
removal  of,  95 

Ross  self-lock  adjustable  shore,  107 
slab  forms,  104 
steel,  135 

steel  floredomes,  137 

systematizing  form-work  on  buildings,  131 
tables  and  diagrams  for  designing,  124 


876 


INDEX 


Forms  for  concrete,  time  required  before  removing,  96 

values  to  use  in  design,  121 

wall  and  pier  forms,  103,  111 

wire  clamps,  119 

Wiscoforms,  138 
Formulas,  flexure,  for  reinforced  concrete  beams,  276- 
280 

for  T-beams,  308 
for  designing  forms,  125 
for  designing  symmetrical  arches,  669-691 
for  percentages  of  steel  in  reinforced  beams,  304, 
313 

Foster  Armstrong  Co.,  183 

Fougner,  Steel  Concrete  Ship-building  Co.,  863 
Foundations,  557-574 

advantage  in  using  reinforced  concrete,  558 

bearing  capacity  of  soils,  557 

cantilever  footings,  568 

combined  column  footings,  565 

column  footings,  559 

examples  of  column  footings,  571 

piles,  557,  572 

plain  concrete  footings,  558 

pressure  on  the  soil,  558 

raft  foundations,  570 

wall  footings,  559 
Four-way  flat-slab  construction,  461-166,  480,  494,  495 
Framed-bent  trestles,  610 
Francis,  749 

Freezing  of  concrete,  78,  236 

French,  A.  W.,  342 

Fuller,  W.  F.,  24,  68,  243,  263 

GF  expanded  metal,  53 
Gage,  steel  wire,  45 
Gaging,  use  of  oils,  240 

use  of  sea  water,  238 
Gang  molds  for  wet-cast  products,  151 
Gardner,  Prof.  Harry,  238 
Garver,  N.  B.,  122 
Gatun  dam,  754 
Gearhart,  783 

Gemco  adjustable  steel  shoring,  107 
Gemco  Mfg.  Co.,  99,  101,  108 
General  Electric  Co.,  139 
General  Fireproofing  Co.,  53,  56,  138 
Geological  investigations  for  dam  sites,  723 
Gibb,  H.  M.,  587 
Gillmore  needles,  841 
Girder  bridges,  613-622 
deck  girders,  613 
through  girders,  617 

forms,  103 
Glue  molds,  160 
Goldbeck,  A.  T.,  253,  254 

tests  by,  605 
Goodwin,  R.  E.,  232 
Grading  crushed  stone,  172 

of  mixtures  in  aggregates,  22 
Grain  bins,  805-810 

conclusions  from  tests,  806 

construction,  809 

design  of  walls,  808 

hexagonal  bins, '809 

horizontal  reinforcement,  808 

Janssen's  pressure  formulas,  805 


Grain  bins,  load  of  walls,  808 

rectangular  section,  808 

thickness  of  walls,  808 

wind  stresses  on  horizontal  section,  808 
Granite,  13 
Granolithic,  206 

finish  of  floors,  432 
Graphical  determination  of  stresses,  406 
Grappier  cement,  2 
Grashof's  theory,  769 
Gravel,  16 

bank-run,  proportioning,  70 

screening,  172 

voids  in,  26 

washing,  173 
Gravity  mixers,  188 

Great  Northern  Ry.  grain  elevator,  809 
Grinding,  surface,  206 

Groined-arch  construction  for  reservoirs,  762,  764 
Grout,  cement,  88 
Grouting,  728 
Guy-line  plants,  203 
Gypsum  plasters,  1 

Hain,  J.  C,  241 

Hand  vs.  machine  mixing  of  concrete,  186 
Handling  concrete  materials,  173-179 

belt  conveyors,  177 

bucket  unloaders  and  conveyors,  177 

bundling  empty  cement  sacks,  178 

cement  in  sacks,  177 

clam-shell  buckets,  176 

conveyance  economies,  174 

sand,  storage  and  care  of,  174 

shoveling  from  car  to  ground,  174 

shovels,  size  and  type,  175 

stone,  care  of,  174 

typical  installation,  179 

unloading  economies,  175 

water,  storage  and  handling,  179 
Hardeners  for  concrete  floors,  207 

chemical,  210 
Hardman,  R.  C,  140 
Harrison,  737 
Hatt,  T.  K.,  482 
Hauland,  J.,  863 
Havermeyer  bars,  43 
Heat  conductivity  of  concrete,  254 
Heating  aggregates,  77 
Hennebique  reinforcing  system,  60 
Henny,  D.  C,  725 
Hering,  R,  258 
Herschel,  748 
High  calcium  quicklime,  2 
Hillberg,  A.  G.,  723 
Hinged  arches,  715-721 
Hinges,  use  in  arch  erection,  659 
Hodges,  Jesse  E.,  104 
Hodges  adjustable  shores,  105 
Hoists  for  handling  concrete,  200 
Hollow-tile  construction,  447 

floors,  designing  problem,  453 

table,  456 
insulation,  515 
weights,  452 
Hooker,  D.  E.,  481 


INDEX 


877 


Hooke's  law,  275 

Hooped  reinforcement  of  columns,  372 
Hoppers  for  concrete  products  manufacture,  154 
Horton,  753 

Hume-Bennett  Lumber  Co.,  745 
Hy-chairs,  145 
Hydrated  lime,  2 

effect  on  concrete,  238 
Hydraulic  cements,  1 

lime,  2 

Hydraulic  Pressed  Steel  Co.,  Ill,  137 
Hydraulic  structures,  723-803 

conduits  and  sewers,  799-803 

culverts,  775-799 

dams,  723-759 

elevated  tanks,  771-775 

reservoirs,  760-765 

standpipes  and  small  tanks,  765-771 
Hydrographic  investigations,  for  dams,  725 
Hydrostatic  pressure,  in  dams,  729 
Hy-rib  construction,  56,  546 

Ice  pressures  on  dams,  732 
Igneous  rock,  13 

Illinois  Central  R.  R.  trestles,  607,  610 
Illinois  Dept.  of  Factory  Investigation,  96 
Illinois    Highway    Commission,    deck-girder  bridges, 
613,  615 

through-girder  bridges,  617 
Impervious  concrete,  rules  for,  89 
Impurities  in  aggregates,  21 
Inertia,  moment  of,  of  beams,  317 

of  continuous  beams,  339 
Influence  lines,  324 

of  arches,  664 
diagrams,  673 
Inland  bar,  44 
Inland  Steel  Co.,  44 
Insulation  for  roof  slabs,  513 
Insurance  Engineering  Station,  263 
Integral  waterproofing  compounds,  87 
International  Association  for  Testing  Materials,  256 
Iowa  Highway  Commission,  abutment  design,  607 

deck-girder  bridges,  613 

through-girder  bridge,  617 
Iowa  State  college,  664 

tests  of  pressure  on  pipes,  778 
Iron,  powdered,  as  a  surface  hardener,  207 

pyrites  in  an  aggregate,  22 

Jackson,  J.  H.,  164 

Janssen's  formulas  for  pressure  in  deep  bins,  805 
Johnson,  E.  F.,  427 
Johnson,  H.  C,  65 
Johnson,  S.  E.,  236 

Joint  Committee  on  Concrete  and  Reinforced  Concrete, 
statement  on:  acids  and  oils,  effect  on  con- 
crete, 257 

analysis  of  aggregates,  24 

bands  on  columns,  528 

bent  bars  for  web  reinforcement,  297 

concrete  barges  and  ships,  863 

concrete  in  sea  water,  257 

corrosion  of  metal  reinforcement  in  concrete,  262 

definition  of  column,  371 

depth  of  concrete  below  rods,  300 

fire  protection  by  concrete,  254 


Joint  Committee  on  Concrete  and  Reinforced  Concrete, 
statement  on:  flange  width  of  T-beams,  308 
flexure  formulas  for  reinforced-concrete  beams, 
276 

floor  slabs,  support  of,  307 

forces  to  be  resisted  by  reinforced  concrete,  273 
permeability  and  waterproofing  of  concrete,  262 
positive  and  negative  moments  of  beams,  318 
regaging,  232 

reinforcing  bars  for  compression  in  beams,  302 
shearing  strength  of  concrete,  301 
spacing  of  reinforcement,  300 

of  vertical  stirrups,  290 
span  length  for  beams  and  slabs,  318 
supports  of  continuous  beams  to  resist  bending 

moment,  339,  340 
tests  for  flat-slab  floors,  483-486 
working  stresses  for  concrete  columns,  373 
of  steel,  37 
Joints  on  concrete  roadways,  214 
Jorgensen,  745 
Jumper,  171 

K.  &  W.  Clamp  Co.,  100 

Kahn  mesh,  52 

Kahn  reinforcing  system,  57 

Kardong  Bros.,  141 

Kaufman,  G.,  258 

Keator  &  Co.,  Edward  O.,  104 

Kensico  Dam,  236 

tests  on  concrete,  261 
Ketchum,  Prof.,  806,  808 
Kinney,  W.  M.,  158 
Kutter's  formula,  727 

L-frame,  429 

Labor,  estimating  costs,  824,  827 
Laboratory  tests  of  mortar  and  concrete,  215 
Lackawanna  R.  R.  Co.,  11 
Lackawanna  Steel  Co.,  60 
Laitance,  74,  75,  86 
deposits,  34 

effect  on  hardness  of  concrete,  241 
Lang  building,  Haverhill,  Mass.,  535 
Lauter  Piano  Co.,  479 

Leflfler's  comprehensive  beam  chart,  348,  370 
Leonard  Co.,  Chicago,  481 
Liberty  Silk  warehouses,  438 
Lime,  1 

hydrated,  2 

hydraulic,  2 

putty,  1 
Limestone,  crushed,  172 

for  cement  manufacture,  6 
Line-of-thrust  theories,  of  stability  of  arches,  659 
Lines,  influence,  see  Influence  lines. 
Linseed  oil  on  concrete  floors,  210 
Loading  tests  of  flat-slab  construction,  480 
Loads,  concentrated,  figuring  beams  for,  324 

floor,  431 

of  arches,  654 

Cooper's  Standard  Loadings,  656 

uniform,  maximum  moments,  330 
moments  in  beams  for,  323 
moving,  figuring  spans  for,  329 
Loam  in  aggregates,  224 


878 


INDEX 


Lock-woven  steel  fabric,  49 

Longitudinal  reinforcement  of  columns,  371,  372 

Lord,  A.  R.,  481,  483,  487 

Lorente,  M.  J.,  344 

Los  Angeles  Building  Ordinance,  381 

Low-charging  mixers,  191 

Lumber  for  forms,  94 

Luten  arch  centering,  707 

truss,  60 
Lyndon,  L.,  747 

McCuUough,  Earnest,  234 

McDaniel,  A.  B.,  122,  235 

Machine  rock  drills,  171 

Machine  vs.  hand-mixing  of  concrete,  186 

Machinery,  bedding,  in  concrete  floors,  437 

McNeilly,  Prof.,  24 

Magnesian  quicklime,  2 

Maney,  G.  A.,  305,  427 

Maney's  method  of  determining  deflection  of  beams, 
305 

Manufacture  and  use  of  concrete  stone,  146-169 
Manufacture  of  natural  cement,  8 

of  Portland  cement,  6-7 
Manure,  effect  on  concrete,  259 
Marion  Malleable  Iron  Works,  111,  119 
Marl,  6 

Marston,  A.,  778,  782 

Massachusetts  Institute  of  Technology,  244 
Materials,  1-62 

aggregates,  12-31 

cement,  1-12 

concrete,  handling  and  storage,  173-179 
reinforcement,  36-62 
water,  31-36 
Maurer,  819 

Maurer's  method  of  determining  deflection  of  beams, 
305 

Maximum  density  tests  of  concrete,  68 

Mayhew,  A.  B.,  260 

Measurement  of  concrete  work,  830 

of  materials  for  concrete,  70 
Measuring  materials  for  concrete  mixer,  192 
Mechanical  analysis  of  aggregates,  23 

proportioning  concrete  by,  68 
Melan  system,  704 
Melick,  C.  A.,  427 
Membranous  waterproofing,  88 
Metal  Building  Materials  Co.,  145 
Metal  lath  and  plaster  partitions,  545 
Metamorphic  rocks,  16 
Methods  of  construction,  63-169,  506 
Meyer  steelforms,  138 
Mica  in  aggregates,  21,  224 
Mills,  A.  P.,  215,  222,  248,  255 

Minneapolis,  St.  Paul  &  Sault  Ste.  Marie  R.  R.,  ore 

dock,  815 
Mixers  for  concrete,  types,  187 

for  manufacture  of  concrete  products,  152 
Mixing  concrete,  72,  186-193 

discharge  of  the  mixer,  192 

drum  speeds,  190 

loading  the  mixer,  190 

low-charging  mixers,  191 

measuring  materials,  192 


Mixing  concrete,  power  loaders,  191 

time  of  operations,  189 
Mixing  concretes  and  mortars,  effect  on  strength,  230 
Modulus  of  elasticity  of  concrete,  846 

of  mortars  and  concretes,  252 

of  steel,  37 
Modulus  of  rupture,  242 

Moisture,  effect  on  mortars  and  concretes,  234,  253 

on  voids  in  sand,  26 
Molding  concrete  and  mortar,  216,  231 
Molds  for  concrete  stone,  149 

for  wet-cast  products,  151 

glue,  for  concrete  products,  160 

of  paraffined  paper,  81 

wood  and  plaster,  for  concrete  products,  159 
Moments  in  continuous  slabs,  306 
Moments  in  rigid  building  frames,  411-430 

analysis,  application  of  method,  414 

conception  of  rigidity,  415 

columns  in  flat-slab  construction,  moments  in,  425 
criteria  for  combined  stresses  in  columns,  426 
diagrams,  421-424 

exterior  columns,  moments  at,  420-425 
interior  columns,  moments  at,  416-420 
L-frames,  429 
laws,  411 

method  of  analysis,  411 

roof  frames,  428 

special  equations,  414 

wind  stresses,  427 
Moments,  of  arches,  diagrams  for,  681 

of  columns,  416-425,  486 

positive  and  negative,  318 

theorem  of  three,  318 

See  also  Shear  and  moment  in  beams. 
Monolithic  beam-and-girder  construction,  439-456 
Morison,  G.  S.,  659 
Morrow,  D.  W.,  476,  477,  478 
Morssen,  C.  M.,  863 
Mortar,  cement,  properties  of,  215-263 

See  also  Cement  mortar,  Portland  cement. 
Morton  dam,  743 
Mosaics,  167 
Movable  dams,  758 
Mueser,  W.,  769 
Multiple-arch  dams,  743 
Mushroom  flat-slab  system,  465 

Natural  cement,  3 

compared  with  Portland.  4 
manufacture,  8 
testing,  8 

Natural  cement  mortar,  strength,  247 

Natural  curing  in  concrete  products  manufacture,  156 

National  Association  of  Cement  Users,  258,  481 

National  Concrete  Co.,  60 

Neat,  mortar,  and  concrete  strength,  217 

Negative  moments,  318 

in  continuous  slabs,  306 
Neutral  axis  of  reinforced-concrete  beams,  315,  316 
Newberry,  S.  B.,  254 
New  England  Column  Clamp  Co.,  99 
New  York  City,  Board  of  Water  Supply,  test  for 
sand,  23 

Building  Code,  465 


INDEX 


879 


New  York  Public  Service  Commission,  specifications  for 
concrete  aggregates,  30 
tests  of  concrete,  79 

of  concrete  aggregates,  27-30 

of  strength  of  concrete,  232 
Non-hydraulic  cements,  1 
Non-staining  cements,  2 
Norcross  patent,  465,  479 
North  Western  Expanded  Metal  Co.,  53,  56 
Norton,  Prof.  C.  L.,  255,  263 
Norway,  concrete  shipbuilding  in,  863 
Notation,  standard,  861 

Ohio  tests  of  slabs  under  concentrated  loading,  604 
Oils,  effect  on  concrete,  257 

use  of,  on  concrete  floors,  210 

used  in  gaging,  210 
Ore  docks,  815 
Ottawa  Silica  Co.,  19 
Oursler,  John,  165 
Overflow  dams,  753 
Ozark  Power  Co.,  748 

Pacific  Gas  and  Electric  Co.,  739 
Page,  L.  W.,  240 
Page  Special  Process  fabric,  49 
Page  Woven  Wire  Fence  Co.,  49 
Paints  for  concrete  floors,  210 
Pallets,  155 

Parabola  of  an  arch,  653 

Paraffine,  used  on  defective  concrete,  87 

Parapet  walls,  on  roofs,  521 

Parker,  P.  A.  M.,  747 

Partitions,  545 

Patents  for  floor  construction,  479 
.  Pathfinder,  Wyo.,  dam  at,  738 
Paul,  C.  H.,  260 
Pavements,  vault-light,  212,  545 
Pennsylvania  Railroad  Co.,  574 

bridge  in  Pittsburgh,  713 
Pent  houses,  553 
Percussion  drills,  172 
Perimeters  of  rods,  table,  354 
Permeability  of  mortar  and  concrete,  262 
Perrine,  H.,  249 
Pervious  concretes,  86 

Philadelphia  and  Reading  R.  R.  bridge,  703 
Pier  abutments  for  bridges,  645 

forms,  103,  111 

trestles,  610 
Piers  and  abutments  of  arch  bridges,  702 

concrete,  371 

of  arches,  653 
Pierson  Engineering  Corporation,  746 
Pigments  for  concrete  floors,  206 
Pile  trestles,  607 
Piles,  concrete,  572 

cast  piles,  574 

composite,  573 

Pedestal,  573 

Raymond,  572 

Simplex,  573 
Piles  in  foundations,  557 
Pilings  for  dams,  728 
Pin-connected  system,  60 
Pipe  culverts,  777 
Pipes,  pressure  in  trenches  on,  778 


Pittsburgh  Building  Code,  465,  478 

ruling  for  flat-slab  construction,  492,  847 
for  flat-slab  panels,  498-501 
Placing  concrete,  73-78 
Placing  of  reinforcement,  139,  142-146 

beam  spacers,  143 

easy  chairs,  143 

securo  locking  spacer,  143 

supporting  reinforcing  bars,  143 

ty-chairs,  145 

tying  slab  and  wall  rods,  142 

various  devices,  145,  146 
Plant,  cost  of,  825 
Plaster  finishes  of  concrete,  93 

molds,  159 

of  Paris,  1,  7 

partitions,  546 
Plums,  21 

Pneumatic  mixers,  188 
Poisson's  ratio,  737,  739 
Porosity  in  concretes,  83 

of  mortar  and  concrete,  262 
Porsgrund  Cement  Works,  863 
Portland  cement,  2 

adulterants,  4 

chemical  action  with  water,  effect  of  weather,  76 

analysis,  834 

properties,  833 
color,  93 

compared  with  natural,  4 
composition,  4 
constitution,  5 

determination  of  soundness,  838 

of  time  of  setting,  838 
fineness,  836 

hardening  rate  in  concrete,  77 
in  proportioning  concretes,  64,  65 
inspection,  834 
manufacture,  6,  7 

mixing  cement  pastes  and  mortars,  837 

mortars,  regaging,  233 

normal  consistency,  837 

packages,  marking,  and  storage,  833 

percentage  of  water,  838 

physical  properties,  833 

rejection,  834 

sampling,  834 

setting  and  hardening,  5 

slag  or  steel,  3 

specific  gravity,  11,  836 

standard  specifications  and  tests,  833-843 

storage  of  test  pieces,  843 

strength,  10 

strength  compared  to  natural  cement,  247 

table  of  colors,  164 

tension  tests,  841 

testing,  8 

time  of  setting,  9 

weight,  12 

Portland  Cement  Association,  report  on  concrete  ships, 
863 

Positive  moments,  318 
Power  loaders,  for  concrete  mixers,  191 
Pressure  method  of  making  concrete  stone,  147 
of  concrete  against  forms,  121 


880 


INDEX 


Pressure  on  pipes  in  trenches,  778 
Pre-use  tests  of  materials,  82 
Prior,  J.  H.,  649 
Proportioning  concrete,  63-72 

arbitrary,  65 

bank-run  gravel,  70 

blast-furnace  slag  and  cinders,  71 

cause  of  weakness,  64 

checking  materials  on  the  job,  69 

crusher-run  stone,  71 

experiments  of  H.  C.  Johnson,  table,  65,  66 

for  high-strength  concretes,  64 

maximum  density  tests,  68 

measurement  of  materials,  70 

mechanical  analysis,  68 

physical  characteristics  of  aggregates,  67 

properties  of  concrete  and  constituent  materials,  63 

theory,  63 

unit,  65 

void  determinations,  65 

void  theory,  64 

water,  71 
Puddling  concrete,  75 
Pull-out  tests,  265,  266 
Pulver,  H.  E.,  236 

Punching  shear,  on  column  footing,  559 
Purdue  University,  tests,  230 
Putty,  lime,  1 
Puzzolan  cement,  2 

Quantities,  estimating,  830-832 
Quarrying  aggregates,  171 
Quicklimes,  1,  2 

Raft  foundations,  570 
Railroad  bridges,  loads,  656 

See  also  Arches. 
Rail-steel  reinforcement  bars,  specifications,  40,  41 
Rankine,  Prof.,  733 

Rankine's  formula  for  resultant  active  earth  pressure,  576 

Ransome  dam,  743 

Ransome  unit  system,  508,  509 

Raymond  piles,  572 

Rebhaun's  construction,  580 

Rectangular  beams,  273-307 

See  also  Beams,  rectangular. 
Reed,  S.  A.,  255 

Regaging  concrete  and  mortars,  232 
Rehbock,  754 

Reinforced  concrete,  advantage  in  foundations,  558 
advantages,  265 
beam  tests,  269 
beams  and  slabs,  273-370 
behavior  under  tension,  271 
bond  between  concrete  and  steel,  265 
building  frames,  moments  in,  411-430 
chimneys,  816-821 
conduits,  803 
dams,  739-745 

effect  of  concrete  setting  under  pressure,  269 
length  of  embedment  of  bars,  270 
properties,  265-272 
pull-out  tests,  266 

ratio  of  the  moduli  of  elasticity,  270 
shrinkage  and  temperature  stresses,  271 


Reinforced  concrete  slabs,  306 
walls,  designing,  587 
special  types,  600 
weight,  272 

work,  estimating,  823-832 
Reinforcement,  bending  and  placing,  139-146 
cost  of,  828 

formulas  for  steel  in  rectangular  beams,  303,  304 
formulas  for  steel  for  T-beams,  313 
of  columns,  371,  372 
of  fiat-slab  floors,  461 
placing,  142-146 

steel  for  compressive  side  of  beams,  302 
transverse  spacing,  300 
web,  285 
Reinforcement  materials,  36-62 
bars,  36-45 

expanded  metal,  50-54 
factors  of  cost  of  bars,  42 
quality  of  steel,  37 
rib  metal,  55 

self-centering  fabrics,  55-57 

steel  specifications  for  bars,  37,  38,  40,  41 

surface,  37 

systems  for  beams,  girders,  and  columns,  57-62 

types  of  reinforcement,  36 

wire  fabric,  45-50 
Reinforcing  counterforted  wall,  596 
Reinforcing  systems,  for  beams,  etc.,  57-62 

Corr,  60 

Cummings,  58 

Hennebique,  60 

Kahn,  57 

Luten  truss,  60 

pin-connected,  60 

shop  fabricated,  60 

unit,  58 

Xpantruss,  60 
Remixed  concrete,  76 
Removal  of  forms  from  concrete,  95 
Reservoir  capacity,  726 
Reservoirs,  760-765 

concrete  floors  for,  761 

concrete  walls  for  open,  763 

construction  details  of  columns  and  roof,  764 

covers  or  roofs,  764 

groined  and  flat  floors,  762 

groined-arch  construction,  764 

open  basins  with  embankment  walls,  761 

partition  and  outside  walls,  764 

provision  for  ice,  764 

quality  of  concrete  for  masonry,  760 

types,  760 

Resisting  moment  of  reinforced-concrete  beams,  316 
Restrained  beams,  318-341 

See  also  Beams,  continuous,  and  restrained. 
Retaining  walls,  575-602 

backfilling  and  drainage,  601 

base  slab  of  cantilever  walls,  590 

bearing  capacity  of  soils,  table,  583 

coeflBcients  of  friction,  table,  582 

construction  of,  601 

design  of  cantilever  or  T-walls  of  reinforced  con- 
crete, 587-592 
of  counterforted  walls,  592-600 


INDEX 


881 


Retaining  walls,  design  of  cantilever  or  T-walls  of  plain 
concrete  wall?,  584 
earth  pressure,  575 
equivalent  surcharge,  580 
expansion  joints  of  cantilever  walls,  592 
factor  of  limitation,  584 

of  safety,  584 
forms  for,  602 

live  load  on  top  of  fill,  580,  581 
pressure  distribution,  581 
reinforcing  counterforted  wall,  596 
stability,  581 

stem  of  cantilever  walls,  589 

Trautwine's  table,  586 

types,  584 

of  reinforced-concrete  walls,  600 

unit  pressures,  583 
Retempered  concrete,  76 
Retopping  concrete  floors,  209 
Rib  bars,  44 

metal,  55 
Ribplex,  57 
Richardson,  C,  248 
Richart,  F.  E.,  412,  413 

Rigidity  of  reinforced-concrete  building  frames,  411 
Roadways,  concrete,  213,  214 
Robinson,  H.  St.  G.,  246 
Rochester  Building  Code,  431 
Rock,  igneous,  13 

metamorphic,  16 

sedimentary,  14 

trap,  14 
Rods,  table  of  areas,  etc.,  354 
Roebling  Construction  Co.,  546 
Roebling  slab  floor,  512 
Roman,  F.  L.,  225 

Roof  design,  in  flat-slab  construction,  496 

frames,  stresses  in,  428 
Roofs,  512-527 

concrete  roof  surfaces,  516 

condensation  on  roof  slabs,  513 

drainage,  518 

insulation,  types  of,  514 

loading,  512 

parapet  walls,  521 

sawtooth  construction,  526 

separate  roof  coverings,  517 

structural  design,  512 

wind  pressure,  513 
Roos  Co.,  H.  W.,  107 
Roos  self-lock  adjustable  shore,  107 
Rotary  drills,  172 
Rubbing  concrete  surfaces,  91,  166 

specification,  93 

S-M-I  flat-slab  construction  system,  471 

Sabin,  L.  C,  164,  233,  234,  248 

Salts,  effect  on  concrete,  236 

Sanborn,  T.,  240 

Sand  as  an  aggregate,  18,  19 

-blasting  concrete  surfaces,  92 

boxes  for  lowering  arch  centers,  710 

cement,  4 

derivation,  220 

effect  of  size,  on  strength  of  mortar,  221 
56 


Sand,  grading  for  concrete,  23 
mechanical  test,  23 
molding,  161 

requirements  as  aggregate,  59 
screening,  172 

selection  of,  as  aggregate,  20 

standard,  19 

storage  and  care  of,  174 

testing  on  the  job,  69 

voids  in,  25-27 

washing,  173 
Sandstone,  15 
Sawtooth  roofs,  526 
Schilling,  Adolph,  165 
Schuler's  charts  for  beams  and  slabs,  350 
Schwada,  J.  P.,  656 
Schwendener,  K.  D.,  298 
Scofield,  Prof.,  230 
Scranton,  Pa.,  Dunning's  dam,  758 
Screening  crushed  stone,  172 

sand  and  gravel,  172 
Screenings,  19 

Sea  water,  effect  on  concrete  and  steel,  256,  864 

on  mortars  and  cements,  238 
Seabury,  G.  T.,  261 
Seasoning  cement,  12 
Seattle  Building  Code,  431 
Securo  locking  spacer,  143 
Sedimentary  rocks,  14 
Self-centering  fabrics,  55-57 

chanelath,  56 

Corr-mesh,  56 

dovetailed  corrugated  sheets,  57 

hy-rib,  56 

ribplex,  57 

self-sentering,  56 
Semi-ellipse  arch,  652 
Setting  of  cement,  9 
Sewage,  effect  on  concrete,  257 
Sewell,  Capt.  J.  S.,  255 
Sewers,  see  Conduits  and  sewers. 
Shaft-hangers,  attaching  to  floors,  434 
Shales,  for  cement  manufacture,  6 
Shallow  bins,  810-815 
Shear  and  moment  in  beams,  318-341 

beam  concentrations,  331 

bending  up  of  bars,  curves,  335 

fixed  and  moving  concentrated  loads,  324 

influence  lines,  324 

maximum  moments  from  uniform  loads,  330 
moving  uniform  loads,  329 

negative  moment  at  ends  of  continuous  beams,  334 

positive  and  negative  moments,  318 

span  length  for  beams  and  slabs,  318 

theorem  of  three  moments,  318 

uniform  load  over  all  spans,  323 

varying  moment  of  inertia  of  continuous  beams,  339 
Shearing  strength  of  mortars  and  concretes,  243 

stresses  of  reinforced-concrete  beams,  280 
Sheet  piling  for  dams,  728 
Sheflfield  Scientific  School,  tests,  225 
Sherwin,  R.  A.,  123,  131 
Ships,  concrete,  863-865 

carrying  capacity  and  displacement,  863 

cost,  864 


882 


INDEX 


Ships,  concrete,  efifect  of  sea  water,  864 

elasticity,  864 

longitudinal  strength,  864 

specifications,  865  * 

speed  of  construction,  865 

transverse  strength,  864 
Shirreffs,  737 

Shop  fabricated  reinforcement  system,  60 
Shores,  Hodges  adjustable,  105 

Roos  self-lock  adjustable,  107 
Shoshone,  Wyo.,  dam  at,  738 
Shovel  for  handling  materials,  175 
Shrinkage  cracks  in  concrete,  84 
prevention,  85 

of  reinforced  concrete,  271 
Shunk,  Francis  R.,  121 
Sidewalk  lights,  212,  545 
Sidewalks,  concrete,  210-212 
Sieves  for  sand  analysis,  23 
Silos,  805-810 
Silt  in  an  aggregate,  21 
Simplex  flat-slab  construction  system,  465 

piles,  573 

Singer  Manufacturing  Co.,  concrete  storage  arrange- 
ments, 179 
Single  column  footings,  559 
Siphonic  spillways  of  dams,  755 
Skeleton  abutments  for  bridges,  648 
Slab  and  girder  bridges,  603-641 

cantilever  bridges,  639-641 

continuous-girder  bridges,  622-638 

girder  bridges,  613-622 
Slab  bridges,  603-612 

abutment  design  of  Iowa  Highway  Commission, 
607 

cantilever  flat-slab  construction,  612 

concrete  pile  trestles,  607 

Illinois  tests,  603 

multiple  spans,  607 

Ohio  tests,  604 

pier  trestles,  610 

single  span,  605 

slabs  under  concentrated  loading,  603 

tests  by  Goldbeck,  605 

trestles  with  framed  bents,  610 
Slab  forms,  104 

reinforcement,  bending,  142 
Slabs,  cross-reinforcement,  307 

designing,  344,  351 

diagrams  of  bending  moments,  362,  363 

floor,  support  of,  307 

in  reinforced  concrete,  273-370 

moments  in  continuous,  306 

provision  for  negative  moment,  306 

reinforced-concrete,  306 

tables  for  spacing  of  rods  in,  358 

See  also  Beams  and  slabs,  Flat-slab  construction. 
Slag,  blast-furnace,  6 

as  an  aggregate,  17 
proportioning  in  concrete,  71 

cement,  2 
Slater,  W.  A.,  481,  603 
Sloping  column  footings,  562 
Sluices  of  dams,  754 
Smith,  A.,  427 


Smulaki,  E.,  471,  482 

Smulski  flat-slab  construction,  471 

Soils,  bearing  capacity  of,  557 

table,  583 
Soundness  of  cement,  10 
Southwick,  L.  T.  B.,  225 
Spacing  of  reinforcement,  300 
Spackman,  H.  S.,  238 
Spading  concrete,  75 
Span  length  for  beams  and  slabs,  318 
Spandrel  details  in  arch  bridges,  691,  694 
Spandrels  of  an  arch,  653 
Spaulding,  R.  E.,  339 
Specific  gravity  of  aggregates,  25 

cement,  11 
Specifications  for  aggregates,  30 

cement,  11 

concrete  stone,  168 
vessels,  865 

Portland  cement,  833-843 

production  of  a  rubbed  surface,  93 

steel  reinforcement  bars,  37,  38,  40,  41 

testing  strength  of  cements,  10 
Spillway  of  dams,  748 
Spillways,  siphonic,  755 
Spiral  Mushroom  System,  479 
SpofiFord,  Prof.  C.  M.,  244 
Spouting  plants,  203 
Spouts  for  transporting  concrete,  195 
Spraying  concrete  stone,  165 
Sprinkler  pipes,  attaching  to  floors,  434 
Stability  of  the  arch,  see  Elastic  theory  of  stability  of 

the  arch. 
Stairs,  549-552 

design,  549 

details,  551 

supporting,  550 
Standard  sand,  19 

Standpipes  and  small  tanks,  765-771 

construction  details,  781 

precautions,  771 

restraint  at  base,  765 

shear  at  base,  767 

small  tanks,  768 

stresses,  analysis,  765 
Staple  chairs,  146 
Statical  moment,  273,  274 

Steam  curing  in  concrete  products  manufacture,  157 

effect  on  hardening  cement  mortar,  235 
Steel  bridges,  concrete  floors  and  abutments  for,  643- 
649 

centers  of  arches,  712 
floredomes,  137 
forms,  135 

frame  construction,  511 
Steel  reinforcement,  cost  of,  828 
effect  of  sea  water  on,  865 
estimating  amount  of,  832 
protection  from  corrosion  by  concrete,  262 
quality,  37 

specifications  for  bars,  37,  38,  40,  41 
wire  gage,  45 

See  also  Reinforced  concrete. 
Steelcrete,  51 

Stepped  column  footings,  562 


INDEX 


883 


Sterling  Wheelbarrow  Co.,  100 
Stevenson,  724 
Stirrups,  vertical,  289 
Stone,  as  an  aggregate,  20 

care  of,  for  concrete,  174 

concrete,  146-169 

crusher-run,  proportioning,  71 

crushers,  172 
Stone  &  Webster  Engineering  Corporation,  139 
Storage  of  cement,  11,  151 

of  concrete  materials,  173-179 

pockets  in  docks,  815 
Strehan,  G.  E.,  249 

Strength  of  beam,  for  moment  and  shear,  301 

of  cement,  10 
Strength  of  mortar  and  concrete,  215-250 

adhesive  strength,  246 

aggregates,  effect  on  strength,  218-222 

cinder  concrete,  248 

columns,  strength  of,  229 

compared  with  neat  cement,  217 

compressive  and  tensile  compared,  227 

consistency,  relation  to  strength,  225 

curing  by  steam,  effect  of,  236 

curing  conditions,  effect  on  strength,  234 

depositing  under  water,  effect  of,  232 

elements,  64 

freezing,  effect  of,  236 

hydrated    lime    and    waterproofing  compounds, 

effect  of,  238 
laboratory  tests,  215 
laitance,  effect  of,  241 
method  of  mixing,  effect,  230 
method  of  placing,  effect,  231 
mica,  clay,  and  loam  in  aggregates,  effect  of,  224 
modulus  of  rupture,  243 
moisture,  effect  of,  234 

natural  and  Portland  cements  compared,  247 

oils,  effect  of,  240 

rate  of  increase,  241 

regaging,  effect,  232 

relation  to  density,  222 

retrogression,  241 

salts,  effect  of,  236 

sea  water  used  in  gaging,  effect  of,  238 
shearing  strength,  243 
transverse  strength,  242 
working  stresses,  250 
Stress,  bending  and  direct,  385-409 

analytical  determination  of,  in  rectangular  sections, 
387 

diagrams  of  compression  over  whole  section,  388- 
393 

diagrams  of  tension  over  part  of  section,  395-402, 
404,  405 

graphical  determination  of  stresses,  406 
hollow  circular  sections,  407 

rectangular  sections,  determination  of  stress  in, 

387,  406 
solid  circular  sections,  409 

tension  over  part  of  section,  diagram,  395-402,  404, 

405 
theory,  385 

See  alao  Moments  in  rigid  building  frames. 
Stresses  in  building  frames,  wind,  427 


Stresses  in  columns,  maximum,  426 

in  dams,  732-734 

in  reinforcing  beams,  273 

in  rigid  viaduct  structures,  625 

of  arches,  diagrams  for,  681 

on  chimneys,  816 

working,  845 

See  also  Moments. 
Structural-steel  columns,  372 

Structural  Materials  Laboratory,  St.  Louis,  see  U.  S. 

Bureau  of  Standards;  U.  S.  Geological  Survey. 
Submerged  storage  for  coal,  815 
Surfaces  of  concrete,  162 

estimating  amount  of  finish,  832 
cost  of  finish,  829 

finishes,  206 
Surfacing  concrete  floors,  93 
Suspended  ceilings,  516 
Sweatt,  B.  J.,  704 
Systems,  reinforcing,  37 

for  beams,  girders,  and  columns,  57-62 

T-abutments,  647 
T-beams,  307-313 

See  also  Beams,  T-beams. 
T-walls  of  reinforced  concrete,  587-592 
Tables,  designing,  for  beams  and  slabs,  341-370 
Talbot,  Prof.  A.  N.,  245 
Tamping  concrete,  75 

stone,  150 
Tanks,  elevated,  771-775 

analysis  of  stresses,  771 

supporting  tower,  774 

small,  see  Standpipes  and  small  tanks. 
Tar  and  gravel  roof,  517 
Taylor,  A.  238,  240 
Taylor,  T.  W.,  175 

Temperature,  effect  on  concreting,  76 

effect  on  water-tightness  of  concrete,  86 

of  concrete  structures,  664 
Temperature  stresses  in  concrete  chimneys,  819 

of  reinforced  concrete,  271 

on  dams,  732 

on  girder  bridges,  636 
Tensile  strength  of  cement,  10 

of  mortar  and  concrete,  227 
Tension  in  reinforced  concrete,  394 

shear  and  diagonal,  845 
Terra-cotta  tile  partitions,  548 

veneer  for  walls,  540 
Testing  materials  on  the  job,  69 

of  cement,  8 
Tests,  autoclave,  11 

field,  of  concrete,  78-82 

for  Portland  cement,  833-843 

of  aggregates,  23,  27-30 

of  flat-slab  floors,  480 

of  materials,  pre-use,  82 

See  also  American  Society  for  Testing  Materials 
Theorem  of  three  moments,  318 
Theory  of  flexure  for  homogeneous  beams,  275 

of  proportioning  concrete,  63 

of  stability  of  the  arch,  659-668 

of  stress,  bending  and  direct,  385 
Thompson,  E.  J„  165 


884 


INDEX 


Thompson,  S.  E.,  225,  238,  341,  481 
Three-hinged  arches,  715-721 

details  of  design,  719 

method  of  analysis,  715 

methods  of  construction,  717 

types  of  hinges,  717 
Three-way  fiat-slab  construction,  461,  476 
Through-girder  bridge,  617 
Thrusts,  of  arches,  diagrams  for,  681 
Tile,  hollow,  weights,  452 
Tiles  as  floor  surface,  433 
Timber  centers  for  arches,  704 
Time  required  before  removing  forms,  96 
Toltz,  Max,  815 
Tooling  concrete  stone,  166 

concrete  surfaces,  90 
Tower  plants,  203 

tanks,  771-775 
Transporting  concrete,  72,  193-203 

barrows,  193 

buckets,  194 

cableways  and  buckets,  195 
carts,  193 
hoists,  200 

regulating  flow  in  spouting  plants,  203 
spouting  plants,  203 
spouts  or  chutes,  195 
Trap  rock,  14 

Trautwine's  table  for  retaining-wall  design,  586 
*Trelease,  F.  J.,  481 
Tremie,  depositing  concrete  by,  76 
Trestles,  concrete  pile,  607 
pier,  610 

with  framed  bents,  610 
Triangle-mesh  wire  fabric,  47 
Trough  mixers,  187 

Trussed  Concrete  Steel  Co.,  44,  52,  55,  56,  137 
Tufa  cement,  4 

Tung  oil  on  concrete  floors,  210 
Turneaure,  819 

Turneaure's  method  of  determining  deflection  of  beams, 
305 

Turner,  C.  A.  P.,  465,  479,  481 
Turner  Construction  Co.,  182,  435 
Turner  Mushroom  flat-slab  bridge,  612 
Two-way  flat-slab  construction,  461,  467,  470 
Ty-chairs,  145 

Tying  slab  and  wall  rods,  142 

U-abutments  for  steel  bridges,  647 
Underwater  concrete,  depositing,  76 
Unit-bilt  construction,  508,  527 
construction,  508-511 

advantages,  508 

method,  508 

Ransome  unit  system,  508,  509 
Unit  Construction  Co.,  508,  526 

costs  of  concrete  work,  823 

of  proportioning  concrete,  65 

reinforcing  system,  58 

Wall  Construction  Co.,  119 

wire  fabric,  48 
United  Shoe  Machinery  Co.,  435,  555 
U.  S.  Bureau  of  Standards,  air-analyzer  perfected  at,  9 

curve  for  proportioning  concrete,  68 


U.  S.  Bureau  of  Standards,  steel  wiTe  gage,  45 

tests,  on  action  of  sea  water  on  concrete,  256 
cinder  concrete,  250 

compressive  and  tensile  strengths  of  concrete, 
227 

concrete,  217,  220 

electrolysis  in  concrete,  258 

effect  of  curing  conditions,  234 

effect  of  waterproofing  compound  on  strength  of 

mortars,  238 
hardening  concrete  by  steam,  235 
mixing  methods,  231 
permeability  of  mortars,  262 
sands  and  aggregates,  223,  224 
stress-strain  of  concrete,  250 
weight  of  concrete,  263 
yield  point  of  mortars,  251 
U,  S.  Dept.  of  Agriculture,  tests  on  expansion  of  concrete 

253 

with  oils  in  gaging  concrete,  240 
U.  S.  Geological  Survey,  tests  on  strength  of  mortar 

and  concrete,  217,  241 
U.  S.  Navy  Dept.,  256 

U.  S.  Reclamation  Service,  260,  725,  736,  738 
Universal  bar  bender,  140 
cone  nuts.  111 

Form  Clamp  Co.,  102,  119,  143 

Portland  Cement  Co.,  783 

sand  tester,  82 

wire  clamp,  119 
University  of  Illinois,  tests  on  bond  for  concrete  and 
steel,  265,  266 

bond  stresses  in  column  footings,  561 

column  footings,  558 

loads  on  pipe  in  trenches,  781 

pressure  of  wet  concrete,  122 

shearing  strength  of  concrete,  245 

slabs  under  concentrated  loading,  603 

strength  of  concrete  columns,  230 

temperature  and  strength  of  concrete,  235 

wind  stresses  in  building  frames,  427 
University  of  Iowa,  254 
University  of  Kansas,  238 
University  of  Michigan,  tests,  253 
University  of  Pennsylvania,  254 
University  of  Wisconsin,  slab  forms  used  at,  104 

tests  on  bond  of  concrete  and  steel,  265,  266 
detection  of  cracks  in  beams,  271 
effect  of  salts  on  concrete,  236 
strength  of  concrete  columns,  230 
Unloading  materials,  economies,  175 
Uplift  of  dams,  731 

Vault-light  pavements,  212 
Vermeule,  725 
Vertical  stirrups,  289 
Vessels,  concrete,  863 
Viaduct  bent,  638 

frames,  628 

structures,  625 
Vicat  method  of  determining  time  of  setting,  838 

needle  apparatus,  9 
Void  theory  of  proportioning,  64 
Voids,  determination  of,  65 

effect  of  moisture  on,  26 


INDEX 


885 


Voids,  in  aggregates,  25-27 

in  concrete  caused  by  excess  water,  34 

Wade,  738 

Wall  and  pier  forms,  103,  111 

footings,  559 

scuppers,  438 
Walls  and  partitions,  532-549 

basement  walls,  545 

bearing  walls,  532 

brick  and  other  veneer,  539 

curtain  walls,  533 

details  of  Lang  building,  Haverhill,  Mass.,  535 

door  openings,  543 

partitions,  545 

window-openings,  540 
Walls,  cantilever,  design  of,  587-592 

counterforted,  design  of,  592-600 

retaining,  575-602 
Wallace  Supplies  Mfg.  Co.,  140 
Washburn,  W.  W.,  707 
Washing  crushed  stone,  172 

sand  and  gravel,  173 
Water,  action  on  concrete,  82 

amount  used  in  mixing  concrete.  72 

percentage  for  standard  mortars,  838 

preheating,  77 

proportioning  in  concrete,  71 
storage  and  handling  in  concrete  work,  179 
Water  for  concrete,  31-36 

bonding  new  concrete  to  old,  35 
cold  weather,  concreting  in,  35 
day's  work  planes,  34 
effect  of  excess  on  concrete  floors,  35 

on  fluxing  of  cement,  32 

on  lubrication  of  mixture,  33 
excess,  prevention  of,  36 
functions,  31 
laitance  deposits,  34 

quantity,  effect  on  strength  of  concrete,  32 

space  occupied  in  concrete,  33 

tests  for  acidity,  31 

voids  caused  by  excess,  34 

waterproof  concrete,  35 
Waterloo  Construction  Co.,  141 
Waterproof  floors,  438 

Waterproofing  compounds,  effect  on  strength  of  con 

Crete,  238 
Waterproofing  concrete,  82-90 
cement  grouting,  88 

effect  of  temperature  and  atmosphere,  86 

integral  waterproofing  compounds,  87 

membranous  waterproofing,  88 

numbers  of  ply  for  various  heads  of  water,  89 

pervious  concretes  and  laitance,  86 

porosity  in  concretes,  83 

protection  of  waterproofing,  89 

rendering  defective  structures  impervious,  87 

resistance  to  water  action,  82 

rules  for  making  concrete  impervious,  89 

shrinkage  cracks,  84 

water  penetration,  83 
Watertown  Arsenal  tests,  229,  248,  249,  259 
Watson,  W.  J.,  «fe  Co.,  466 
Watson  flat-slab  system,  466 
Weakness  of  concrete,  64 


Weather,  effect  on  concrete,  76 
Weathering  qualities  of  concrete,  255 
Web  reinforcement  of  beams,  285 

bonding  of  web  and  flange  of  T-beam,  308 
Wedge-shaped  beams,  314 
Wegmann,  E.,  730,  735,  754 
Weight  of  cement,  12 

of  mortar  and  concrete,  263 

of  reinforced  concrete,  272 
Weights  of  rods,  table,  354 
Weiss,  C,  412 
Weld.  F.  F.,  656 
Welded  wire  fabric,  46 
Welland  canal  concrete  tests,  79 
Wellman,  G.  A.,  225 
Westinghouse  Church  Kerr  &  Co.,  82 
Wet-cast  method  of  making  concrete  stone,  148 

agitation  after  mixing,  153 

gang  molds  for,  151 
Wheelbarrows  for  concrete  products  manufacture,  155 
Wheeler,  Gen.  E.  S.,  246 
Whipple,  Harvey,  146 
White,  Prof.  A.  H.,  253 
Whited,  W.,  808 
Wig,  R.  J.,  87 
Wight  &  Co.,  W.  W.,  49 
Willis,  W.  N.,  225 
Wilson,  W.  M.,  412,  427 
Wind  pressure,  formula,  513 
on  dams,  732 

stresses  in  chimneys,  818 
in  deep  bins,  808 
in  building  frames,  427 
Window  openings,  540 
Wing  abutments  for  bridges,  646 
Wire  fabric,  45-50 

lock-woven,  49 

trian^le-mesh,  47 

unit,  48 

welded,  46 

Wisco  reinforcing  mesh,  50 
Wire  form  clamps,  119 
Wire  glass,  541 
Wisco  reinforcing  mesh,  50 
Wiscoforms,  138 
Witherow  Steel  Co..  50,  138 
Withey,  Prof.,  475 
Wolf,  A.  M.,  520 
Wolfe,  W.  S.,  316,  406 
Wood  molds.  159 

Woodard,  737  /  ■    '  ' 

Wooden  floors,  432  / 
Woolson,  Prof.  I.  H.,  254  '  '  '  >' 

Worcester,  J.  R.,  558 

Working  stresses,  axial  sompr'ifesiorj,  ,i?45  , 

bond,  846  .  ;  ; 

for  concrete  columns,  373  '  '  ^  \,  >' 

for  steel,  37 

modulus  of  elasticity,  846 
of  concrete,  845  ,  j  > 

reinforcement,  846  ,  ^  \^  ^'  \  ' 

shear  and  diagonal  tension,  845  '  '  ^  \  ^ 

Xpantruss  reinforcing  system,  60 

Yield  point  of  mortars  and  concretes,  25] 


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3  3125  00000  4578 


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